NAME	COUPON	PRICE	YIELD	1 MONTH	1 YEAR	TIME (EST)
GB3:GOV 3 Month	0.00	4.42	4.55%	+33	+451	12:31 AM
GB6:GOV 6 Month	0.00	4.59	4.76%	+11	+458	12:31 AM
GB12:GOV 12 Month	0.00	4.41	4.62%	-2	+424	12:31 AM
GT2:GOV 2 Year	4.25	100.07	4.21%	-13	+332	12:31 AM
GT5:GOV 5 Year	3.88	100.93	3.66%	-10	+215	12:31 AM
GT10:GOV 10 Year	4.13	104.89	3.53%	-5	+177	12:31 AM
GT30:GOV 30 Year	4.00	106.22	3.65%	+10	+157	12:31 AM

Treasury Inflation Protected Securities (TIPS) (1/10/2023)

NAME	COUPON	PRICE	YIELD	1 MONTH	1 YEAR	TIME (EST)
GTII5:GOV 5 Year	1.63	100.66	1.48%	+5	+280	1/9/2023
GTII10:GOV 10 Year	0.63	93.91	1.31%	+1	+209	1/9/2023
GTII20:GOV 20 Year	0.75	87.82	1.48%	+7	+179	1/9/2023
GTII30:GOV 30 Year	0.13	69.44	1.41%	+14	+160	1/9/2023

Federal Reserve Rates (1/10/2023)

RATE	CURRENT	1 YEAR PRIOR
FDFD:IND Fed Funds Rate	4.32	0.07
FDTR:IND Fed Reserve Target	4.50	0.25
PRIME:IND Prime Rate	7.50	3.25

Municipal Bonds (1/10/2023)

NAME	YIELD	1 DAY	1 MONTH	1 YEAR	TIME (EST)
BVMB1Y:IND Muni Bonds 1 Year Yield	2.54%	-4	+2	+222	1/9/2023
BVMB2Y:IND Muni Bonds 2 Year Yield	2.38%	-4	-11	+199	1/9/2023
BVMB5Y:IND Muni Bonds 5 Year Yield	2.35%	-5	-15	+159	1/9/2023
BVMB10Y:IND Muni Bonds 10 Year Yield	2.45%	-4	-14	+126	1/9/2023
BVMB30Y:IND Muni Bonds 30 Year Yield	3.42%	-4	-9	+174	1/9/2023

https://www.bloomberg.com/markets/rates-bonds/government-bonds/us

In Class Exercise:

· Please draw the yield curve based on the above information;

· What can be predicted from the current yield curve?

· What is TIPs? What is municipal bond? What is Fed Fund Rate?

· Why are the TIPS’ rates negative?

For Daily Treasury rates such as the following, please visit

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield

Date 1 Mo 2 Mo 3 Mo 4 Mo 6 Mo 1 Yr 2 Yr 3 Yr 5 Yr 7 Yr 10 Yr 20 Yr 30 Yr

01/03/2023 4.17 4.42 4.53 4.70 4.77 4.72 4.40 4.18 3.94 3.89 3.79 4.06 3.88

01/04/2023 4.20 4.42 4.55 4.69 4.77 4.71 4.36 4.11 3.85 3.79 3.69 3.97 3.81

01/05/2023 4.30 4.55 4.66 4.75 4.81 4.78 4.45 4.18 3.90 3.82 3.71 3.96 3.78

01/06/2023 4.32 4.55 4.67 4.74 4.79 4.71 4.24 3.96 3.69 3.63 3.55 3.84 3.67

01/09/2023 4.37 4.58 4.70 4.74 4.83 4.69 4.19 3.93 3.66 3.60 3.53 3.83 3.66

For class discussion: Why do interest rates change daily? Interest rates are determined by whom in the U.S.?

“ interest rates are determined by the Federal Open Market Committee (FOMC), which consists of seven governors of the Federal Reserve Board and five Federal Reserve Bank presidents. The FOMC meets eight times a year to determine the near-term direction of monetary policy and interest rates.”

Who Determines Interest Rates?

`https://www.investopedia.com/ask/answers/who-determines-interest-rates/`

By NICK K. LIOUDIS Updated Aug 15, 2019

Interest rates are the cost of borrowing money. They represent what creditors earn for lending you money. These rates are constantly changing, and differ based on the lender, as well as your creditworthiness. Interest rates not only keep the economy functioning, but they also keep people borrowing, spending, and lending. But most of us don't really stop to think about how they are implemented or who determines them. This article summarizes the three main forces that control and determine interest rates.

KEY TAKEAWAYS

Interest rates are the cost of borrowing money and represent what creditors earn for lending money.
Central banks raise or lower short-term interest rates to ensure stability and liquidity in the economy.
Long-term interest rates are affected by demand for 10- and 30-year U.S. Treasury notes.
Low demand for long-term notes leads to higher rates, while higher demand leads to lower rates.
Retail banks also control rates based on the market, their business needs, and individual customers.

Short-Term Interest Rates: Central Banks

In countries using a centralized banking model, short-term interest rates are determined by central banks. A government's economic observers create a policy that helps ensure stable prices and liquidity. This policy is routinely checked so the supply of money within the economy is neither too large, which causes prices to increase, nor too small, which can lead to a drop in prices.

In the U.S., interest rates are determined by the Federal Open Market Committee (FOMC), which consists of seven governors of the Federal Reserve Board and five Federal Reserve Bank presidents. The FOMC meets eight times a year to determine the near-term direction of monetary policy and interest rates. The actions of central banks like the Fed affect short-term and variable interest rates.

If the monetary policymakers wish to decrease the money supply, they will raise the interest rate, making it more attractive to deposit funds and reduce borrowing from the central bank. Conversely, if the central bank wishes to increase the money supply, they will decrease the interest rate, which makes it more attractive to borrow and spend money.

The Fed funds rate affects the prime rate—the rate banks charge their best customers, many of whom have the highest credit rating possible. It's also the rate banks charge each other for overnight loans.

The U.S. prime rate remained at 3.25% between Dec. 16, 2008 and Dec. 17, 2015, when it was raised to 3.5%.

Long-Term Interest Rates: Demand for Treasury Notes

Many of these rates are independent of the Fed funds rate, and, instead, follow 10- or 30-year Treasury note yields. These yields depend on demand after the U.S. Treasury Department auctions them off on the market. Lower demand tends to result in high interest rates. But when there is a high demand for these notes, it can push rates down lower.

If you have a long-term fixed-rate mortgage, car loan, student loan, or any similar non-revolving consumer credit product, this is where it falls. Some credit card annual percentage rates are also affected by these notes.

These rates are generally lower than most revolving credit products but are higher than the prime rate.

Many savings account rates are also determined by long-term Treasury notes.

Other Rates: Retail Banks

Retail banks are also partly responsible for controlling interest rates. Loans and mortgages they offer may have rates that change based on several factors including their needs, the market, and the individual consumer.

For example, someone with a lower credit score may be at a higher risk of default, so they pay a higher interest rate. The same applies to credit cards. Banks will offer different rates to different customers, and will also increase the rate if there is a missed payment, bounced payment, or for other services like balance transfers and foreign exchange.

Monday 1/15/2020

For daily yield curve, please visit https://www.gurufocus.com/yield_curve.php

`Understanding the yield curve (video)`

`Introduction to the yield curve (khan academy)`

Summary of Yield Curve Shapes and Explanations

Normal Yield Curve
When bond investors expect the economy to hum along at normal rates of growth without significant changes in inflation rates or available capital, the yield curve slopes gently upward. In the absence of economic disruptions, investors who risk their money for longer periods expect to get a bigger reward — in the form of higher interest — than those who risk their money for shorter time periods. Thus, as maturities lengthen, interest rates get progressively higher and the curve goes up.

Steep Curve – Economy is improving
Typically the yield on 30-year Treasury bonds is three percentage points above the yield on three-month Treasury bills. When it gets wider than that — and the slope of the yield curve increases sharply — long-term bond holders are sending a message that they think the economy will improve quickly in the future.

Inverted Curve – Recession is coming
At first glance an inverted yield curve seems like a paradox. Why would long-term investors settle for lower yields while short-term investors take so much less risk? The answer is that long-term investors will settle for lower yields now if they think rates — and the economy — are going even lower in the future. They're betting that this is their last chance to lock in rates before the bottom falls out.

Flat or Humped Curve

To become inverted, the yield curve must pass through a period where long-term yields are the same as short-term rates. When that happens the shape will appear to be flat or, more commonly, a little raised in the middle.

Unfortunately, not all flat or humped curves turn into fully inverted curves. Otherwise we'd all get rich plunking our savings down on 30-year bonds the second we saw their yields start falling toward short-term levels.

On the other hand, you shouldn't discount a flat or humped curve just because it doesn't guarantee a coming recession. The odds are still pretty good that economic slowdown and lower interest rates will follow a period of flattening yields.

Formula --- Break down of interest rate

r = r* + IP + DRP + LP + MRP

r = required return on a debt security

r* = real risk-free rate of interest

IP = inflation premium

DRP = default risk premium

LP = liquidity premium

MRP = maturity risk premium

MRP_t = 0.1% (t – 1)

DRP_t + LP_t = Corporate spread * (1.02)^(t−1)

Assignments:

· Chapter six case study (due with first mid term exam) --- video is available on blackboard under collaborate/recording,

as well as here www.jufinance.com/video/fin435_chapter_6_case_video_1.mp4 (1/18/2023)

www.jufinance.com/video/fin435_chapter_6_case_video_2.mp4 (1/23/2023)

· Critical thinking question 1: Why are TIPS yields so low? Shall you invest in TIPS? Why or why not? (optional for extra credits)

· Critical thinking question 2: Do you think we will enter a recession as predicted by the inverted yield curve? (optional for extra credits)

What is interest rates

https://www.youtube.com/watch?v=Pod73wrvdSQ

Gerald Celente: Low Interest Rates are Building the Biggest Bubble in Modern History - 9/21/14

https://www.youtube.com/watch?v=pTpK6Te6tYI

How interest rates are set

https://www.youtube.com/watch?v=Oz5hNemSdWc

What happens if Fed raise interest rates

https://www.youtube.com/watch?v=4OP-3Ui6K1s

What Is the Relationship Between Inflation and Interest Rates?

By `JEAN FOLGER` Updated Dec 6, 2019

Inflation and interest rates are often linked and frequently referenced in macroeconomics. Inflation refers to the rate at which prices for goods and services rise. In the United States, the interest rate, or the amount charged by a lender to a borrower, is based on the federal funds rate that is determined by the Federal Reserve (sometimes called "the Fed").

By setting the target for the federal funds rate, the Fed has at its disposal a powerful tool that it uses to influence the rate of inflation. This tool enables the Fed to expand or contract the money supply as needed to achieve target employment rates, stable prices, and stable economic growth.

KEY TAKEAWAYS

There is an inverse correlation between interest rates and the rate of inflation.
In the U.S, the Federal Reserve is responsible for implementing the country's monetary policy, including setting the federal funds rate which influences the interest rates banks charge borrowers.
In general, when interest rates are low, the economy grows and inflation increases.
Conversely, when interest rates are high, the economy slows and inflation decreases.

The Inverse Correlation Between Interest Rates and Inflation

Under a system of fractional reserve banking, interest rates and inflation tend to be inversely correlated. This relationship forms one of the central tenets of contemporary monetary policy: Central banks manipulate short-term interest rates to affect the rate of inflation in the economy.

The below chart demonstrates the inverse correlation between interest rates and inflation. In the chart, CPI refers to the Consumer Price Index, a measurement that tracks changes in prices. Changes in the CPI are used to identify periods of inflation and deflation.

In general, as interest rates are reduced, more people are able to borrow more money. The result is that consumers have more money to spend, causing the economy to grow and inflation to increase.

The opposite holds true for rising interest rates. As interest rates are increased, consumers tend to save as returns from savings are higher. With less disposable income being spent as a result of the increase in the interest rate, the economy slows and inflation decreases.

To better understand how the relationship between inflation and interest rates works, it's important to understand the banking system, the quantity theory of money, and the role interest rates play.

Fractional Reserve Banking

The world currently uses a fractional reserve banking system. When someone deposits $100 into the bank, they maintain a claim on that $100. The bank, however, can lend out those dollars based on the reserve ratio set by the central bank. If the reserve ratio is 10%, the bank can lend out the other 90%, which is $90 in this case. A 10% fraction of the money stays in the bank vaults.

As long as the subsequent $90 loan is outstanding, there are two claims totaling $190 in the economy. In other words, the supply of money has increased from $100 to $190. This is a simple demonstration of how banking grows the money supply.

Quantity Theory of Money

In economics, the quantity theory of money states that the supply and demand for money determines inflation. If the money supply grows, prices tend to rise, because each individual piece of paper becomes less valuable.

Hyperinflation is an economic term used to describe extreme inflation where price increases are rapid and uncontrolled. While central banks generally target an annual inflation rate of around 2% to 3% as an acceptable rate for a healthy economy, hyperinflation goes well beyond this. Countries that experience hyperinflation have an inflation rate of 50% or more per month.

Interest Rates, Savings, Loans, and Inflation

The interest rate acts as a price for holding or loaning money. Banks pay an interest rate on savings in order to attract depositors. Banks also receive an interest rate for money that is loaned from their deposits.

When interest rates are low, individuals and businesses tend to demand more loans. Each bank loan increases the money supply in a fractional reserve banking system. According to the quantity theory of money, a growing money supply increases inflation. Thus, low interest rates tend to result in more inflation. High interest rates tend to lower inflation.

This is a very simplified version of the relationship, but it highlights why interest rates and inflation tend to be inversely correlated.

The Federal Open Market Committee

The Federal Open Market Committee (FOMC) meets eight times each year to review economic and financial conditions and decide on monetary policy. Monetary policy refers to the actions taken that affect the availability and cost of money and credit. At these meetings, short-term interest rate targets are determined.

Using economic indicators such as the Consumer Price Index (CPI) and the Producer Price Indexes (PPI), the Fed will establish interest rate targets intended to keep the economy in balance. By moving interest rate targets up or down, the Fed attempts to achieve target employment rates, stable prices, and stable economic growth. The Fed will raise interest rates to reduce inflation and decrease rates to spur economic growth.

Investors and traders keep a close eye on the FOMC rate decisions. After each of the eight FOMC meetings, an announcement is made regarding the Fed's decision to increase, decrease, or maintain key interest rates. Certain markets may move in advance of the anticipated interest rate changes and in response to the actual announcements. For example, the U.S. dollar typically rallies in response to an interest rate increase, while the bond market falls in reaction to rate hikes.

Here’s what the inverted yield curve means for your portfolio

https://www.cnbc.com/2022/10/31/what-an-inverted-yield-curve-means-for-the-economy.html

PUBLISHED MON, OCT 31 20223:29 PM EDT

Kate Dore, CFP®

KEY POINTS

· When shorter-term government bonds have higher yields than long-term, which is known as yield curve inversions, it’s one signal of a future recession.

· “The yield curve is not perfect, but it does better in general than standard forecasts,” said Robert Barbera, director of Johns Hopkins Center for Financial Economics.

· As investors brace for another interest rate hike from the Federal Reserve, many are closely watching signals about the future of the economy.

This week, investors are expecting the fourth 0.75 percentage point increase, which may continue to affect government bond yields.

As the Fed takes further action to fight inflation, many are watching the so-called “inverted yield curve,” one sign there’s an economic slump on the horizon.

The “yield curve” is a snapshot of the bond market, showing the interest investors may expect to earn from bonds with different maturities. These expectations may change based on what’s happening in the economy.

What the inverted yield curve means

Generally, longer-term bonds pay more than bonds with shorter maturities. Since longer-maturity bonds are more vulnerable to price changes, investors expect a “premium,” explained Preston Caldwell, head of U.S. economics for Morningstar Research Services.

“In normal times, the yield curve slopes upwards,” he said. But there’s currently a downward sloping curve, also known as an “inverted yield,” with the 2-year Treasury paying more than the 10-year Treasury

We are positioning for a U.S. recession in 2023, says JPMorgan’s Elyse Ausenbaugh

While many experts believe the inverted yield curve is one signal of a future recession, Caldwell said it’s more “correlative,” showing how the markets expect the Federal Reserve to respond in the near term.

What’s more, he said there’s “too much focus” on the “will there or won’t there be recession” question, and not enough attention on the severity of a possible recession, which the yield curve doesn’t show, he said.

‘Real economic indicators are going to suffer’

While a yield curve inversion is only one signal of a possible recession, it shouldn’t be ignored, particularly at the lower end of the curve, experts say.

“Economists have a very, very consistent record of not forecasting recessions,” said Robert Barbera, director of the Center for Financial Economics at Johns Hopkins University. “The yield curve is not perfect, but it does better in general than standard forecasts.”

However, it “certainly looks like short rates are going up until that inflation rate breaks in a big way,” he said. “And unfortunately, if we look at the history of that dynamic, it’s likely that real economic indicators are going to suffer alongside or ahead of that break for inflation.”

Videos (optional)

Super inverted yield curve doesn't work very well for markets, says Wells Fargo's Schumacher

The yield curve is predicting we've already seen a peak in interest rates, says Ed Yardeni

(optional)

https://ycharts.com/indicators/10_2_year_treasury_yield_spread

2-year Treasury yield tops 10-year rate, a ‘yield curve’ inversion that could signal a recession

PUBLISHED THU, MAR 31 20225:09 PM EDTUPDATED THU, MAR 31 20229:13 PM EDT

Patti Domm

The 2-year and 10-year Treasury yields inverted for the first time since 2019 on Thursday, sending a possible warning signal that a recession could be on the horizon.

The bond market phenomenon means the rate of the 2-year note is now higher than the 10-year note yield.

This part of the yield curve is the most closely watched and typically given the most credence by investors that the economy could be heading for a downturn when it inverts. The 2-year to 10-year spread was last in negative territory in 2019, before pandemic lockdowns sent the global economy into a steep recession in early 2020.

The yield on the 10-year Treasury fell to 2.331%, while the yield on the 2-year Treasury was at 2.337% at one point in late trading Thursday. After a brief inversion, both yields were basically trading at the 2.34% level in the latest trading.

When the curve inverts, “there has been a better than two-thirds chance of a recession at some point in the next year and a greater than 98% chance of a recession at some point in the next two years,” according to Bespoke.

Some data providers showed the 2-10 spread technically inverted for a few seconds earlier Tuesday, but CNBC data did not confirm the inversion until now. And to be sure, many economists believe the curve needs to stay inverted for a substantial amount of time before it gives a valid signal.

In general, a simple way to look at the importance of the yield curve is to think about what it means for a bank. The yield curve measures the spread between a bank’s cost of money versus what it will make by lending it out or investing it over a longer period of time. If banks can’t make money, lending slows and so does economic activity.

While the yield curve has sent somewhat reliable signals about pending recessions, there is often a long time lag and analysts say there needs to be corroborating evidence before investors need to fear a recession is around the corner.

Some of those other signals could include a slowdown in hiring and a sudden increase in unemployment, or early warnings in ISM and other data that manufacturing activity could be slowing. Analysts say the yield curve’s inversion could also reverse should there be a resolution to the war in Ukraine or the Federal Reserve pauses in its rate-hiking cycle.

According to MUFG Securities, the yield curve inverted 422 days ahead of the 2001 recession, 571 days ahead of the 2007-to-2009 recession and 163 days before the 2020 recession.

“Most of time, it is a recession harbinger but not all the time,” said Julian Emanuel, head of equity, derivatives and quantitative strategy at Evercore ISI. He noted one time when the curve inverted but the economy avoided a recession was in 1998 during the Russian debt crisis which was followed by the Long Term Capital Management failure.

“The nice thing about the last 30-year history is that there’s been so few recessions that you don’t want to say something is a golden rule, particularly when there are not enough observations and there’s one big standout to that rule,” he said.

Bespoke notes that after six instances where the 2-year and 10-year yields inverted going back to 1978, the stock market continued to perform positively. The S&P 500 was up an average 1.6% a month after the inversions but was up an average 13.3% a year later.

“Basically what tends to happen is over the long haul is that yes in most cases there is a recession, but many times it is six- to 18-months in the distance and the stock market does not tend to peak until between two and 12-months prior to the onset of a recession,” said Emanuel. “Again, while the probability of a recession in Europe has become a base case, that’s not the case for the U.S.”

Some bond pros do not believe the yield curve inversion is as reliable a recession predictor as it once was because the Federal Reserve has become such a big player in the market. The Fed’s nearly $9 trillion balance sheet holds many Treasurys, and strategists believe it has suppressed interest rates at the long end, meaning the yields of the 10-year note and the 30-year bond should be higher.

In fact, Richard Bernstein Associates notes that if the Fed had never engaged in quantitative easing, the 10-year yield could be closer to 3.7%. Were it not for the central bank’s bond-buying program, the yield curve for the 2-year and the 10-year would then be more like 100 basis points apart, instead of inverted. (1 basis point equals 0.01%.)

Strategists say the 2-year yield has climbed most rapidly since it is the part of the curve most reflective of Fed rate hikes. The 10-year has also moved higher on the Fed, but it has also been held back by flight-to-quality trades as investors keep an eye on the Ukraine war. Yields move opposite price.

Some market pros believe the 3-month yield to the 10-year yield is a more accurate recession forecaster, and that curve has not flattened at all. That spread has been widening, a signal for better economic growth.

https://www.cnbc.com/2022/03/31/2-year-treasury-yield-tops-10-year-rate-a-yield-curve-inversion-that-could-signal-a-recession.html (video)

Chapter 6 Interest rate Part II: Term Structure of Interest rate

Calculator

Question for discussion: If a% and b% are both known to investors, such as the bank rates, how much is the future interest rate, such as c%?

(1+a)^N = (1+b)^m *(1+c)^(N-M)

Either earning a% of interest rate for N years,

or b% of interest rate for M years, and then c% of interest rate for (N-M) years,

investors should be indifferent. Right?

Then,

(1+a)^N = (1+b)^m *(1+c)^(N-M)è c = ((1+a)^N / (1+b)^m)^(1/(N-M))-1

Or approximately,

N*a = M*b +(N-M)*(c)è c = (N*a – M*b) /(N-M)

What Is Expectations Theory `(video`)

Expectations theory attempts to predict what short-term interest rates will be in the future based on current long-term interest rates. The theory suggests that an investor earns the same amount of interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today. The theory is also known as the "unbiased expectations theory.”

Understanding Expectations Theory

The expectations theory aims to help investors make decisions based upon a forecast of future interest rates. The theory uses long-term rates, typically from government bonds, to forecast the rate for short-term bonds. In theory, long-term rates can be used to indicate where rates of short-term bonds will trade in the future (https://www.investopedia.com/terms/e/expectationstheory.asp)

Expectations Theory

By CHRIS B. MURPHY Updated Apr 21, 2019

Example of Calculating Expectations Theory

Let's say that the present bond market provides investors with a two-year bond that pays an interest rate of 20% while a one-year bond pays an interest rate of 18%. The expectations theory can be used to forecast the interest rate of a future one-year bond.

The first step of the calculation is to add one to the two-year bond’s interest rate. The result is 1.2.
The next step is to square the result or (1.2 * 1.2 = 1.44).
Divide the result by the current one-year interest rate and add one or ((1.44 / 1.18) +1 = 1.22).
To calculate the forecast one-year bond interest rate for the following year, subtract one from the result or (1.22 -1 = 0.22 or 22%).

In this example, the investor is earning an equivalent return to the present interest rate of a two-year bond. If the investor chooses to invest in a one-year bond at 18% the bond yield for the following year’s bond would need to increase to 22% for this investment to be advantageous.

Expectations theory attempts to predict what short-term interest rates will be in the future based on current long-term interest rates
The theory suggests that an investor earns the same amount of interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today
In theory, long-term rates can be used to indicate where rates of short-term bonds will trade in the future

Expectations theory aims to help investors make decisions by using long-term rates, typically from government bonds, to forecast the rate for short-term bonds.

Disadvantages of Expectations Theory

Investors should be aware that the expectations theory is not always a reliable tool. A common problem with using the expectations theory is that it sometimes overestimates future short-term rates, making it easy for investors to end up with an inaccurate prediction of a bond’s yield curve.

Another limitation of the theory is that many factors impact short-term and long-term bond yields. The Federal Reserve adjusts interest rates up or down, which impacts bond yields including short-term bonds. However, long-term yields might not be as impacted because many other factors impact long-term yields including inflation and economic growth expectations. As a result, the expectations theory doesn't take into account the outside forces and fundamental macroeconomic factors that drive interest rates and ultimately bond yields.

Chapter 6 In class exercise

1 You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums:

Inflation premium = 3.25%
Liquidity premium = 0.6%
Maturity risk premium = 1.8%
Default risk premium = 2.15%

On the basis of these data, what is the real risk-free rate of return? (answer: 2.25%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

30-day T-bills = short term Treasury Security è Default = liquidity = maturity = 0

So 30-day T-bills = 5.5% = r* + inflation =r* + 3.25%

2 The real risk-free rate is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?(answer: 6%, 6.33%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

2-year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity=0 as given

Inflation = average of inflations from year 1 to year 2 = (2% + 4%)/2 = 3%

So 2-year T-notes = r* + inflation = 3% + 3% = 6%

3-year T-notes = short term Treasury Security è Default = liquidity = 0, maturity=0 as given

Inflation = average of inflations from year 1 to year 2 = (2% + 4% +4%)/3 = 3.33%

So 2-year T-notes = r* + inflation = 3% + 3.33% = 6.33%

3 A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 8%. Assume that the liquidity premium on the corporate bond is 0.5%. What is the default risk premium on the corporate bond? (answer: 1.5%)

Solution:

General equation: Rate = r* + Inflation + Default + liquidity + maturity

10 year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity is not zero

So 10-year T-notes = r* + inflation + maturity = 6%

10 year corporate bond rate = r* + Inflation + Default + liquidity + maturity = 8%

Its liquidity = 0.5%, its maturity = 10-year-notes’ maturity.

Comparing 10 year T-notes and 10 year corporate bonds, we get default = 8%-6%-0.5%=1.5%

	r*	inflation	default	liquity	maturity
10 - year- T-notes = 6%	same	same	0	0	same
10 year corp bonds = 8%	same	same	?	1.50%	same

4 The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.2%. What is the maturity risk premium for the 2-year security? (answer: 0.2%)

General equation: Rate = r* + Inflation + Default + liquidity + maturity

2-year T-notes = intermediate term Treasury Security è Default = liquidity = 0, maturity=?

2-year T-notes = 6.2% = r* + inflation + maturity = 3% + 3% + maturity

5 One-year Treasury securities yield 5%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? (answer: 5.5%)

Or,

Real Interest rate in the US from 2000-2022

https://fred.stlouisfed.org/series/REAINTRATREARAT1YE

Three Month T-Bill rate (a proxy of the risk free rate)

https://www.cnbc.com/quotes/US3M

Chapter 7

ppt

Market data website:

1. FINRA

http://finra-markets.morningstar.com/BondCenter/Default.jsp (FINRA bond market data)

2. WSJ

Market watch on Wall Street Journal has daily yield curve and bond yield information.

http://www.marketwatch.com/tools/pftools/

https://www.youtube.com/watch?v=yph8TRldW6k

Simplified Balance Sheet of WalMart

Balance Sheet of WalMart https://www.nasdaq.com/market-activity/stocks/wmt/financials

Period Ending:	1/31/2022	1/31/2021	1/31/2020	1/31/2019
Current Assets
Cash and Cash Equivalents	$14,760,000	$17,741,000	$9,465,000	$7,722,000
Short-Term Investments	--	--	--	--
Net Receivables	$8,280,000	$6,516,000	$6,284,000	$6,283,000
Inventory	$56,511,000	$44,949,000	$44,435,000	$44,269,000
Other Current Assets	$1,519,000	$20,861,000	$1,622,000	$3,623,000
Total Current Assets	$81,070,000	$90,067,000	$61,806,000	$61,897,000
Long-Term Assets
Long-Term Investments	--	--	--	--
Fixed Assets	$112,624,000	$109,848,000	$127,049,000	$111,395,000
Goodwill	$29,014,000	$28,983,000	$31,073,000	$31,181,000
Intangible Assets	--	--	--	--
Other Assets	$22,152,000	$23,598,000	$16,567,000	$14,822,000
Deferred Asset Charges	--	--	--	--
Total Assets	$244,860,000	$252,496,000	$236,495,000	$219,295,000
Current Liabilities
Accounts Payable	$82,172,000	$87,349,000	$69,549,000	$69,647,000
Short-Term Debt / Current Portion of Long-Term Debt	$3,724,000	$3,830,000	$6,448,000	$7,830,000
Other Current Liabilities	$1,483,000	$1,466,000	$1,793,000	--
Total Current Liabilities	$87,379,000	$92,645,000	$77,790,000	$77,477,000
Long-Term Debt	$39,107,000	$45,041,000	$48,021,000	$50,203,000
Other Liabilities	$13,009,000	$12,909,000	$16,171,000	--
Deferred Liability Charges	$13,474,000	$14,370,000	$12,961,000	$11,981,000
Misc. Stocks	$8,638,000	$6,606,000	$6,883,000	$7,138,000
Minority Interest	--	--	--	--
Total Liabilities	$161,607,000	$171,571,000	$161,826,000	$146,799,000
Stock Holders Equity
Common Stocks	$276,000	$282,000	$284,000	$288,000
Capital Surplus	$86,904,000	$88,763,000	$83,943,000	$80,785,000
Retained Earnings	--	--	--	--
Treasury Stock	$4,839,000	$3,646,000	$3,247,000	$2,965,000
Other Equity	-$8,766,000	-$11,766,000	-$12,805,000	-$11,542,000
Total Equity	$83,253,000	$80,925,000	$74,669,000	$72,496,000
Total Liabilities & Equity	$244,860,000	$252,496,000	$236,495,000	$219,295,000

For discussion:

· What is this “long term debt”?

· Who is the lender of this “long term debt”?

So this long term debt is called bond in the financial market. Where can you find the pricing information and other specifications of the bond issued by WMT?

Investing Basics: Bonds(video)

Relationship between bond prices and interest rates (Khan academy)

FINRA – Bond market information

http://finra-markets.morningstar.com/BondCenter/Default.jsp

Go to http://finra-markets.morningstar.com/BondCenter/Default.jsp , the bond market data website of FINRA to find bond information. For example, find bond sponsored by Wal-mart

Or, just go to www.finra.org, è Investor center è market data è bond è corporate bond

https://finra-markets.morningstar.com/BondCenter/Results.jsp

2. Understand what is coupon, coupon rate, yield, yield to maturity, market price, par value, maturity, annual bond, semi-annual bond, current yield.

Refer to the following bond at http://finra-markets.morningstar.com/BondCenter/BondDetail.jsp?ticker=C104227&symbol=WMT.GP

Reading material:

Interest rate risk — When Interest rates Go up, Prices of Fixed-rate Bonds Fall, issued by SEC at https://www.sec.gov/files/ib_interestraterisk.pdf

Question: What shall investors do as interest rates are expected to rise in March 2022?

All Bonds are Subject to Interest Rate Risk—Even If the Bonds Are Insured or Government Guaranteed

There is a misconception that, if a bond is insured or is a u.s. government obligation, the bond will not lose value. In fact, the U.S. government does not guarantee the market price or value of the bond if you sell the bond before it matures. This is because the market price or value of the bond can change over time based on several factors, including market interest rates. https://www.sec.gov/files/ib_interestraterisk.pdf

Relationship between bond prices and interest rates (Khan academy)

Here’s how rising interest rates may affect your bond portfolio in retirement

PUBLISHED WED, JAN 19 20228:00 AM EST, Kate Dore, CFP®

https://www.cnbc.com/2022/01/19/heres-how-rising-interest-rates-may-affect-your-bond-portfolio-.html

KEY POINTS

· Generally, market interest rates and bond prices move in opposite directions, meaning as rates increase, bond values will typically fall.

· Retirees may reduce interest rate risk by choosing bonds with a shorter duration, which are less sensitive to rate hikes.

· However, rising interest rates may still be good for retirees with a longer timeline, experts say.

Many retirees rely on bonds for income, lower risk and portfolio growth. However, as the Federal Reserve prepares to raise interest rates, some worry about the effects on their nest egg.

The cost of living has swelled for months, with the Consumer Price Index, the key measure of inflation, rising 7% year over year in December, the fastest since 1982, according to the U.S. Department of Labor.

Last week, Federal Reserve Chairman Jerome Powell said he expects a series of rate hikes this year, with reduced pandemic support from the central bank, to quell rising inflation.

This may alarm investors since market interest rates and bond prices typically move in opposite directions, meaning higher rates generally cause bond values to fall, known as interest rate risk.

For example, let’s say you have a 10-year $1,000 bond paying a 3% coupon. If market interest rates rise to 4% in one year, the asset will still pay 3%, but the bond’s value may drop to $925.

The reason for the price dip is new bonds may be issued with the higher 4% coupon, making the original 3% bond less attractive unless someone can buy it at a discount.

With higher yields elsewhere, investors tend to sell their current bonds to purchase the higher-paying ones, and heavy selling causes prices to slide, explained certified financial planner Brad Lineberger, president of Carlsbad, California-based Seaside Wealth Management.

Why bond duration matters

Another fundamental concept of bond investing is so-called duration, measuring a bond’s sensitivity to interest rate changes. Although it’s expressed in years, it’s different from the bond’s maturity since it factors in the coupon, time to maturity and yield paid through the term.

As a rule of thumb, the longer a bond’s duration, the more sensitive it will be to interest rate hikes, and the more its price will decline, Lineberger said.

Generally, if you’re trying to reduce interest rate risk, you’ll want to consider bonds or bond funds with a shorter duration, said Paul Winter, a CFP and owner of Five Seasons Financial Planning in Salt Lake City.

“Also, bonds with higher coupon rates and lower credit quality tend to be less sensitive to higher interest rates, other factors being equal,” he said.

A longer timeline

While rising interest rates will cause bond values to decrease, eventually, the declines will be more than offset as bonds mature and can be reinvested for higher yields, said CFP Anthony Watson, founder and president of Thrive Retirement Specialists in Dearborn, Michigan.

“Rising interest rates are good for retirees with a longer-term time frame,” he said, and that’s most people in their retirement years.

The best way to manage interest rate risk is with a diversified portfolio, including international bonds, with short to immediate maturities that are less affected by rate hikes and can be reinvested sooner, Watson said.

For class discussion:

What is duration? How to calculate a bond’s duration? a portfolio’s duration?

Bond Portfolio Duration (FYI)

https://analystnotes.com/cfa-study-notes-calculate-the-duration-of-a-portfolio-and-explain-the-limitations-of-portfolio-duration.html

There are two ways to calculate the duration of a bond portfolio:

1) The weighted average of the time to receipt of aggregate cash flows. This method is based on the cash flow yield, which is the internal rate of return on the aggregate cash flows.

Limitations: This method cannot be used for bonds with embedded options or for floating-rate notes due to uncertain future cash flows. The cash flow yield is not commonly calculated. The change in cash flow yield is not necessarily the same as the change in the yields-to-maturity on the individual bonds. Interest rate risk is not usually expressed as a change in the cash flow yield.

2) The weighted average of the durations of individual bonds that compose the portfolio. The weight is the proportion of the portfolio that a bond comprises.

Portfolio Duration = w₁D₁ + w₂D₂ + w₃D₃ + ... + w_kD_k

w_i= the market value of bond i / market value of the portfolio

D_i = the duration of bond i

k = the number of bonds in the portfolio

This method is simpler to use and quite accurate when the yield curve is flat. Its main limitation is that it assumes a parallel shift in the yield curve.

In class exercises

Bond Pricing Excel Formula

To calculate bond price in EXCEL (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

1. AAA firm’ bonds will mature in eight years, and coupon is $65. YTM is 8.2%. Bond’s market value? ($903.04, abs(pv(8.2%, 8, 65, 1000))

· Rate 8.2%

· Nper 8

· Pmt 65

· Pv ?

· FV 1000

2. AAA firm’s bonds’ market value is $1,120, with 15 years maturity and coupon of $85. What is YTM? (7.17%, rate(15, 85, -1120, 1000))

· Rate ?

· Nper 15

· Pmt 85

· Pv -1120

· FV 1000

3. Sadik Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)? (7.74%, rate(5, 105, -1180, 1100)) What is their yield to maturity (YTM)? (8.35%, rate(15, 105, -1180, 1000))

· Rate ?

· Nper 15

· Pmt 105

· Pv -1180

· FV 1000

4. Malko Enterprises’ bonds currently sell for $1,050. They have a 6-year maturity, an annual coupon of $75, and a par value of $1,000. What is their current yield? (7.14%, 75/1050)

5. Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? ($1,105.69, abs(pv(8.4%/2, 20*2, 9.5%*1000/2, 1000)) )

· Rate 8.4%/2

· Nper 20*2

· Pmt 95/2

· Pv ?

· FV 1000

6. Grossnickle Corporation issued 20-year, non-callable, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity? ($1,232.15, abs(pv(5.5%, 19, 75, 1000)))

· Rate 7.5%/2

· Nper 19

· Pmt 75

· Pv ?

· FV 1000

7. McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.) (2.62%, YTM = rate(25, 90, -1250, 1000), YTC = rate(5, 90, -1250, 1050))

· Rate ? ------------ ?

· Nper 25 ------------- 5

· Pmt 90 ------------ 90

· Pv -1250 ------------ -1250

· FV 1000 ------------ 1000

8. Taussig Corp.'s bonds currently sell for $1,150. They have a 6.35% annual coupon rate and a 20-year maturity, but they can be called in 5 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds? (4.2%, rate(5, 63.5, -1150, 1067.5))

9. A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now? ($930.11, rate(25, 85, -925, 1000), abs(pv( rate(25, 85, -925, 1000), 20, 85, 1000))

Assignment:

Chapter 7 Case Study – Due with the first mid term exam

· Case video part I – did in class on 1/30/2023

· Case video part II – did in class on 2/1/2023

Critical thinking question= (optional for extra credits)

· How to trade bonds when market interest rates rise? (optional for extra credits)

· Critical thinking question: Calculate the duration and the convexity of the following bond:

Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what are the duration and the convexity of this bond?

· ---- FYI: https://www.youtube.com/watch?v=cjlq08iDlIw

· bond-convexity-calculator

Bond Pricing Formula (FYI)

Bond Pricing Excel Formula

To calculate bond price in EXCEL (annual coupon bond):

Price=abs(pv(yield to maturity, years left to maturity, coupon rate*1000, 1000)

To calculate yield to maturity (annual coupon bond)::

Yield to maturity = rate(years left to maturity, coupon rate *1000, -price, 1000)

To calculate bond price (semi-annual coupon bond):

Price=abs(pv(yield to maturity/2, years left to maturity*2, coupon rate*1000/2, 1000)

To calculate yield to maturity (semi-annual coupon bond):

Yield to maturity = rate(years left to maturity*2, coupon rate *1000/2, -price, 1000)*2

Bond Calculator

Bond Duration Calculator (FYI)

https://exploringfinance.com/bond-duration-calculator/

Duration (FYI)

By ADAM HAYES Updated August 18, 2021, Reviewed by GORDON SCOTT,

Fact checked by KIRSTEN ROHRS SCHMITT

https://www.investopedia.com/terms/d/duration.asp

What Is Duration?

Duration is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates. A bond's duration is easily confused with its term or time to maturity because certain types of duration measurements are also calculated in years.

However, a bond's term is a linear measure of the years until repayment of principal is due; it does not change with the interest rate environment. Duration, on the other hand, is non-linear and accelerates as the time to maturity lessens.

KEY TAKEAWAYS

· Duration measures a bond's or fixed income portfolio's price sensitivity to interest rate changes.

· Macaulay duration estimates how many years it will take for an investor to be repaid the bond’s price by its total cash flows.

· Modified duration measures the price change in a bond given a 1% change in interest rates.

· A fixed income portfolio's duration is computed as the weighted average of individual bond durations held in the portfolio.

How Duration Works

Duration can measure how long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows. Duration can also measure the sensitivity of a bond's or fixed income portfolio's price to changes in interest rates.

In general, the higher the duration, the more a bond's price will drop as interest rates rise (and the greater the interest rate risk). For example, if rates were to rise 1%, a bond or bond fund with a five-year average duration would likely lose approximately 5% of its value.

Certain factors can affect a bond’s duration, including:

Time to maturity: The longer the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but have different maturities. A bond that matures faster—say, in one year—would repay its true cost faster than a bond that matures in 10 years. Consequently, the shorter-maturity bond would have a lower duration and less risk.

Coupon rate: A bond’s coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception of their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk.

Types of Duration

The duration of a bond in practice can refer to two different things. The Macaulay duration is the weighted average time until all the bond's cash flows are paid. By accounting for the present value of future bond payments, the Macaulay duration helps an investor evaluate and compare bonds independent of their term or time to maturity.

The second type of duration is called modified duration. Unlike Macaulay's duration, modified duration is not measured in years. Modified duration measures the expected change in a bond's price to a 1% change in interest rates.

In order to understand modified duration, keep in mind that bond prices are said to have an inverse relationship with interest rates. Therefore, rising interest rates indicate that bond prices are likely to fall, while declining interest rates indicate that bond prices are likely to rise.

Macaulay Duration

Macaulay duration finds the present value of a bond's future coupon payments and maturity value. Because Macaulay duration is a partial function of the time to maturity, the greater the duration, the greater the interest-rate risk or reward for bond prices.

Macaulay duration can be calculated manually as follows:

https://exploringfinance.com/bond-duration-calculator/

Modified Duration

The modified duration of a bond helps investors understand how much a bond's price will rise or fall if the YTM rises or falls by 1%. This is an important number if an investor is worried that interest rates will be changing in the short term. The modified duration of a bond with semi-annual coupon payments can be found with the following formula:

Usefulness of Duration

Investors need to be aware of two main risks that can affect a bond's investment value: credit risk (default) and interest rate risk (interest rate fluctuations). Duration is used to quantify the potential impact these factors will have on a bond's price because both factors will affect a bond's expected YTM.

For example, if a company begins to struggle and its credit quality declines, investors will require a greater reward or YTM to own the bonds. In order to raise the YTM of an existing bond, its price must fall. The same factors apply if interest rates are rising and competitive bonds are issued with a higher YTM.

The duration of a zero-coupon bond equals its time to maturity since it pays no coupon.

Duration Strategies

However, a long-duration strategy describes an investing approach where a bond investor focuses on bonds with a high duration value. In this situation, an investor is likely buying bonds with a long time before maturity and greater exposure to interest rate risks. A long-duration strategy works well when interest rates are falling, which usually happens during recessions.

A short-duration strategy is one where a fixed-income or bond investor is focused on buying bonds with a small duration. This usually means the investor is focused on bonds with a small amount of time to maturity. A strategy like this would be employed when investors think interest rates will rise or when they are very uncertain about interest rates and want to reduce their risk.

Why Is It Called Duration?

Duration measures a bond price's sensitivity to changes in interest rates—so why is it called duration? A bond with a longer time to maturity will have a price that is more sensitive to interest rates, and thus a larger duration than a short-term bond.

What Else Does Duration Tell You?

As a bond's duration rises, its interest rate risk also rises because the impact of a change in the interest rate environment is larger than it would be for a bond with a smaller duration. Fixed-income traders will use duration, along with convexity, to manage the riskiness of their portfolio and to make adjustments to it.

Bond Duration Calculator (FYI)

https://exploringfinance.com/bond-duration-calculator/

Computing Duration Excel (video, FYI)

DURATION function in Excel

The DURATION function, one of the Financial functions, returns the Macauley duration for an assumed par value of $100. Duration is defined as the weighted average of the present value of cash flows, and is used as a measure of a bond price's response to changes in yield.

Syntax

DURATION(settlement, maturity, coupon, yld, frequency, [basis])

Important: Dates should be entered by using the DATE function, or as results of other formulas or functions. For example, use DATE(2018,5,23) for the 23rd day of May, 2018. Problems can occur if dates are entered as text.

The DURATION function syntax has the following arguments:

Settlement: The security's settlement date. The security settlement date is the date after the issue date when the security is traded to the buyer.

Maturity: The security's maturity date. The maturity date is the date when the security expires.

Coupon: The security's annual coupon rate.

Yld Required. The security's annual yield.

Frequency: The number of coupon payments per year. For annual payments, frequency = 1; for semiannual, frequency = 2; for quarterly, frequency = 4.

Basis Optional. The type of day count basis to use.

https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038

0:02 / 1:54

Excel DURATION function - how to use DURATION function (video)

Convexity in Bonds: Definition, Meaning, and Examples (FYI only)

By JAMES CHEN Updated January 02, 2023 Reviewed by CIERRA MURRY Fact checked by PETE RATHBURN

https://www.investopedia.com/terms/c/convexity.asp#:~:text=Convexity%20is%20a%20measure%20of%20the%20curvature%20in%20the%20relationship,said%20to%20have%20negative%20convexity.

bond-convexity-calculator

Change in price = [–Modified Duration *Change in yield] +[1/2 * Convexity*(change in yield)²]

https://www.wallstreetmojo.com/convexity-of-a-bond-formula-duration/\

What Is Convexity?

Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields.

Convexity is thus a measure of the curvature in the relationship between bond prices and interest rates. It reflects the rate at which the duration of a bond changes as interest rates change. Duration is a measure of a bond's sensitivity to changes in interest rates. It represents the expected percentage change in the price of a bond for a 1% change in interest rates.

KEY TAKEAWAYS

· Convexity is a risk-management tool, used to measure and manage a portfolio's exposure to market risk.

· Convexity is a measure of the curvature in the relationship between bond prices and bond yields.

· Convexity demonstrates how the duration of a bond changes as the interest rate changes.

· If a bond's duration increases as yields increase, the bond is said to have negative convexity.

· If a bond's duration rises and yields fall, the bond is said to have positive convexity.

Before explaining convexity, it's important to know how bond prices and market interest rates relate to one another. As interest rates fall, bond prices rise. Conversely, rising market interest rates lead to falling bond prices. This opposite reaction is because as rates rise, the bond may fall behind in the payout they offer a potential investor in comparison to other securities.

Bond Duration

Bond duration measures the change in a bond's price when interest rates fluctuate. If the duration of a bond is high, it means the bond's price will move to a greater degree in the opposite direction of interest rates.

Duration, on the other hand, measures the bond's sensitivity to the change in interest rates. For example, if rates were to rise 1%, a bond or bond fund with a 5-year average duration would likely lose approximately 5% of its value.

Convexity and Risk

Convexity builds on the concept of duration by measuring the sensitivity of the duration of a bond as yields change. Convexity is a better measure of interest rate risk, concerning bond duration. Where duration assumes that interest rates and bond prices have a linear relationship, convexity allows for other factors and produces a slope.

Duration can be a good measure of how bond prices may be affected due to small and sudden fluctuations in interest rates. However, the relationship between bond prices and yields is typically more sloped, or convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates.

As convexity increases, the systemic risk to which the portfolio is exposed increases. The term systemic risk became common during the financial crisis of 2008 as the failure of one financial institution threatened others. However, this risk can apply to all businesses, industries, and the economy as a whole.

The risk to a fixed-income portfolio means that as interest rates rise, the existing fixed-rate instruments are not as attractive. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. Typically, the higher the coupon rate or yield, the lower the convexity—or market risk—of a bond. This lessening of risk is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less interest rate risk to the investor. However, other risks, like default risk, etc., might still exist.

Example of Convexity

Imagine a bond issuer, XYZ Corporation, with two bonds currently on the market: Bond A and Bond B. Both bonds have a face value of $100,000 and a coupon rate of 5%. Bond A, however, matures in 5 years, while Bond B matures in 10 years.

Using the concept of duration, we can calculate that Bond A has a duration of 4 years while Bond B has a duration of 5.5 years. This means that for every 1% change in interest rates, Bond A's price will change by 4% while Bond B's price will change by 5.5%.

Now, let's say that interest rates suddenly increase by 2%. This means that the price of Bond A should decrease by 8% while the price of Bond B will decrease by 11%. However, using the concept of convexity, we can predict that the price change for Bond B will actually be less than expected based on its duration alone. This is because Bond B has a longer maturity, which means it has a higher convexity. The higher convexity of Bond B acts as a buffer against changes in interest rates, resulting in a relatively smaller price change than expected based on its duration alone.

Negative and Positive Convexity

If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the bond price will decline by a greater rate with a rise in yields than if yields had fallen. Therefore, if a bond has negative convexity, its duration would increase—the price would fall. As interest rates rise, and the opposite is true.

If a bond's duration rises and yields fall, the bond is said to have positive convexity. In other words, as yields fall, bond prices rise by a greater rate—or duration—than if yields rose. Positive convexity leads to greater increases in bond prices. If a bond has positive convexity, it would typically experience larger price increases as yields fall, compared to price decreases when yields increase.

Under normal market conditions, the higher the coupon rate or yield, the lower a bond's degree of convexity. In other words, there's less risk to the investor when the bond has a high coupon or yield since market rates would have to increase significantly to surpass the bond's yield. So, a portfolio of bonds with high yields would have low convexity and subsequently, less risk of their existing yields becoming less attractive as interest rates rise.

Consequently, zero-coupon bonds have the highest degree of convexity because they do not offer any coupon payments. For investors looking to measure the convexity of a bond portfolio, it's best to speak to a financial advisor due to the complex nature and the number of variables involved in the calculation.

The Bottom Line

Convexity is a measure of the curvature of its duration, or the relationship between bond prices and yields. It is used to describe the way in which the duration of a bond changes in response to changes in interest rates. When a bond's price is more sensitive to changes in interest rates, it is said to have higher convexity. Convexity is important for bond investors because it can impact the value of their investments. For example, when interest rates rise, the prices of most bonds tend to fall, and the magnitude of the price decline is typically greater for bonds with higher convexity. Conversely, when interest rates fall, the prices of most bonds tend to rise, and the magnitude of the price increase is typically greater for bonds with higher convexity.

There are several factors that can impact the convexity of a bond, including the bond's coupon rate, maturity, and credit quality. Higher coupon bonds, for example, tend to have higher convexity than lower coupon bonds because they are more sensitive to changes in interest rates. Similarly, longer-term bonds tend to have higher convexity than shorter-term bonds because they are exposed to interest rate risk for a longer period of time.

Bond investors can use convexity to their advantage by managing their bond portfolios to take advantage of changes in interest rates. For example, an investor who anticipates rising interest rates might choose to hold a portfolio of bonds with low convexity, while an investor who anticipates falling interest rates might choose to hold a portfolio of bonds with high convexity.

How "Convexity" Impacts Bond Yields (youtube)

How companies like Amazon, Nike and FedEx avoid paying federal taxes (FYI) --- Special Topic

PUBLISHED THU, APR 14 20228:05 AM EDT

https://www.cnbc.com/2022/04/14/how-companies-like-amazon-nike-and-fedex-avoid-paying-federal-taxes-.html

The current United States tax code allows some of the biggest company names in the country to not pay any federal corporate income tax.

In fact, at least 55 of the largest corporations in America paid no federal corporate income taxes on their 2020 profits, according to the Institute on Taxation and Economic Policy. The companies include names like Whirlpool, FedEx, Nike, HP and Salesforce.

“If a large, very profitable company isn’t paying the federal income tax, then we have a real fairness problem on our hands,” Matthew Gardner, a senior fellow at the Institute on Taxation and Economic Policy (ITEP), told CNBC.

What’s more, it is entirely legal and within the parameters of the tax code that corporations can end up paying no federal corporate income tax, which costs the U.S. government billions of dollars in lost revenue.

″[There’s] a bucket of corporate tax breaks that are deliberately in the tax code … . And overall, they cost the federal government roughly $180 billion each year. And for comparison, the corporate tax brings in about $370 billion of revenue a year,” Chye-Ching Huang, executive director of the NYU Tax Law Center, told CNBC, citing research from the Tax Foundation.

CNBC reached out to FedEx, Nike, Salesforce and HP for comment. They either declined to provide a statement or did not respond before publication.

The 55 corporations cited by ITEP would have paid a collective total of $8.5 billion. Instead, they received $3.5 billion in tax rebates, collectively draining $12 billion from the U.S. government, according to the institute. The figures don’t include corporations that paid only some but not all of these taxes.

“I think the fundamental issue here is there are two different ways in which corporations book their profits,” Garrett Watson, senior policy analyst at the Tax Foundation, told CNBC. “The amount of profits that corporations may be reporting for financial purposes may be very different from the profits that they are reporting [for tax purposes.]”

Some tax expenditures, which come in many different forms, are used by some companies to take advantage of rules that enable them to lower their effective tax rates.

For example, Gardner’s research into Amazon’s taxes from 2018 to 2021 showed a reported $79 billion of pretax U.S. income. Amazon paid a collective $4 billion in federal corporate income tax in those four years, equating to an effective annual tax rate of 5.1%, according to Gardner’s ITEP report, about a quarter of the federal corporate tax rate of 21%.

Amazon told CNBC in a statement, “In 2021, we reported $2.3 billion in federal income tax expense, $5.2 billion in other federal taxes, and more than $4 billion in state and local taxes of all types. We also collected an additional $22 billion in sales taxes for U.S. states and localities.”

One controversial form of federal tax expenditure is the offshoring of profits. The foreign corporate income tax — anywhere between 0% and 10.5% — can incentivize the shifting of profits to tax havens.

For example, Whirlpool, a U.S. company known for manufacturing home appliances both in the U.S. and Mexico, was cited in a recent case involving both U.S. and Mexican taxes.

″[Whirlpool] did that by having the Mexican operation owned by a Mexican company with no employees, and then having that Mexican company owned by a Luxembourg holding company that had one employee,” Huang told CNBC. “And then it tried to claim that due to the combination of the U.S., Mexico and Luxembourg tax rules ... it was trying to take advantage of the disconnect between all of those tax systems to to avoid tax and all of those countries and of court said, no, that goes too far.”

Whirlpool defended its actions in a statement to CNBC: “The case before the Sixth Circuit has never been about trying to avoid U.S. taxes on the profits earned in Mexico. This tax dispute has always been about when those profits are taxed in the U.S. In fact, years before the original Tax Court decision in 2020, Whirlpool had already paid U.S. tax on 100% of the profits it earned in Mexico. Simply put, the IRS thought Whirlpool should have paid those U.S. taxes earlier.”

Average effective corporate tax rate falls to 9% with tax reform, estimates UPenn Wharton (CNBC, video)

Despite record profits in 2021, many corporations are paying barely any taxes

19 profitable Fortune 100 corporations that reported they will owe little or no taxes for 2021

https://www.americanprogress.org/article/these-19-fortune-100-companies-paid-next-to-nothing-or-nothing-at-all-in-taxes-in-2021/

Critical thinking question= (optional for extra credits)

· Shall we fix this tax loophole problem and how? (optional for extra credits)

Chapter 8 Risk and Return

ppt

Equations

1. Expected return and standard deviation

Calculator

Given a probability distribution of returns, the expected return can be calculated using the following equation:

where

E[R] = the expected return on the stock,
N = the number of states,
p_i = the probability of state i, and
R_i = the return on the stock in state i.

Given an asset's expected return, its variance can be calculated using the following equation:

where

N = the number of states,
p_i = the probability of state i,
R_i = the return on the stock in state i, and
E[R] = the expected return on the stock.

The standard deviation is calculated as the positive square root of the variance.

http://www.zenwealth.com/businessfinanceonline/RR/MeasuresOfRisk.html

2. Two stock portfolio equations:

Calculator

W1 and W2 are the percentage of each stock in the portfolio.

Portfolio Variance Part 1 (youtube)

r₁₂ = the correlation coefficient between the returns on stocks 1 and 2,
s₁₂ = the covariance between the returns on stocks 1 and 2,
s₁ = the standard deviation on stock 1, and
s₂ = the standard deviation on stock 2.

s₁₂ = the covariance between the returns on stocks 1 and 2,
N = the number of states,
p_i = the probability of state i,
R_1i = the return on stock 1 in state i,
E[R₁] = the expected return on stock 1,
R_2i = the return on stock 2 in state i, and
E[R₂] = the expected return on stock 2.

3.. Historical returns

Holding period return (HPR) = (Selling price – Purchasing price + dividend)/ Purchasing price

HPR calculator

4. CAPM model

· What Is the Capital Asset Pricing Model?

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital.

R_i = R_f + β_i *( R_m - R_f) ------ CAPM model

R_i = Expected return of investment

R_f = Risk-free rate

β_i = Beta of the investment

R_m = Expected return of market

(R_m - R_f) = Market risk premium

CAPM calculator

· What is Beta? Where to find Beta?

· SML – Security Market Line

RISK and Return General Template

In Class Exercise

1. An investor currently holds the following portfolio: He invested 30% of the fund in Apple with Beta equal 1.1. He also invested 40% in GE with Beta equal 1.6. The rest of his fund goes to Ford, with Beta equal 2.2. Use the above information to answer the following questions.

1) The beta for the portfolio is? (1.63)

Solution:

0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63(weighted average of beta)

2) The three month Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is 10% (this is market return). Now calculate the portfolio’s return. 15.04%

Solution:

0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63--- This is beta and then plug into the CAPM.

Return = 2% + 1.63*(10%-2%) = 15.04%

Refer to the following graph. The three month Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is 10% (this is market return).

2. What is the value of A? 2%

Solution: This is the intercept of the SML

3. What is the value of B? 10%

Solution:

B is the market return, so 10%, since Beta =1

4. How much is the slope of the above security market line? 8%

Solution:

Slope = rise/run = (10%-2%)/(1-0), just compare risk free rate (Beta=0) and market return (beta=1)

5. Your uncle bought Apple in January, year 2000 for $30. The current price of Apple is $480 per share. Assume there are no dividend ever paid. Calculate your uncle’s holding period return. 15 times

Solution:

Holding period return = (480-30)/30 =1500%=15 times

6. Your current portfolio’s BETA is about 1.2. Your total investment is worth around $200,000. You uncle just gave you $100,000 to invest for him. With this $100,000 extra funds in hand, you plan to invest the whole $100,000 in additional stocks to increase your whole portfolio’s BETA to 1.5 (Your portfolio now worth $200,000 plus $100,000). What is the average BETA of the new stocks to achieve your goal? (hint: write down the equation of the portfolio’s Beta first) 2.10

Solution:

Total amount = 200000 + 100000 +100000=400000

New portfolio beta = 1.2*((200000+100000)/400000) + X*(100000/400000) = 1.5 è X=2.1

Years Market r Stock A Stock B

1 3% 16% 5%

2 -5% 20% 5%

3 1% 18% 5%

4 -10% 25% 5%

5 6% 14% 5%

· Calculate the average returns of the market r and stock A and stock B. (Answer: -1%, 18.6%, 5%)

· Calculate the standard deviations of the market, stock A, & stock B (Answer: 6.44%, 4.21%; 0 )

· Calculate the correlation of stock market r and stock a. (Answer: -0.98)

· Assume you invest 50% in stock A and 50% in stock B. Calculate the average return and the standard deviation of the portfolio. (Answer: 11.8%; 2.11%)

Calculate beta of stock A and beta of stock B, respectively (Answer: -0.64, 0)

Solution of Question 7

Efficient Frontier Exercise ? (FYI only)

Chapter 8 Case study – due with the first mid term exam

case study video part i

case study video part ii

Nov 2, 2021,07:30am EDT|86,690 views

No Recession In 2022—But Watch Out In 2023

Bill Conerly

https://www.forbes.com/sites/billconerly/2021/11/02/no-recession-in-2022-but-watch-out-in-2023/?sh=311d693e3555

A recession will come to the United States economy, but not in 2022. Federal Reserve policy will lead to more business cycles, which many businesses are not well prepared for. The downturn won’t come in 2022, but could arrive as early as 2023. If the Fed avoids recession in 2023, then look for a more severe slump in 2024 or 2025.

Recessions usually come from demand weakness, but supply problems can also trigger a downturn. In 2022 demand for goods and services will be strong. Consumers have plenty of money, thanks to past earnings, stimulus payments and extra unemployment insurance. They have paid down their credit card balances. Even though they also increased their car loans outstanding as they upgraded their rides, their general condition is good. Employment will increase thanks to the spending, reinforcing the income gains that enable expenditures.

Businesses, too, have plenty of cash on hand. Not only have profits been good, but the Paycheck Protection Program gave nearly $800 billion to businesses. Companies want to buy computers, equipment and machinery to substitute for the workers they cannot find, and this spending will help manufacturers of the equipment.

Homebuilders will construct as many homes as they can, though that will be limited by buildable lots, skilled labor and building materials. Non-residential construction will slowly gain ground, especially in warehouse space and suburban offices.

The government will spend, not only at the federal level but also among state and local entities. The federal government has no worries about deficits, while state and local governments are flush with federal money.

The spending side of the economy has little risk of recession in 2022, but could supply problems trigger a recession?

Supply chain problems can have negative impacts when factories have to shut down for lack of parts, as happened in the automobile industry. Recently Ford Europe’s Gunnar Herrmann told CNBC, “It’s not only semiconductors. You find shortages or constraints all over the place,” mentioning lithium, plastics and steel in particular. The automobile industry has laid off workers at multiple plants, mostly for a few weeks, but some long term. When workers are laid off for lack of materials to assemble, then the economy suffers. Most of the shortages under discussion, however, are limiting growth rather than cutting back on current production.

So the supply challenge we have is not an actual reduction in materials available, just insufficient materials to meet the stronger demand. Despite the snarls at the ports of Long Beach and Los Angeles, more inbound containers are hitting the docks than in 2019. Mostly we are seeing supply as a limit on growth rather than a cause of recession.

Much of the supply limitation prevents growth, but does not push spending downward. Businesses are cutting back on variety. A shirt in a particular size may only be available in a few colors, not 16. That is unfortunate, and may discourage a few shoppers, but for the most part we’ll still be buying goods.

Job losses from vaccine mandate layoffs could push the economy toward recession, given that 31% of people over age 18 are not fully vaccinated. The various mandates cover about 100 million workers. Some of those 31 million unvaccinated workers subject to mandates will get their shots, but others certainly won’t. In the worst of the pandemic recession, the country lost 22 million jobs. Losing 31 million jobs because of vaccine mandates—or even half that number—would be disastrous. And because it would be disastrous, it will not happen. The Biden administration almost certainly will pull back the mandate before accepting such a harsh result rise in unemployment.

Though 2022 is unlikely to host a recession, 2023 and 2024 are extremely risky. The Federal Reserve will start tapering its quantitative stimulus soon, and sometime in mid-2022 it will begin raising short-term interest rates. The economy reacts with a time lag of about one year, plus or minus. The greatest risk in the near term is that the Fed realizes that much of the recent inflation is long-lasting rather than transitory. They will then hit the brakes. Because of the time lag, the Fed may decide to stomp down harder on the brakes, triggering a recession.

If the Fed avoids an over-reaction recession, it risks not bringing inflation down at all. The longer the Fed waits, the more work they will need to do later. We’ll still have massive fiscal stimulus plus the lagged effects of past monetary stimulus. Public anger over inflation will provoke a stronger Fed response by 2025 at the latest, but probably earlier.

Can a recession be completely avoided in the next few years? Theoretically it’s possible. The Fed would have to tighten at just the right time, in just the right magnitude, then return to neutral at just the right time. It could happen, but the odds are very, very slim. The people at the Fed are smart and knowledgeable, but the task is too difficult for mere mortals. So businesses should enjoy their gains in 2022 while developing contingency plans to be ready for the nearly-inevitable recession.

What Is the Capital Asset Pricing Model?

R_i = R_f + β_i *( R_m - R_f) ------ CAPM model

R_i = Expected return of investment

R_f = Risk-free rate

β_i = Beta of the investment

R_m = Expected return of market

(R_m - R_f) = Market risk premium

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return.

For example, imagine an investor is contemplating a stock worth $100 per share today that pays a 3% annual dividend. The stock has a beta compared to the market of 1.3, which means it is riskier than a market portfolio. Also, assume that the risk-free rate is 3% and this investor expects the market to rise in value by 8% per year.

The expected return of the stock based on the CAPM formula is 9.5%.

The expected return of the CAPM formula is used to discount the expected dividends and capital appreciation of the stock over the expected holding period. If the discounted value of those future cash flows is equal to $100 then the CAPM formula indicates the stock is fairly valued relative to risk.

(https://www.investopedia.com/terms/c/capm.asp)

Finding Beta Value (https://finance.zacks.com/stock-beta-value-8004.html)

The current beta value of a company stock is provided for free by many online financial news services, including Morningstar, Google Finance and Yahoo Finance. Online brokerage services provide more extensive tracking of a company's beta measurements, including historical trends. Beta is sometimes listed under "market data" or other similar headings, as it describes past market performance. A stock with a beta of 1.0 has the same price volatility as the market index, meaning if the market gains, the stock makes gains at the same rate. A stock with a beta of greater than 1.0 is riskier and has greater price fluctuations, while stocks with beta values of less than 1.0 are steadier and generally larger companies.

Examples of Beta

Beta is often measured against the S&P 500 index. An S&P 500 stock with a beta of 2.0 produced a 20 percent increase in returns during a period of time when the S&P 500 Index grew only 10 percent. This same measurement also means the stock would lose 20 percent when the market dropped by only 10 percent. High beta values, including those more than 1.0, are volatile and carry more risk along with greater potential returns. The measurement doesn't distinguish between upward and downward movements. Investing Daily notes that investors try to use stocks with high beta values to quickly recoup their investments after sharp market losses.

Small-Cap Stocks

Beta values are useful to evaluate stock prices of smaller companies. These small-capitalization stocks are attractive to investors because their price volatility can promise greater returns, but Market Watch recommends only buying small-cap stocks with beta values of less than 1.0. The beta value is also a component of the Capital Asset Pricing Model, which helps investors analyze the risk of an investment and the returns needed to make it profitable.

The Importance of Diversification

`https://www.youtube.com/watch?v=RoqAcdTFVFY`

Understanding Diversification in Stock Trading to Avoid Losses

`https://www.youtube.com/watch?v=FrmoXog9zig`

How to Build a Portfolio | by Wall Street Survivor

`https://www.youtube.com/watch?v=V48NECmT3Ns`

Understanding the Fama and French Three Factor Model

https://www.investopedia.com/terms/f/famaandfrenchthreefactormodel.asp

Nobel Laureate Eugene Fama and researcher Kenneth French, former professors at the University of Chicago Booth School of Business, attempted to better measure

market returns and, through research, found that value stocks outperform growth stocks. Similarly, small-cap stocks tend to outperform large-cap stocks. As an

evaluation tool, the performance of portfolios with a large number of small-cap or value stocks would be lower than the CAPM result, as the Three-Factor Model

adjusts downward for observed small-cap and value stock outperformance.

The Fama and French model has three factors: the size of firms, book-to-market values, and excess return on the market. In other words, the three factors used

are small minus big (SMB), high minus low (HML), and the portfolio's return less the risk-free rate of return. SMB accounts for publicly traded companies

with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns

in comparison to the market.

Fama and French’s Five Factor Model

Researchers have expanded the Three-Factor model in recent years to include other factors. These include "momentum," "quality," and "low volatility,"

among others. In 2014, Fama and French adapted their model to include five factors. Along with the original three factors, the new model adds the concept that

companies reporting higher future earnings have higher returns in the stock market, a factor referred to as profitability.

The fifth factor, referred to as "investment", relates the concept of internal investment and returns, suggesting that companies directing profit towards

major growth projects are likely to experience losses in the stock market.

Small Minus Big (SMB): Definition and Role in Fama/French Model

By WILL KENTON Updated November 30, 2020 Reviewed by DAVID KINDNESS

https://www.investopedia.com/terms/s/small_minus_big.asp

What Does Small Minus Big Mean?

Small minus big (SMB) is one of the three factors in the Fama/French stock pricing model. Along with other factors, SMB is used to explain portfolio returns.

This factor is also referred to as the "small firm effect," or the "size effect," where size is based on a company's market capitalization.

KEY TAKEAWAYS

· Small minus big (SMB) is a factor in the Fama/French stock pricing model that says smaller companies outperform larger ones over the long-term.

· High minus low (HML) is another factor in the model that says value stocks tend to outperform growth stocks.

· Beyond the original three factors in the Fama/French model—the SMB, HML, and market factors—the model has been expanded to include other factors, such as momentum, quality, and low volatility.

Understanding Small Minus Big (SMB)

Small minus big is the excess return that smaller market capitalization companies return versus larger companies. The Fama/French Three-Factor Model is an extension of the Capital Asset Pricing Model (CAPM). CAPM is a one-factor model, and that factor is the performance of the market as a whole. This factor is known as

the market factor. CAPM explains a portfolio's returns in terms of the amount of risk it contains relative to the market. In other words, according to CAPM, the

primary explanation for the performance of a portfolio is the performance of the market as a whole.

The Fama/Three-Factor model adds two factors to CAPM. The model essentially says there are two other factors in addition to market performance

that consistently contribute to a portfolio's performance. One is SMB, where if a portfolio has more small-cap companies in it, it should outperform the market

over the long run.

Small Minus Big (SMB) vs. High Minus Low (HML)

The third factor in the Three-Factor model is High Minus Low (HML). "High" refers to companies with a high book value-to-market value ratio. "Low'"

refers to companies with a low book value-to-market value ratio. This factor is also referred to as the "value factor" or the "value versus growth factor"

because companies with a high book to market ratio are typically considered "value stocks."

Companies with a low market-to-book value are typically "growth stocks." And research has demonstrated that value stocks outperform growth stocks in the long

run. So, in the long run, a portfolio with a large proportion of value stocks should outperform one with a large proportion of growth stocks.

Special Considerations

The Fama/French model can be used to evaluate a portfolio manager's returns. Essentially, if the portfolio's performance can be attributed to the three factors, then the portfolio manager has not added any value or demonstrated any skill.

This is because if the three factors can completely explain the portfolio's performance, then none of the performance can be attributed to the manager's ability.

A good portfolio manager should add to a performance by picking good stocks. This outperformance is also known as "alpha."

Application of the Fama French 5 factor model

https://blog.quantinsti.com/fama-french-five-factor-asset-pricing-model/

Five Factor Investing with ETFs (youtube)

The theoretical starting point for the Fama-French five-factor model is the dividend discount model as the model states that the value of a stock today is dependent

upon future dividends. Fama and French use the dividend discount model to get two new factors from it, investment and profitability (Fama and French, 2014).

The empirical tests of the Fama French models aim to explain average returns on portfolios formed to produce large spreads in Size, B/M, profitability and investment.

Firstly, the model is applied to portfolios formed on size, B/M, profitability and investment. The portfolio returns to be explained are from improved versions of the

sorts that produce the factor.

Secondly, the five-factor model’s performance is compared to the three-factor model’s performance with regards to explaining average returns associated with

major anomalies not targeted by the model (Fama and French, 2014).

With the addition of profitability and investment factors, the five-factor model time series regression has the equation below:

R_it - RF_t = a_i + b_i(RM_t — RF_t) + s_iSMB_t+ h_iHML_t + r_iRMW_t + c_iCMA_t + e_it

Where:

R_it is the return in month t of one of the portfolios

RF_t is the riskfree rate

Rm - Rf is the return spread between the capitalization-weighted stock market and cash

SMB is the return spread of small minus large stocks (i.e. the size effect)

HML is the return spread of cheap minus expensive stocks (i.e. the value effect)

RMW is the return spread of the most profitable firms minus the least profitable

CMA is the return spread of firms that invest conservatively minus aggressively (AQR, 2014)

The purpose of the regression test is to observe whether the five-factor model captures average returns on the variables and to see which variables are positively

or negatively correlated to each other and additionally identifying the size of the regression slopes and how all these factors are related to and affect average

returns of stocks values.

The tests done by Fama and French (2014) show that the value factor HML is redundant for describing average returns when profitability and investment factors

have been added into the equation and that for applications were sole interest is abnormal returns, a four or five-factor model can be used but if portfolio tilts are

also of interest in addition to abnormal returns then the five-factor model is best to use.

The results also show that the Fama-French five-factor model explains between 71% and 94% of the cross-section variance of expected returns for the size,

value, profitability and investment portfolios.

It has been proven that a five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than

the three-factor model in that it lessens the anomaly average returns left unexplained.

The new model shows that the highest expected returns are attained by companies that are small, profitable and value companies with no major growth prospects

(Fama and French, 2014).

The Fama-French five-factor model’s main setback, however, is its failure to capture the low average returns on small stocks whose returns perform like those of firms

that invest a lot in spite of low profitability as well as the model’s performance being indifferent to the way its factors are defined (Fama and French, 2015).

Efficient Frontier (FYI only)

Excel template (www.jufinance.com/efficient_frontier_excel)

Sample Study

Efficient Portfolio Frontier explained: Solver (Excel) - YouTube

Critical thinking challenge: Based on 8 stocks of your choice, generate an efficient frontier (earn 5 extra points added to the first midterm exam)

Hint: (from chatgpt, FYI)

The goal of the efficient frontier is to help investors identify the optimal portfolio that provides the maximum return for a given level of risk, or the minimum risk for a given level of return. The efficient frontier is a graph that shows the different possible combinations of risk and return for a given set of investments or assets. It represents the set of portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of return.

By plotting different portfolios on the efficient frontier, investors can evaluate the risk-return trade-offs of different investment options and choose the portfolio that best meets their investment objectives. The efficient frontier provides a way to quantify the trade-offs between risk and return and to help investors make informed decisions about their investment strategies.

Step 1:

Portfolio Return:

Portfolio Return = w1 * r1 + w2 * r2 + w3 * r3 + w4 * r4 + w5 * r5 + w6 * r6 + w7 * r7 + w8 * r8

where: w1, w2, w3, w4, w5, w6, w7, w8 are the weights of each stock in the portfolio, and r1, r2, r3, r4, r5, r6, r7, r8 are the returns of each stock in the portfolio.

Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w1^2 * sigma1^2 + w2^2 * sigma2^2 + w3^2 * sigma3^2 + w4^2 * sigma4^2 + w5^2 * sigma5^2 + w6^2 * sigma6^2 + w7^2 * sigma7^2 + w8^2 * sigma8^2 + 2 * w1 * w2 * rho12 * sigma1 * sigma2 + 2 * w1 * w3 * rho13 * sigma1 * sigma3 + 2 * w1 * w4 * rho14 * sigma1 * sigma4 + 2 * w1 * w5 * rho15 * sigma1 * sigma5 + 2 * w1 * w6 * rho16 * sigma1 * sigma6 + 2 * w1 * w7 * rho17 * sigma1 * sigma7 + 2 * w1 * w8 * rho18 * sigma1 * sigma8 + 2 * w2 * w3 * rho23 * sigma2 * sigma3 + 2 * w2 * w4 * rho24 * sigma2 * sigma4 + 2 * w2 * w5 * rho25 * sigma2 * sigma5 + 2 * w2 * w6 * rho26 * sigma2 * sigma6 + 2 * w2 * w7 * rho27 * sigma2 * sigma7 + 2 * w2 * w8 * rho28 * sigma2 * sigma8 + 2 * w3 * w4 * rho34 * sigma3 * sigma4 + 2 * w3 * w5 * rho35 * sigma3 * sigma5 + 2 * w3 * w6 * rho36 * sigma3 * sigma6 + 2 * w3 * w7 * rho37 * sigma3 * sigma7 + 2 * w3 * w8 * rho38 * sigma3 * sigma8 + 2 * w4 * w5 * rho45 * sigma4 * sigma5 + 2 * w4 * w6 * rho46 * sigma4 * sigma6 + 2 * w4 * w7 * rho47 * sigma4 * sigma7 + 2 * w4 * w8 * rho48 * sigma4 * sigma8 + 2 * w5 * w6 * rho56 * sigma5 * sigma6 + 2 * w5 * w7 * rho57 * sigma5 * sigma7 + 2 * w5 * w8 * rho58 * sigma5 * sigma8 + 2 * w6 * w7 * rho67 * sigma6 * sigma7 + 2 * w6 * w8 * rho68 * sigma6 * sigma8 + 2 * w7 * w8 * rho78 * sigma7 * sigma8)

where: sigma1, sigma2, sigma3, sigma4, sigma5, sigma6, sigma7, sigma8 are the standard deviations of each stock in the portfoliorho12, rho13, rho14, rho15, rho16, rho17, rho18, rho23, rho24, rho25, rho26, rho27, rho28, rho34, rho35, rho36, rho37, rho38, rho45, rho46, rho47, rho48, rho56, rho57, rho58, rho67, rho68, and rho78 are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

For example, rho12 represents the correlation coefficient between the returns of stock 1 and stock 2, rho23 represents the correlation coefficient between the returns of stock 2 and stock

Step 2: Draw CML (Capital market line)

To draw a tangent line from the risk-free rate to the efficient frontier, follow these steps:

· Determine the risk-free rate: The risk-free rate is the rate of return an investor can earn with zero risk. It is typically represented by the yield on a short-term U.S. Treasury bill.

· Find the portfolio with the highest Sharpe ratio: The Sharpe ratio is a measure of risk-adjusted return that takes into account the portfolio's expected return and standard deviation. The portfolio with the highest Sharpe ratio is the portfolio that offers the best risk-adjusted return.

· Calculate the slope of the tangent line: The slope of the tangent line is equal to the Sharpe ratio of the portfolio with the highest Sharpe ratio.

· Draw the tangent line: The tangent line starts at the risk-free rate on the y-axis and has a slope equal to the Sharpe ratio of the portfolio with the highest Sharpe ratio. The tangent line intersects the efficient frontier at the point where the portfolio with the highest Sharpe ratio is located.

The tangent line represents the optimal portfolio for an investor who wants to maximize their risk-adjusted return. Any portfolio on the tangent line is a combination of the risk-free asset and the portfolio with the highest Sharpe ratio.

The tangent line drawn from the risk-free rate to the efficient frontier is called the Capital Market Line (CML). The CML is a graphical representation of the concept of the Capital Asset Pricing Model (CAPM), which is a widely used model in finance that describes the relationship between the risk and expected return of an asset or a portfolio.

The CML is the straight line that connects the risk-free rate to the point of tangency with the efficient frontier, which represents the optimal portfolio for an investor who wants to maximize their risk-adjusted return. The slope of the CML is the market risk premium, which is the excess return that investors require to invest in a risky asset rather than a risk-free asset. The CML can be used to determine the required return for any level of risk, and it provides a benchmark for evaluating the performance of different investment portfolios.

In Class Demonstration Results: Excel File (FYI)

· In class video part i

· In class video part ii

Modern Portfolio Theory: What MPT Is and How Investors Use It

By THE INVESTOPEDIA TEAM Updated September 10, 2021 Reviewed by PETER WESTFALL Fact checked by SUZANNE KVILHAUG

https://www.investopedia.com/terms/m/modernportfoliotheory.asp

What Is the Modern Portfolio Theory (MPT)?

The modern portfolio theory (MPT) is a practical method for selecting investments in order to maximize their overall returns within an acceptable level of risk. This mathematical framework is used to build a portfolio of investments that maximize the amount of expected return for the collective given level of risk.

American economist Harry Markowitz pioneered this theory in his paper "Portfolio Selection," which was published in the Journal of Finance in 1952. He was

later awarded a Nobel Prize for his work on modern portfolio theory.

A key component of the MPT theory is diversification. Most investments are either high risk and high return or low risk and low return. Markowitz argued that investors could achieve their best results by choosing an optimal mix of the two based on an assessment of their individual tolerance to risk.

KEY TAKEAWAYS

· The modern portfolio theory (MPT) is a method that can be used by risk-averse investors to construct diversified portfolios that maximize their returns without unacceptable levels of risk.

· The modern portfolio theory can be useful to investors trying to construct efficient and diversified portfolios using ETFs.

· Investors who are more concerned with downside risk might prefer the post-modern portfolio theory (PMPT) to MPT.

Understanding the Modern Portfolio Theory (MPT)

The modern portfolio theory argues that any given investment's risk and return characteristics should not be viewed alone but should be evaluated by how it affects the overall portfolio's risk and return. That is, an investor can construct a portfolio of multiple assets that will result in greater returns without a higher level of risk.

As an alternative, starting with a desired level of expected return, the investor can construct a portfolio with the lowest possible risk that is capable of producing that return.

Based on statistical measures such as variance and correlation, a single investment's performance is less important than how it impacts the entire portfolio.

The MPT assumes that investors are risk-averse, meaning they prefer a less risky portfolio to a riskier one for a given level of return. As a practical matter, risk aversion implies that most people should invest in multiple asset classes.

Benefits of the MPT

The MPT is a useful tool for investors who are trying to build diversified portfolios. In fact, the growth of exchange-traded funds (ETFs) made the MPT more relevant by giving investors easier access to a broader range of asset classes.

For example, stock investors can reduce risk by putting a portion of their portfolios in government bond ETFs. The variance of the portfolio will be significantly lower because government bonds have a negative correlation with stocks. Adding a small investment in Treasuries to a stock portfolio will not have a large impact on expected returns because of this loss-reducing effect.

Looking for Negative Correlation

Similarly, the MPT can be used to reduce the volatility of a U.S. Treasury portfolio by putting 10% in a small-cap value index fund or ETF. Although small-cap value stocks are far riskier than Treasuries on their own, they often do well during periods of high inflation when bonds do poorly. As a result, the portfolio's

overall volatility is lower than it would be if it consisted entirely of government bonds. Moreover, the expected returns are higher.

The modern portfolio theory allows investors to construct more efficient portfolios. Every possible combination of assets can be plotted on a graph, with the portfolio's

risk on the X-axis and the expected return on the Y-axis. This plot reveals the most desirable combinations for a portfolio.

For example, suppose Portfolio A has an expected return of 8.5% and a standard deviation of 8%. Assume that Portfolio B has an expected return of 8.5% and a standard deviation of 9.5%. Portfolio A would be deemed more efficient because it has the same expected return but lower risk.

It is possible to draw an upward sloping curve to connect all of the most efficient portfolios. This curve is called the efficient frontier.

Investing in a portfolio underneath the curve is not desirable because it does not maximize returns for a given level of risk.

What Are the Benefits of the Modern Portfolio Theory?

The modern portfolio theory can be used to diversify a portfolio in order to get a better return overall without a bigger risk.

Another benefit of the modern portfolio theory (and of diversification) is that it can reduce volatility. The best way to do that is to choose assets that have a

negative correlation, such as U.S. treasuries and small-cap stocks.

Ultimately, the goal of the modern portfolio theory is to create the most efficient portfolio possible.

What Is the Importance of the Efficient Frontier in the MPT?

The efficient frontier is a cornerstone of the modern portfolio theory. It is the line that indicates the combination of investments that will provide the highest level

of return for the lowest level of risk.

When a portfolio falls to the right of the efficient frontier, it possesses greater risk relative to its predicted return. When it falls beneath the slope of the efficient frontier, it offers a lower level of return relative to risk.

Firm Mid Term exam around 2/22/2023

Study guide (Similar to case study, in class)

Chapter 9 Stock Return Evaluation

ppt

For class discussion:

· What is dividend growth model? Why can we use dividend to estimate a firm’s intrinsic value?

· Are future dividends predictable?

· Refer to the following table for WMT’s dividend history

https://www.nasdaq.com/market-activity/stocks/wmt/dividend-history

WMT Dividend History

· EX-DIVIDEND DATE 12/08/2022

· DIVIDEND YIELD N/A

· ANNUAL DIVIDEND $2.24

· P/E RATIO 33.29

Ex/EFF DATE	TYPE	CASH AMOUNT	DECLARATION DATE	RECORD DATE	PAYMENT DATE
12/07/2023	CASH	$0.57	02/21/2023	12/08/2023	01/02/2024
08/10/2023	CASH	$0.57	02/17/2023	08/11/2023	09/05/2023
05/04/2023	CASH	$0.57	02/21/2023	05/05/2023	05/30/2023
03/16/2023	CASH	$0.57	02/21/2023	03/17/2023	04/03/2023
12/08/2022	CASH	$0.56	02/17/2022	12/09/2022	01/03/2023
08/11/2022	CASH	$0.56	02/17/2022	08/12/2022	09/06/2022
05/05/2022	CASH	$0.56	02/17/2022	05/06/2022	05/31/2022
03/17/2022	CASH	$0.56	02/17/2022	03/18/2022	04/04/2022
12/09/2021	CASH	$0.55	02/18/2021	12/10/2021	01/03/2022
08/12/2021	CASH	$0.55	02/18/2021	08/13/2021	09/07/2021
05/06/2021	CASH	$0.55	02/18/2021	05/07/2021	06/01/2021
03/18/2021	CASH	$0.55	02/18/2021	03/19/2021	04/05/2021
12/10/2020	CASH	$0.54	02/18/2020	12/11/2020	01/04/2021
08/13/2020	CASH	$0.54	02/18/2020	08/14/2020	09/08/2020
05/07/2020	CASH	$0.54	02/18/2020	05/08/2020	06/01/2020
03/19/2020	CASH	$0.54	02/18/2020	03/20/2020	04/06/2020
12/05/2019	CASH	$0.53	02/19/2019	12/06/2019	01/02/2020
08/08/2019	CASH	$0.53	02/19/2019	08/09/2019	09/03/2019
05/09/2019	CASH	$0.53	02/19/2019	05/10/2019	06/03/2019
03/14/2019	CASH	$0.53	02/19/2019	03/15/2019	04/01/2019
12/06/2018	CASH	$0.52	02/21/2018	12/07/2018	01/02/2019
08/09/2018	CASH	$0.52	02/21/2018	08/10/2018	09/04/2018
05/10/2018	CASH	$0.52	02/20/2018	05/11/2018	06/04/2018
03/08/2018	CASH	$0.52	02/20/2018	03/09/2018	04/02/2018
12/07/2017	CASH	$0.51	02/21/2017	12/08/2017	01/02/2018
08/09/2017	CASH	$0.51	02/21/2017	08/11/2017	09/05/2017
05/10/2017	CASH	$0.51	02/21/2017	05/12/2017	06/05/2017
03/08/2017	CASH	$0.51	02/21/2017	03/10/2017	04/03/2017
12/07/2016	CASH	$0.50	02/18/2016	12/09/2016	01/03/2017
08/10/2016	CASH	$0.50	02/18/2016	08/12/2016	09/06/2016
05/11/2016	CASH	$0.50	02/18/2016	05/13/2016	06/06/2016
03/09/2016	CASH	$0.50	02/18/2016	03/11/2016	04/04/2016
12/02/2015	CASH	$0.49	02/19/2015	12/04/2015	01/04/2016
08/05/2015	CASH	$0.49	02/19/2015	08/07/2015	09/08/2015
05/06/2015	CASH	$0.49	02/19/2015	05/08/2015	06/01/2015
03/11/2015	CASH	$0.49	02/19/2015	03/13/2015	04/06/2015
12/03/2014	CASH	$0.48	02/20/2014	12/05/2014	01/05/2015
08/06/2014	CASH	$0.48	02/20/2014	08/08/2014	09/03/2014
05/07/2014	CASH	$0.48	02/20/2014	05/09/2014	06/02/2014
03/07/2014	CASH	$0.48	02/20/2014	03/11/2014	04/01/2014
12/04/2013	CASH	$0.47	02/21/2013	12/06/2013	01/02/2014
08/07/2013	CASH	$0.47	02/21/2013	08/09/2013	09/03/2013
05/08/2013	CASH	$0.47	02/21/2013	05/10/2013	06/03/2013
03/08/2013	CASH	$0.47	02/21/2013	03/12/2013	04/01/2013
12/05/2012	CASH	$0.3975	03/01/2012	12/07/2012	12/27/2012
08/08/2012	CASH	$0.3975	03/01/2012	08/10/2012	09/04/2012
05/09/2012	CASH	$0.3975	03/01/2012	05/11/2012	06/04/2012
03/08/2012	CASH	$0.3975	03/01/2012	03/12/2012	04/04/2012
12/07/2011	CASH	$0.365	03/03/2011	12/09/2011	01/03/2012
08/10/2011	CASH	$0.365	03/03/2011	08/12/2011	09/06/2011
05/11/2011	CASH	$0.365	03/03/2011	05/13/2011	06/06/2011
03/09/2011	CASH	$0.365	03/03/2011	03/11/2011	04/04/2011
12/08/2010	CASH	$0.3025	03/04/2010	12/10/2010	01/03/2011
08/11/2010	CASH	$0.3025	03/04/2010	08/13/2010	09/07/2010
05/12/2010	CASH	$0.3025	03/04/2010	05/14/2010	06/01/2010
03/10/2010	CASH	$0.3025	03/04/2010	03/11/2010
12/09/2009	CASH	$0.2725	03/05/2009	12/10/2009
08/12/2009	CASH	$0.2725	03/05/2009	08/14/2009	09/08/2009
05/13/2009	CASH	$0.2725	03/05/2009	05/15/2009	06/01/2009
03/11/2009	CASH	$0.2725	03/05/2009	03/13/2009	04/06/2009
12/11/2008	CASH	$0.2375	03/06/2008	12/15/2008	01/02/2009
08/13/2008	CASH	$0.2375	03/06/2008	08/15/2008	09/02/2008
05/14/2008	CASH	$0.2375	03/06/2008	05/16/2008	06/02/2008
03/12/2008	CASH	$0.2375	03/06/2008	03/14/2008	04/07/2008
12/12/2007	CASH	$0.22	03/08/2007	12/14/2007	01/02/2008
08/15/2007	CASH	$0.22	03/08/2007	08/17/2007	09/04/2007
05/16/2007	CASH	$0.22	03/08/2007	05/18/2007	06/04/2007
03/14/2007	CASH	$0.22	03/08/2007	03/16/2007	04/02/2007
12/13/2006	CASH	$0.1675	03/02/2006	12/15/2006	01/02/2007
08/16/2006	CASH	$0.1675	03/02/2006	08/18/2006	09/05/2006
05/17/2006	CASH	$0.1675	03/02/2006	05/19/2006	06/05/2006
03/15/2006	CASH	$0.1675	03/02/2006	03/17/2006	04/03/2006
12/14/2005	CASH	$0.15
08/17/2005	CASH	$0.15	03/03/2005	08/19/2005	09/06/2005
05/18/2005	CASH	$0.15	03/03/2005	05/20/2005	06/06/2005
03/16/2005	CASH	$0.15	03/03/2005	03/18/2005	04/04/2005
12/15/2004	CASH	$0.13	03/02/2004	12/17/2004	01/03/2005
08/18/2004	CASH	$0.13	03/02/2004	08/20/2004	09/07/2004
05/19/2004	CASH	$0.13	03/02/2004	05/21/2004	06/07/2004
03/17/2004	CASH	$0.13	03/02/2004	03/19/2004	04/05/2004

Can you estimate the expected dividend in 2023? And in 2024? And on and on…

Can you write down the math equation now?

WMT stock price = ?

Can you calculate now? It is hard right because we assume dividend payment goes to infinity. How can we simplify the calculation?

We can assume that dividend grows at certain rate, just as the table on the right shows.

Discount rate is r (based on Beta and CAPM learned in chapter 6)

Dividend growth model:

Refer to http://www.calculatinginvestor.com/2011/05/18/gordon-growth-model/

· Now let’s apply this Dividend growth model in problem solving.

Dividend Growth Model Calculator (www.jufinance.com/stock )

Equations

Po = D1/(r-g) = Do*(1+g)/(r-g),

Where D1= next dividend; Do = just paid dividend; r=stock return; g= dividend growth rate; Po= current market price

Dividend Yield = D1/Po = Do*(1+g) / Po

Capital gain yield = (P1/Po) -1 = g

Total return = dividend yield + capital gain yield = D1/Po + g

Non-constant dividend growth model (www.jufinance.com/dcf)

Equations

P_n = D_n+1/(r-g) = D_n*(1+g)/(r-g), since year n, dividends start to grow at a constant rate.

Where D_n+1= next dividend in year n+1;

Do = just paid dividend in year n;

r=stock return; g= dividend growth rate;

Pn= current market price in year n;

Po = npv(r, D1, D2, …, Dn+Pn)

Or,

Po = D1/(1+r) + D2/(1+r)^2 + … + (Dn+Pn)/(1+r)^n

Case Study (due with the Second Midterm Exam)

Case video in class part I (Thanks, Ethan and Ted)

Case video in class part II (Thanks, Ethan and Ted)

In class exercise

1. You expect AAA Corporation to generate the following free cash flows over the next five years:

Year	1	2	3	4	5
FCF ($ millions)	75	84	96	111	120

Since year 6, you estimate that AAA's free cash flows will grow at 6% per year. WACC of AAA = 15%

· Calculate the enterprise value for DM Corporation.

· Assume that AAA has $500 million debt and 14 million shares outstanding, calculate its stock price.

Answer:

Enterprise value = npv(15%, 75, 84, 96, 111, 120+120*(1+6%)/(15%-6%)) = 1017.66

(or, equity value = 75/(1+15%) + 84/(1+15%)^2 + 96/(1+15%)^3 + 111/(1+15%)^4 + (120+120*(1+6%)/(15%-6%))/(1+15%)^5

Equity value = 1017.66-500 = 517.66

Stock price = 517.66/14=37

NPV Excel syntax

Syntax

NPV(rate,value1,value2, ...)

Rate is the rate of discount over the length of one period.

Value1, value2, ... are 1 to 29 arguments representing the payments and income.

· Value1, value2, ... must be equally spaced in time and occur at the end of each period. NPV uses the order of value1, value2, ... to interpret the order of cash flows. Be sure to enter your payment and income values in the correct sequence.

2. AAA’s divided yield = 2.5%, equity cost = 10%, and its dividends will grow at a constant rate of g. How much is g?

A) 2.5%

B) 5.0%

C) 10.0%

D) 7.5%

Answer:

Dividend yield + capital gain yield = total return = 10%, and g= capital yield = dividend growth rate, so g = 10% - 2.5% = 7.5%

3. AAA pays no dividend currently. However, you expect it pay an annual dividend of $0.56/share 2 years from now with a growth rate of 4% per year thereafter. Its equity cost = 12%, then its stock price=?

A) $4.67

B) $5.00

C) $6.25

D) $7.00

Answer:

Stock price = Po = npv(12%, 0, 0.56 + 0.56*(1+4%)/(12%-4%)) = 6.25

Or, Po = 0.56/(1+12%)^2 + 0.56*(1+4%)/(12%-4%) /(1+12%)^2 = 6.25

4. AAA expects to have earnings of $2.50 per share this coming year. It will retain all of the earnings for the next year. For the following 4 years, it will retain 50% of its earnings. It will retain 25% of its earnings after that. Each year, retained earnings will be used in new projects with a return of 20% per year as expected. The rest of retained earnings will paid to shareholders as dividends. Its equity cost = 10%. Its stock price=?

A) $40.80

B) $44.70

C) $59.80

D) $63.50

Year	EPS	Retained Earnings	Growth in Earnings (.20 × R.E.)	Dividends
1	$2.50	$2.50
2
3
4
5

Hint: after year 5, the growth rate =0.2/3.99 = 5%

Answer:

Year	EPS	Retained Earnings	Growth in Earnings (.20 × R.E.)	Dividends
1	$2.50	$2.50	0.5	0
2	3	1.5	0.3	1.5
3	3.3	1.65	0.33	1.65
4	3.63	1.82	0.36	1.82
5	3.99	1	0.2	3

after year 5, the growth rate =0.2/3.99 = 5% = growth in earnings / EPS

So price at year 4 = 3/(10%-5%) =60

So current stock price = 1.5/(1+10%)^2 + 1.65/(1+10%)^3 + 1.82/(1+10%)^4 + 60/(1+10%)^4 = 44.70

Or price = npv(10%, 0, 1.5, 1.65, 1.82+60)

Stock screening tools

· Reuters stock screener to help select stocks

http://stockscreener.us.reuters.com/Stock/US/

· FINVIZ.com

http://finviz.com/screener.ashx

· WSJ stock screen

http://online.wsj.com/public/quotes/stock_screener.html

· Simply the Web's Best Financial Charts

Stock charts

MSN Money

You can find analyst rating from MSN money

For instance,

ANALYSTS RATINGS

Zacks average brokerage recommendation is Moderate Buy

RECOMMENDATIONS	CURRENT	1 MONTH AGO	2 MONTHS AGO	3 MONTHS AGO
Strong Buy	26	26	25	24
Moderate Buy	4	4	4	4
Hold	8	8	8	9
Moderate Sell	0	0	0	0
Strong Sell	0	0	0	0
Mean Rec.	1.51	1.51	1.53	1.58

Summary of stock screening rules from class discussion

PEG<1

PE<15 (? FB’s PE>100?)

Growth rate<20

ROE>10%

Analyst ranking: strong buy only

Zacks average =1 (from Ranking stocks using PEG ratio)

current price>5

How to pick stocks

Capital Asset Pricing Model (CAPM)Explained

https://www.youtube.com/watch?v=JApBhv3VLTo

Ranking stocks using PEG ratio

https://www.youtube.com/watch?v=bekW_hTehNU

P/E Ratio Summary by industry (FYI)

(http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/pedata.html

*Industry Name*	*#of firms*	Current PE	Expected growth - next 5 years	PEG Ratio
Advertising	40	42.07	7.24%	2.19
Aerospace/Defense	87	45.24	11.46%	2.08
Air Transport	17	12.40	6.46%	2.00
Apparel	51	19.94	11.32%	2.33
Auto & Truck	18	15.03	18.35%	0.80
Auto Parts	62	23.32	12.64%	1.17
Bank (Money Center)	11	17.09	7.54%	1.86
Banks (Regional)	612	33.24	9.43%	1.87
Beverage (Alcoholic)	28	31.31	20.06%	0.95
Beverage (Soft)	35	28.28	10.77%	2.99
Broadcasting	27	31.34	7.59%	2.58
Brokerage & Investment Banking	42	31.77	11.70%	1.39
Building Materials	39	28.83	14.98%	1.58
Business & Consumer Services	169	59.52	12.94%	2.01
Cable TV	14	25.74	10.25%	2.51
Chemical (Basic)	38	28.39	14.14%	1.38
Chemical (Diversified)	7	281.02	18.82%	2.28
Chemical (Specialty)	99	145.32	12.34%	2.04
Coal & Related Energy	30	13.36	NA	NA
Computer Services	111	48.66	12.36%	1.37
Computers/Peripherals	58	26.11	15.79%	1.14
Construction Supplies	49	35.67	15.00%	2.21
Diversified	24	38.63	12.48%	1.96
Drugs (Biotechnology)	459	127.65	27.31%	0.65
Drugs (Pharmaceutical)	185	46.35	20.47%	1.32
Education	34	132.99	11.91%	2.35
Electrical Equipment	118	29.63	15.09%	1.75
Electronics (Consumer & Office)	24	35.28	12.77%	4.86
Electronics (General)	167	56.36	17.82%	1.42
Engineering/Construction	49	28.75	12.30%	1.92
Entertainment	90	312.73	11.54%	1.56
Environmental & Waste Services	87	73.67	12.83%	2.43
Farming/Agriculture	34	22.90	15.33%	1.42
Financial Svcs. (Non-bank & Insurance)	264	41.45	11.62%	0.88
Food Processing	87	36.08	9.46%	2.55
Food Wholesalers	15	50.79	8.70%	3.03
Furn/Home Furnishings	31	17.82	13.40%	1.43
Green & Renewable Energy	22	89.05	11.05%	2.91
Healthcare Products	251	161.11	16.55%	2.27
Healthcare Support Services	115	38.56	14.52%	1.37
Heathcare Information and Technology	112	174.42	15.21%	2.52
Homebuilding	32	883.19	17.58%	0.99
Hospitals/Healthcare Facilities	35	58.93	6.50%	2.09
Hotel/Gaming	70	34.20	13.18%	1.90
Household Products	131	46.52	11.60%	1.61
Information Services	61	60.11	14.92%	2.42
Insurance (General)	21	34.97	10.46%	2.11
Insurance (Life)	25	152.83	7.82%	1.52
Insurance (Prop/Cas.)	50	120.04	11.56%	1.64
Investments & Asset Management	165	99.35	13.11%	1.31
Machinery	126	47.35	14.03%	1.82
Metals & Mining	102	28.08	30.62%	0.92
Office Equipment & Services	24	18.92	12.25%	1.72
Oil/Gas (Integrated)	5	45.20	25.77%	1.26
Oil/Gas (Production and Exploration)	311	25.17	1.81%	7.33
Oil/Gas Distribution	16	313.75	10.00%	3.77
Oilfield Svcs/Equip.	130	87.54	40.24%	0.90
Packaging & Container	25	51.42	9.31%	2.31
Paper/Forest Products	21	40.11	9.62%	2.09
Power	61	25.25	5.41%	2.07
Precious Metals	111	29.92	24.26%	2.47
Publishing & Newspapers	41	53.87	7.90%	2.75
R.E.I.T.	244	58.88	6.81%	3.65
Real Estate (Development)	20	20.24	NA	NA
Real Estate (General/Diversified)	10	216.85	NA	NA
Real Estate (Operations & Services)	60	486.19	13.63%	1.39
Recreation	70	27.16	12.23%	1.90
Reinsurance	3	11.75	8.75%	2.27
Restaurant/Dining	81	37.50	15.04%	1.70
Retail (Automotive)	25	14.30	16.63%	0.96
Retail (Building Supply)	8	46.86	20.46%	1.21
Retail (Distributors)	92	120.38	15.04%	1.45
Retail (General)	18	96.81	7.88%	2.93
Retail (Grocery and Food)	14	28.23	7.90%	1.75
Retail (Online)	61	73.27	20.77%	3.70
Retail (Special Lines)	106	43.48	11.59%	1.52
Rubber& Tires	4	13.28	9.50%	0.85
Semiconductor	72	49.82	15.68%	1.30
Semiconductor Equip	45	37.81	16.67%	0.97
Shipbuilding & Marine	9	18.23	13.50%	1.96
Shoe	11	95.38	12.39%	2.17
Software (Entertainment)	13	67.28	14.94%	2.56
Software (Internet)	305	205.58	27.74%	1.03
Software (System & Application)	255	209.66	17.06%	1.90
Steel	37	28.91	12.22%	1.53
Telecom (Wireless)	18	64.32	10.83%	2.27
Telecom. Equipment	104	114.62	14.42%	1.36
Telecom. Services	66	61.28	5.99%	2.77
Tobacco	24	29.52	10.33%	1.30
Transportation	18	82.37	15.49%	1.74
Transportation (Railroads)	8	27.22	10.56%	2.26
Trucking	30	29.95	21.01%	1.54
Utility (General)	18	27.54	5.50%	4.30
Utility (Water)	23	141.22	8.99%	3.66
Total Market	7247	71.28	13.60%	1.58
Total Market (without financials)	6057	75.42	14.19%	1.64

Details about how to derive the model mathematically (FYI)

The Gordon growth model is a simple discounted cash flow (DCF) model which can be used to value a stock, mutual fund, or even the entire stock market. The model is named after Myron Gordon who first published the model in 1959.

The Gordon model assumes that a financial security pays a periodic dividend (D) which grows at a constant rate (g). These growing dividend payments are assumed to continue forever. The future dividend payments are discounted at the required rate of return (r) to find the price (P) for the stock or fund.

Under these simple assumptions, the price of the security is given by this equation:

In this equation, I’ve used the “0” subscript on the price (P) and the “1” subscript on the dividend (D) to indicate that the price is calculated at time zero and the dividend is the expected dividend at the end of period one. However, the equation is commonly written with these subscripts omitted.

Obviously, the assumptions built into this model are overly simplistic for many real-world valuation problems. Many companies pay no dividends, and, for those that do, we may expect changing payout ratios or growth rates as the business matures.

Despite these limitations, I believe spending some time experimenting with the Gordon model can help develop intuition about the relationship between valuation and return.

Deriving the Gordon Growth Model Equation

The Gordon growth model calculates the present value of the security by summing an infinite series of discounted dividend payments which follows the pattern shown here:

Multiplying both sides of the previous equation by (1+g)/(1+r) gives:

We can then subtract the second equation from the first equation to get:

Rearranging and simplifying:

Finally, we can simplify further to get the Gordon growth model equation

What Is a DRIP Investment, How It Works, Benefits (FYI)

By BRIAN BEERS Updated December 12, 2021 Reviewed by THOMAS J. CATALANO Fact checked by MARCUS REEVES

https://www.investopedia.com/ask/answers/what-is-a-drip/

What Is a Drip?

The word DRIP is an acronym for "dividend reinvestment plan", but DRIP also happens to describe the way the plan works. With DRIPs, the cash dividends that an investor receives from a company are reinvested to purchase more stock, making the investment in the company grow little by little.

KEY TAKEAWAYS

· A DRIP is a dividend reinvestment plan whereby cash dividends are reinvested to purchase more stock in the company.

· DRIPs use a technique called dollar-cost averaging (DCA) intended to average out the price at which you buy stock as it moves up or down.

· DRIPs help investors accumulate additional shares at a lower cost since there are no commissions or brokerage fees.

How DRIPs Work

A dividend is a reward to shareholders, which can come in the form of a cash payment that is paid via a check or a direct deposit to investors. DRIPs allow investors the choice to reinvest the cash dividend and buy shares of the company's stock.

Many brokerage houses offer clients the ability to reinvest dividends in the underlying securities they hold through a DRIP program. However, investors have the option of purchasing shares directly from the respective company, through direct stock purchase plans (DSPPs).

Fractional Shares

The "dripping" of dividends is not limited to whole shares, which makes these plans somewhat unique. The corporation keeps detailed records of share ownership percentages.

For example, let's say that the TSJ Sports Conglomerate paid a $10 dividend on a stock that traded at $100 per share. Every time there was a dividend payment, investors within the DRIP plan would receive one-tenth of a share.

Benefits of DRIPs

DRIPs offer a number of benefits for both the investors buying shares with their cash dividends and the companies offering DRIP programs.

Benefits to Investors

DRIPs use a technique called dollar-cost averaging (DCA) intended to average out the price at which you buy stock as it moves up or down over a long period. You are never buying the stock right at its peak or at its low with dollar-cost averaging.

Company-operated DRIPS are popular with shareholders as a lower-cost option to accumulate additional shares. There are often no commissions or brokerage fees involved. Many companies offer shares at a discount through their DRIP ranging from 3 to 5% off the current share price.

The price discount combined with no trading commissions allows investors to lower their cost basis for owning a company's shares. As a result, DRIPs can help investors save money on buying additional shares of stock versus had they bought them on the open market.

Benefits to Companies

Companies that offer DRIP programs receive investment dollars or capital from shareholders. Companies can use that capital to reinvest back into the company.

Shareholders or investors that are part of a company's DRIP program are less likely to sell their shares if the company has one bad earnings report or if the overall market declines. In other words, the investors that are engaged in the DRIP program are typically long-term investors in the company.

Special Considerations

It's important to note that the cash dividends that are reinvested into DRIPs are still considered taxable income by the Internal Revenue Service (IRS) and must be reported.

Also, when investors who purchased shares via a company's own DRIP program want to sell their shares, they must sell them back to the company directly. In other words, the shares are not sold on the open market via a broker. Instead, a request to sell the shares must be made with the company, whereby the company will, in turn, redeem the shares at the prevailing stock price. .

Stock Splits

https://stock.walmart.com/investors/stock-information/dividend-history/default.aspx

Wal-Mart Stores, Inc. was incorporated on Oct. 31, 1969. On Oct. 1, 1970, Walmart offered 300,000 shares of its common stock to the public at a price of $16.50 per share. Since that time, we have had 11 two-for-one (2:1) stock splits. On a purchase of 100 shares at $16.50 per share on our first offering, the number of shares has grown as follows:

2:1 Stock Splits	Shares	Cost per Share	Market Price on Split Date	Record Date	Distributed
On the Offering	100	$16.50
May 1971	200	$8.25	$47.00	5/19/71	6/11/71
March 1972	400	$4.125	$47.50	3/22/72	4/5/72
August 1975	800	$2.0625	$23.00	8/19/75	8/22/75
Nov. 1980	1,600	$1.03125	$50.00	11/25/80	12/16/80
June 1982	3,200	$0.515625	$49.875	6/21/82	7/9/82
June 1983	6,400	$0.257813	$81.625	6/20/83	7/8/83
Sept. 1985	12,800	$0.128906	$49.75	9/3/85	10/4/85
June 1987	25,600	$0.064453	$66.625	6/19/87	7/10/87
June 1990	51,200	$0.032227	$62.50	6/15/90	7/6/90
Feb. 1993	102,400	$0.016113	$63.625	2/2/93	2/25/93
March 1999	204,800	$0.008057	$89.75	3/19/99	4/19/99

Elon Musk’s SpaceX to split its private stock 10-for-1

PUBLISHED FRI, FEB 18 20221:43 PM ESTUPDATED FRI, FEB 18 20222:38 PM EST

Michael Sheetz

https://www.cnbc.com/2022/02/18/elon-musks-spacex-performing-10-for-1-stock-split.html

KEY POINTS

· Elon Musk’s SpaceX is splitting the value of its common stock 10-for-1, CNBC has learned.

With SpaceX valued at $560 a share during its most recent sale, the split reduces SpaceX’s common stock to $56 a share, according to a company-wide email obtained by CNBC.

A stock split is cosmetic and does not fundamentally change anything about the company.

Elon Musk’s SpaceX is splitting the value of its common stock 10-for-1, CNBC has learned, with the company’s valuation having soared to more than $100 billion.

The split means that for each share of SpaceX stock owned as of Thursday, a holder now has 10 shares after the conversion. With SpaceX valued at $560 a share during its most recent sale, the split reduces SpaceX’s common stock to $56 a share, according to a company-wide email obtained by CNBC.

“The split has no impact on the overall valuation of the company or on the overall value of your SpaceX holdings,” the email said.

SpaceX did not immediately respond to CNBC’s request for comment.

As the email to employees emphasizes, a stock split is cosmetic and does not fundamentally change anything about the company. Companies occasionally perform stock splits, such as high-growth tech companies such as Apple or Google-parent Alphabet, and the move is typically seen as a way to make the shares more accessible or manageable.

This is the first time SpaceX has performed a stock split, according to multiple people familiar with the private company.

The company’s valuation has soared in the last few years as SpaceX has raised billions to fund work on two capital-intensive projects: the next generation rocket Starship and its global satellite internet network Starlink.

What is SpaceX stock?

SpaceX is not a publicly traded company. That means you cannot buy SpaceX stock in the public market. Unless you are extremely wealthy or have a large stake in a company that has a stake in SpaceX, it’s unlikely you will ever be able to own anything resembling SpaceX shares, for now.

SpaceX still does of course have stakeholders. Founder Elon Musk, who also founded famed electric vehicle manufacturer Tesla, funded the company initially with funds from his sale of popular online payments platform PayPal. Other equity firms, like Founders Fund and Valor Equity Partners, also have significant stake in SpaceX.

How to buy SpaceX stock

As mentioned, the only people buying SpaceX stock aren’t individuals — they’re large corporations and equity firms. For instance, Google and Fidelity together invested around a billion dollars in 2015 for a 10% stake in the company.

How much does SpaceX’s stock cost?

SpaceX’s shares are valued at $56 per share.

SpaceX is not a publicly traded company; therefore, publicly traded SpaceX stock (which doesn’t exist) has no price.

The only way to know how much SpaceX shares could be worth would be to look at the company’s last evaluation. In October of 2021, it was reported that a private shareholder sold shares for a price of $560 per share. That puts the worth of SpaceX at $100 billion, the second highest valued private company in the world.

However, SpaceX went through a 10-1 stock split in February of 2022 meaning that for every one share a holder owned, they now own 10. This also reduces the price of the share, meaning the current price of a single share of SpaceX is now $56. A stock split doesn’t change anything about the company except for the number of shares.

SpaceX stock symbol

SpaceX is not a publicly traded company; therefore, publicly traded SpaceX stock (which doesn’t exist) has no stock ticker symbol. If it did have one, SPCX would probably be a good fit.

When will SpaceX go public?

Elon Musk has stated that SpaceX will not go public any time soon. Musk has stated that short-term demands of shareholders could ruin the company’s chance of colonizing Mars, the long term goal of SpaceX. Once that goal is achieved, Musk might rethink keeping SpaceX private.

https://spaceexplored.com/guides/spacex-stock/

https://www.yardeni.com/pub/stylegrval.pdf

Chapter 10 WACC

ppt

One option (if beta is given)

Another option (if dividend is given):

WACC Formula

WACC calculator (annual coupon bond)

(www.jufinance.com/wacc)

WACC calculator (semi-annual coupon bond)

(www.jufinance.com/wacc_1)

WACC Calculator help videos FYI

Summary of Equations

Discount rate to figure out the value of projects is called WACC (weighted average cost of capital)

WACC = weight of debt * cost of debt + weight of equity *( cost of equity)

· Wd= total debt / Total capital = total borrowed / total capital

· We= total equity/ Total capital

· Cost of debt = rate(nper, coupon, -(price – flotation costs), 1000)*(1-tax rate)

· Cost of Equity = D1/(Po – Flotation Cost) + g

· D1: Next period dividend; Po: Current stock price; g: dividend growth rate

· Note: flotation costs = flotation percentage * price

· Or if beta is given, use CAPM model

1. Cost of equity = risk free rate + beta *(market return – risk free rate)

2. Cost of equity = risk free rate + beta * market risk premium

Discussion:

· Cheaper to raise capital from debt market. Why? Why not 100% financing via borrowing?

· Why tax rate cannot reduce firms’ cost of equity?

· Please refer to the following excel worksheet to learn how to calculate WACC of Hertz (7.99%).

· Excel file is here. Thanks to Chris, Brian and Hanna, the CFA competition team of 2017.

(FYI: Hertz Global Holdings Inc (NYSE:HTZ) WACC %:3.74% As of 2/26/2022

As of today, Hertz Global Holdings Inc's weighted average cost of capital is 3.74%. Hertz Global Holdings Inc's ROIC % is 7.26% (calculated using TTM income statement data). Hertz Global Holdings Inc generates higher returns on investment than it costs the company to raise the capital needed for that investment. It is earning excess returns. A firm that expects to continue generating positive excess returns on new investments in the future will see its value increase as growth increases. https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc)

In Class Exercise

1. IBM financed 10m via debt coupon 5%, 10 year, price is $950 and flotation is 7% of the price, tax 40%.

IBM financed 20m via equity. D1=$5. Po=50, g is 5%. Flotation cost =0. So WACC?

Answer:

· Wd=1/3. We=2/3.

· Kd = rate(10, 5%*1000, -(950-950*7%), 1000)*(1-40%)------ after tax cost of debt

· Ke = 5/(50 – 0) + 5% -------- cost of equity

· WACC = Wd*Kd +We*Ke =

2. Firm AAA sold a noncallable bond now has 20 years to maturity. 9.25% annual coupon rate, paid semiannually, sells at a price = $1,075, par = $1,000. Tax rate = 40%, calculate after tax cost of debt (5.08%)

Answer:

· after tax cost of debt = rate(nper, coupon, -(price-flotation), 1000)*(1-tax rate)

· After tax of debt = rate(20*2, 9.25%*1000/2, -(1075-0), 1000)*(1-40%)=5.08%

3. Firm AAA’s equity condition is as follows. D₁ = $1.25; P₀ = $27.50; g = 5.00%; and Flotation = 6.00% of price. Calculate cost of equity (9.84%)

Answer:

· Cost of equity = D1/(Po-flotation) + g= 1.25/(27.5-6%*27.5) + 5% = 9.84%

4. Continue from above. Firm AAA raised 10m from the capital market. In it, 3m is from the debt market and the rest from the equity market. Calculate WACC.

Answer:

· WACC = Wd*Kd +We*Ke =

· WACC = (3/10)*5.08% + (7/10)*9.84%

5. Common stock currently sells = $45.00 / share; and earn $2.75 /share this year, payout ratio is 70%, and its constant growth rate = 6.00%. New stock can be sold at the current price, a flotation cost =8%. How much would the cost of new stock beyond the cost of retained earnings?

Answer:

Expected EPS₁ $2.75

Payout ratio 70%

Current stk price $45.00

g 6.00%

F 8.00%

D₁ $1.925

r_s = D₁/P₀ + g 10.28%

r_e =D₁/(P₀ × (1 − F)) + g 10.65%

Difference = r_e – r_s 0.37%

6. (1) The firm's noncallable bonds mature in 20 years, an 8.00% annual coupon, a market price of $1,050.00. (2) tax rate = 40%. (3) The risk-free rate=4.50%, the market risk premium = 5.50%, stock’s beta =1.20. (4) capital structure consists of 35% debt and 65% common equity. What is its WACC?

Answer:

Coupon rate 8.00%

Maturity 20

Bond price $1,050.00

Par value $1,000

Tax rate 40%

r_RF 4.50%

RP_M 5.50%

b 1.20

Weight debt 35%

Weight equity 65%

Bond yield 7.51%

A-T cost of debt 4.51%

Cost of equity, r_s= r_RF + b(RP_M) 11.10%

WACC = w_d(r_d)(1 – T) + w_c(r_s) = 8.79%

WACC Case study (due with the 2^nd mid term exam)

Case Video in class completed (Thanks, Ethan and Maggie)

FYI: WACC calculator https://fairness-finance.com/fairness-finance/finance/calculator/wacc.dhtml

Cost of Capital by Sector (US)

https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/wacc.html

*Industry Name*	*Number of Firms*	*Beta*	*Cost of Equity*	*E/(D+E)*	*Std Dev in Stock*	*Cost of Debt*	*Tax Rate*	*After-tax Cost of Debt*	*D/(D+E)*	*Cost of Capital*
Advertising	58	1.63	13.57%	68.97%	52.72%	5.88%	6.39%	4.41%	31.03%	10.73%
Aerospace/Defense	77	1.41	12.28%	79.33%	37.56%	5.50%	8.60%	4.13%	20.67%	10.59%
Air Transport	21	1.42	12.29%	34.92%	37.73%	5.50%	10.47%	4.13%	65.08%	6.98%
Apparel	39	1.32	11.75%	65.98%	38.51%	5.50%	12.04%	4.13%	34.02%	9.15%
Auto & Truck	31	1.54	13.03%	66.58%	52.61%	5.88%	3.00%	4.41%	33.42%	10.15%
Auto Parts	37	1.47	12.64%	70.10%	39.52%	5.50%	9.30%	4.13%	29.90%	10.09%
Bank (Money Center)	7	1.08	10.30%	31.61%	19.59%	4.73%	16.25%	3.55%	68.39%	5.68%
Banks (Regional)	557	0.5	6.88%	60.75%	16.76%	4.73%	18.84%	3.55%	39.25%	5.57%
Beverage (Alcoholic)	23	1.01	9.90%	81.36%	49.87%	5.50%	9.39%	4.13%	18.64%	8.82%
Beverage (Soft)	31	1.3	11.62%	86.75%	41.72%	5.50%	6.42%	4.13%	13.25%	10.63%
Broadcasting	26	1.32	11.73%	40.51%	46.90%	5.50%	15.76%	4.13%	59.49%	7.21%
Brokerage & Investment Banking	30	1.2	11.04%	33.21%	28.00%	5.50%	15.32%	4.13%	66.79%	6.42%
Building Materials	45	1.28	11.47%	77.56%	29.19%	5.50%	16.71%	4.13%	22.44%	9.82%
Business & Consumer Services	164	1.17	10.84%	78.45%	45.78%	5.50%	9.43%	4.13%	21.55%	9.39%
Cable TV	10	1.26	11.34%	48.25%	25.41%	5.50%	21.95%	4.13%	51.75%	7.60%
Chemical (Basic)	38	1.25	11.29%	67.43%	46.58%	5.50%	9.83%	4.13%	32.57%	8.95%
Chemical (Diversified)	4	1.41	12.27%	63.19%	39.49%	5.50%	12.02%	4.13%	36.81%	9.27%
Chemical (Specialty)	76	1.28	11.47%	78.49%	42.32%	5.50%	10.75%	4.13%	21.51%	9.89%
Coal & Related Energy	19	1.45	12.51%	82.16%	61.96%	5.88%	2.28%	4.41%	17.84%	11.06%
Computer Services	80	1.17	10.84%	75.44%	47.78%	5.50%	6.47%	4.13%	24.56%	9.19%
Computers/Peripherals	42	1.29	11.55%	91.31%	48.73%	5.50%	9.13%	4.13%	8.69%	10.90%
Construction Supplies	49	1.26	11.39%	76.85%	35.11%	5.50%	10.52%	4.13%	23.15%	9.71%
Diversified	23	1.04	10.05%	82.48%	57.84%	5.88%	2.98%	4.41%	17.52%	9.06%
Drugs (Biotechnology)	598	1.24	11.26%	86.71%	58.41%	5.88%	0.94%	4.41%	13.29%	10.35%
Drugs (Pharmaceutical)	281	1.27	11.41%	88.02%	64.88%	5.88%	2.37%	4.41%	11.98%	10.57%
Education	33	1.1	10.42%	76.56%	41.81%	5.50%	7.10%	4.13%	23.44%	8.94%
Electrical Equipment	110	1.59	13.32%	81.62%	58.55%	5.88%	4.47%	4.41%	18.38%	11.68%
Electronics (Consumer & Office)	16	1.54	13.02%	85.87%	39.56%	5.50%	3.98%	4.13%	14.13%	11.76%
Electronics (General)	138	1.2	11.02%	84.16%	44.94%	5.50%	6.29%	4.13%	15.84%	9.92%
Engineering/Construction	43	1.2	10.99%	75.99%	35.17%	5.50%	13.30%	4.13%	24.01%	9.34%
Entertainment	110	1.45	12.49%	75.03%	57.81%	5.88%	3.45%	4.41%	24.97%	10.47%
Environmental & Waste Services	62	1.02	9.91%	79.66%	48.09%	5.50%	5.42%	4.13%	20.34%	8.73%
Farming/Agriculture	39	1.14	10.65%	74.70%	54.43%	5.88%	6.64%	4.41%	25.30%	9.07%
Financial Svcs. (Non-bank & Insurance)	223	0.89	9.14%	9.05%	27.15%	5.50%	14.61%	4.13%	90.95%	4.58%
Food Processing	92	0.92	9.33%	77.60%	34.23%	5.50%	7.74%	4.13%	22.40%	8.16%
Food Wholesalers	14	1.12	10.55%	68.42%	32.42%	5.50%	11.94%	4.13%	31.58%	8.52%
Furn/Home Furnishings	32	1.27	11.43%	64.13%	41.91%	5.50%	12.67%	4.13%	35.87%	8.81%
Green & Renewable Energy	19	1.6	13.39%	45.23%	67.60%	7.01%	6.73%	5.26%	54.77%	8.93%
Healthcare Products	254	1.16	10.78%	88.81%	50.94%	5.88%	3.70%	4.41%	11.19%	10.07%
Healthcare Support Services	131	1.16	10.77%	80.90%	47.79%	5.50%	6.74%	4.13%	19.10%	9.50%
Heathcare Information and Technology	138	1.47	12.62%	87.56%	53.87%	5.88%	4.30%	4.41%	12.44%	11.60%
Homebuilding	32	1.5	12.80%	75.57%	33.33%	5.50%	17.81%	4.13%	24.43%	10.68%
Hospitals/Healthcare Facilities	34	1.17	10.85%	53.41%	51.19%	5.88%	9.56%	4.41%	46.59%	7.85%
Hotel/Gaming	69	1.46	12.55%	60.03%	38.05%	5.50%	8.14%	4.13%	39.97%	9.18%
Household Products	127	1.16	10.74%	86.56%	56.83%	5.88%	6.73%	4.41%	13.44%	9.89%
Information Services	73	1.4	12.22%	88.45%	45.11%	5.50%	12.45%	4.13%	11.55%	11.29%
Insurance (General)	21	1.23	11.17%	76.63%	43.76%	5.50%	10.26%	4.13%	23.37%	9.53%
Insurance (Life)	27	0.94	9.46%	51.97%	28.89%	5.50%	11.41%	4.13%	48.03%	6.90%
Insurance (Prop/Cas.)	51	0.8	8.65%	82.33%	27.67%	5.50%	10.92%	4.13%	17.67%	7.85%
Investments & Asset Management	600	0.62	7.58%	72.28%	9.91%	4.73%	4.01%	3.55%	27.72%	6.47%
Machinery	116	1.22	11.16%	82.75%	32.36%	5.50%	10.37%	4.13%	17.25%	9.94%
Metals & Mining	68	1.29	11.54%	82.27%	70.06%	7.01%	4.15%	5.26%	17.73%	10.43%
Office Equipment & Services	16	1.18	10.87%	59.95%	35.22%	5.50%	19.53%	4.13%	40.05%	8.17%
Oil/Gas (Integrated)	4	0.98	9.69%	89.68%	30.55%	5.50%	14.22%	4.13%	10.32%	9.11%
Oil/Gas (Production and Exploration)	174	1.26	11.35%	83.28%	56.98%	5.88%	4.60%	4.41%	16.72%	10.19%
Oil/Gas Distribution	23	0.99	9.77%	58.34%	33.55%	5.50%	6.90%	4.13%	41.66%	7.42%
Oilfield Svcs/Equip.	101	1.38	12.05%	75.41%	46.90%	5.50%	7.07%	4.13%	24.59%	10.10%
Packaging & Container	25	0.95	9.54%	61.74%	24.43%	4.73%	14.66%	3.55%	38.26%	7.25%
Paper/Forest Products	7	1.38	12.10%	69.51%	42.84%	5.50%	12.76%	4.13%	30.49%	9.66%
Power	48	0.73	8.19%	56.45%	17.18%	4.73%	12.30%	3.55%	43.55%	6.17%
Precious Metals	74	1.23	11.21%	85.97%	72.54%	7.01%	2.87%	5.26%	14.03%	10.37%
Publishing & Newspapers	20	1.11	10.50%	70.34%	30.92%	5.50%	9.67%	4.13%	29.66%	8.61%
R.E.I.T.	223	1.06	10.20%	56.39%	21.54%	4.73%	3.38%	3.55%	43.61%	7.30%
Real Estate (Development)	18	1.52	12.89%	47.05%	51.25%	5.88%	6.66%	4.41%	52.95%	8.40%
Real Estate (General/Diversified)	12	0.79	8.57%	71.52%	28.66%	5.50%	9.37%	4.13%	28.48%	7.31%
Real Estate (Operations & Services)	60	1.35	11.87%	47.79%	44.43%	5.50%	5.47%	4.13%	52.21%	7.83%
Recreation	57	1.42	12.30%	65.76%	42.13%	5.50%	9.49%	4.13%	34.24%	9.50%
Reinsurance	1	0.83	8.81%	68.92%	19.37%	4.73%	6.48%	3.55%	31.08%	7.17%
Restaurant/Dining	70	1.41	12.26%	76.47%	41.15%	5.50%	8.54%	4.13%	23.53%	10.34%
Retail (Automotive)	30	1.52	12.91%	63.50%	35.71%	5.50%	15.84%	4.13%	36.50%	9.70%
Retail (Building Supply)	15	1.79	14.51%	82.50%	37.55%	5.50%	13.39%	4.13%	17.50%	12.69%
Retail (Distributors)	69	1.28	11.45%	71.65%	37.08%	5.50%	13.59%	4.13%	28.35%	9.38%
Retail (General)	15	1.36	11.98%	83.35%	31.53%	5.50%	21.26%	4.13%	16.65%	10.67%
Retail (Grocery and Food)	13	0.67	7.85%	60.31%	28.26%	5.50%	16.45%	4.13%	39.69%	6.37%
Retail (Online)	63	1.49	12.71%	83.91%	59.41%	5.88%	4.09%	4.41%	16.09%	11.38%
Retail (Special Lines)	78	1.48	12.64%	71.86%	38.59%	5.50%	15.02%	4.13%	28.14%	10.25%
Rubber& Tires	3	0.84	8.86%	23.24%	39.79%	5.50%	0.00%	4.13%	76.76%	5.22%
Semiconductor	68	1.61	13.43%	89.88%	38.40%	5.50%	8.18%	4.13%	10.12%	12.49%
Semiconductor Equip	30	1.76	14.32%	89.46%	41.57%	5.50%	10.94%	4.13%	10.54%	13.24%
Shipbuilding & Marine	8	0.94	9.49%	71.93%	41.16%	5.50%	6.23%	4.13%	28.07%	7.98%
Shoe	13	1.33	11.77%	91.73%	39.37%	5.50%	10.70%	4.13%	8.27%	11.13%
Software (Entertainment)	91	1.36	11.98%	95.42%	58.71%	5.88%	3.82%	4.41%	4.58%	11.63%
Software (Internet)	33	1.55	13.09%	84.99%	55.24%	5.88%	2.37%	4.41%	15.01%	11.79%
Software (System & Application)	390	1.47	12.61%	91.44%	52.11%	5.88%	3.40%	4.41%	8.56%	11.91%
Steel	28	1.34	11.85%	77.76%	38.30%	5.50%	14.95%	4.13%	22.24%	10.14%
Telecom (Wireless)	16	1.03	10.00%	60.55%	51.92%	5.88%	3.83%	4.41%	39.45%	7.80%
Telecom. Equipment	79	1.23	11.20%	89.54%	41.35%	5.50%	4.06%	4.13%	10.46%	10.46%
Telecom. Services	49	0.88	9.12%	45.93%	55.37%	5.88%	6.54%	4.41%	54.07%	6.57%
Tobacco	15	2	15.76%	80.61%	44.06%	5.50%	9.83%	4.13%	19.39%	13.51%
Transportation	18	1.06	10.17%	77.21%	28.05%	5.50%	16.39%	4.13%	22.79%	8.79%
Transportation (Railroads)	4	1.11	10.46%	78.46%	16.34%	4.73%	16.57%	3.55%	21.54%	8.97%
Trucking	35	1.55	13.06%	69.49%	41.17%	5.50%	14.79%	4.13%	30.51%	10.33%
Utility (General)	15	0.64	7.65%	57.41%	14.97%	4.73%	13.20%	3.55%	42.59%	5.90%
Utility (Water)	16	1.15	10.73%	69.74%	27.96%	5.50%	8.45%	4.13%	30.26%	8.73%
Total Market	7165	1.16	10.75%	65.14%	41.37%	5.50%	7.52%	4.13%	34.86%	8.44%
Total Market (without financials)	5649	1.29	11.56%	79.11%	47.98%	5.50%	6.38%	4.13%	20.89%	10.01%

Recommended websites for WACC

Tesla

· https://www.gurufocus.com/term/wacc/TSLA/WACC-Percentage/Tesla

· https://valueinvesting.io/TSLA/valuation/wacc // cost of equity = long term bond rate + premium

Wal-Mart

· https://www.gurufocus.com/term/wacc/WMT/WACC-Percentage/Walmart#:~:text=As%20of%20today%20(2023%2D03,cost%20of%20capital%20is%206.42%25.

· https://valueinvesting.io/WMT/valuation/wacc

Apple

· https://www.gurufocus.com/term/wacc/AAPL/WACC-Percentage/Apple

· https://valueinvesting.io/AAPL/valuation/wacc

Amazon

· https://valueinvesting.io/AMZN/valuation/wacc

· https://www.gurufocus.com/term/wacc/AMZN/WACC-Percentage/Amazon.com

Chapter 11: Capital Budgeting

ppt

calculator Excel Template

1. NPV Excel syntax

Syntax

NPV(rate,value1,value2, ...)

Rate is the rate of discount over the length of one period.

Value1, value2, ... are 1 to 29 arguments representing the payments and income.

2. IRR Excel syntax

Syntax

IRR(values, guess)

Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.

Guess is a number that you guess is close to the result of IRR.

Or, PI = NPV / CFo +1

Profitable index (PI) =1 + NPV / absolute value of CFo

3. MIRR( values, finance_rate, reinvest_rate ) ----- Excel

Where the function arguments are as follows:

Values

An array of values (or a reference to a range of cells containing values) representing the series of cash flows (investment and net income values) that occur at regular periods.

These must contain at least one negative value (representing payment) and at least one positive value (representing income).

finance_rate

The interest rate paid on the money used in the cash flows.

reinvest_rate

The interest rate paid on the reinvested cash flows.

Modified Internal Rate of Return (MIRR)

By ADAM HAYES Updated June 12, 2022 Reviewed by DAVID KINDNESS Fact checked by JIWON MA

Video https://www.investopedia.com/terms/m/mirr.asp

What Is Modified Internal Rate of Return (MIRR)?

The modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's cost of capital and that the initial outlays are financed at the firm's financing cost. By contrast, the traditional internal rate of return (IRR) assumes the cash flows from a project are reinvested at the IRR itself. The MIRR, therefore, more accurately reflects the cost and profitability of a project.

Meanwhile, the internal rate of return (IRR) is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. Both MIRR and IRR calculations rely on the formula for NPV.

KEY TAKEAWAYS

· MIRR improves on IRR by assuming that positive cash flows are reinvested at the firm's cost of capital.

· MIRR is used to rank investments or projects a firm or investor may undertake.

· MIRR is designed to generate one solution, eliminating the issue of multiple IRRs.

What MIRR Can Tell You

The MIRR is used to rank investments or projects of unequal size. The calculation is a solution to two major problems that exist with the popular IRR calculation. The first main problem with IRR is that multiple solutions can be found for the same project. The second problem is that the assumption that positive cash flows are reinvested at the IRR is considered impractical in practice. With the MIRR, only a single solution exists for a given project, and the reinvestment rate of positive cash flows is much more valid in practice. The MIRR allows project managers to change the assumed rate of reinvested growth from stage to stage in a project. The most common method is to input the average estimated cost of capital, but there is flexibility to add any specific anticipated reinvestment rate.

The Difference Between MIRR and IRR

Even though the internal rate of return (IRR) metric is popular among business managers, it tends to overstate the profitability of a project and can lead to capital budgeting mistakes based on an overly optimistic estimate. The modified internal rate of return (MIRR) compensates for this flaw and gives managers more control over the assumed reinvestment rate from future cash flow. An IRR calculation acts like an inverted compounding growth rate. It has to discount the growth from the initial investment in addition to reinvested cash flows. However, the IRR does not paint a realistic picture of how cash flows are actually pumped back into future projects. Cash flows are often reinvested at the cost of capital, not at the same rate at which they were generated in the first place. IRR assumes that the growth rate remains constant from project to project. It is very easy to overstate potential future value with basic IRR figures. Another major issue with IRR occurs when a project has different periods of positive and negative cash flows. In these cases, the IRR produces more than one number, causing uncertainty and confusion. MIRR solves this issue as well.

Limitations of Using MIRR

The first limitation of MIRR is that it requires you to compute an estimate of the cost of capital in order to make a decision, a calculation that can be subjective and vary depending on the assumptions made. As with IRR, the MIRR can provide information that leads to sub-optimal decisions that do not maximize value when several investment options are being considered at once. MIRR does not actually quantify the various impacts of different investments in absolute terms; NPV often provides a more effective theoretical basis for selecting investments that are mutually exclusive. It may also fail to produce optimal results in the case of capital rationing. MIRR can also be difficult to understand for people who do not have a financial background. Moreover, the theoretical basis for MIRR is also disputed among academics.

Homework: Case study questions (due with the second midterm exam)

Case study video in class spring 2022 FYI – completed (Thanks, Ted and Maggie)

· Sorry for the mistake in class for accidentally closing the recording in class

· Thanks to Ted and Maggie for taking the lead in class for this case study.

Case study video in class 3/23/2023 – Part II (Thanks, Ted and Christian)

Let’s have some fun with ChatGPT – generate NPV Calculator by ChatGPT

Here are step-by-step instructions:

1. Ask ChatGPT to generate a NPV calculator using JavaScript in HTML format. You can ask something like: "Hey ChatGPT, could you please generate a NPV calculator using JavaScript in HTML format to calculate the NPV, given cash flows and the discount rate?"

2. ChatGPT should respond with the code for the calculator. Copy the code to your clipboard.

3. Open Notepad or any other text editor and paste the code into a new document.

4. Save the file as an HTML file. You can name it anything you like, but make sure the file extension is ".html". For example, you can name it "npv_calculator.html".

5. Open the saved HTML file in your web browser (e.g. Chrome, Firefox, etc.) by double-clicking on the file or right-clicking and selecting "Open with". The NPV calculator should load and be ready to use.

6. Test the calculator by entering different values for the cash flows and the disount rate. Make sure the calculated NPV is correct and matches your expectations.

7. If you find any issues with the calculator, you can ask ChatGPT to generate it again with the desired changes.

Or use the code from my experiment with ChatGPT earlier this week to get both NPV and NFV

<!DOCTYPE html>

<html>

<head>

<title>Net Present and Future Value Calculator</title>

function calculateNPV() {

var initialInvestment = parseFloat(document.getElementById("initial-investment").value);

var discountRate = parseFloat(document.getElementById("discount-rate").value);

var cashFlows = document.getElementById("cash-flows").value.trim();

// check for empty input

if (cashFlows === "") {

document.getElementById("npv-result").innerHTML = "";

document.getElementById("nfv-result").innerHTML = "";

document.getElementById("error-message").innerHTML = "Please enter at least one cash flow.";

return;

}

// split input into an array of cash flows

cashFlows = cashFlows.split(",");

// parse each cash flow and check for invalid input

for (var i = 0; i < cashFlows.length; i++) {

var cashFlow = parseFloat(cashFlows[i]);

if (isNaN(cashFlow)) {

document.getElementById("npv-result").innerHTML = "";

document.getElementById("nfv-result").innerHTML = "";

document.getElementById("error-message").innerHTML = "Invalid cash flow entered at position " + (i+1) + ".";

return;

}

cashFlows[i] = cashFlow;

}

// calculate net present value

var npv = -initialInvestment;

for (var i = 0; i < cashFlows.length; i++) {

npv += cashFlows[i] / Math.pow(1 + discountRate, i+1);

}

// calculate net future value

var nfv = npv * Math.pow(1 + discountRate, cashFlows.length);

// display results

document.getElementById("npv-result").innerHTML = "Net Present Value: $" + npv.toFixed(2);

document.getElementById("nfv-result").innerHTML = "Net Future Value: $" + nfv.toFixed(2);

document.getElementById("error-message").innerHTML = "";

}

</script>

</head>

<body>

<h1>Net Present and Future Value Calculator</h1>

<label for="initial-investment">Initial Investment:</label>

<label for="discount-rate">Discount Rate:</label>

<label for="cash-flows">Cash Flows:</label>

<button onclick="calculateNPV()">Calculate NPV and NFV</button>

</body>

</html>

Another example for MIRR:

<!DOCTYPE html>

<html>

<head>

<title>Modified Internal Rate of Return (MIRR) Calculator</title>

</head>

<body>

<h1>Modified Internal Rate of Return (MIRR) Calculator</h1>

<label for="initial-investment">Initial Investment:</label>

<label for="cash-flows">Cash Flows (comma separated):</label>

<label for="finance-rate">Finance Rate (%):</label>

<label for="reinvest-rate">Reinvestment Rate (%):</label>

<button onclick="calculateMIRR()">Calculate MIRR</button>

function calculateMIRR() {

const initialInvestment = parseFloat(document.getElementById("initial-investment").value);

const cashFlows = document.getElementById("cash-flows").value.split(",").map(Number);

const financeRate = parseFloat(document.getElementById("finance-rate").value) / 100;

const reinvestRate = parseFloat(document.getElementById("reinvest-rate").value) / 100;

// Calculate terminal value of cash flows

const terminalValue = cashFlows.reduce((pv, cf, i) => {

return pv + cf / Math.pow(1 + reinvestRate, i + 1);

}, 0);

// Calculate MIRR

const numerator = terminalValue + initialInvestment;

const denominator = Math.pow(1 + financeRate, cashFlows.length);

const mirr = Math.pow(numerator / denominator, 1 / cashFlows.length) - 1;

document.getElementById("result").value = mirr.toFixed(4);

}

</script>

</body>

</html>

Second Midterm Exam

· 3/27/2023

· in class

· similar to case studies

· chapters 9, 10, 11

One common method for evaluating a firm is the Discounted Cash Flow (DCF) analysis. This method involves estimating the future cash flows of the firm and discounting them back to their present value using a discount rate.

Video – General Introduction DCF

Here are the detailed steps and equations involved in the DCF analysis:

· Estimate future cash flows: The first step is to estimate the future cash flows that the firm is expected to generate. This typically involves forecasting revenue, expenses, and capital expenditures for a number of years into the future. Let's denote these cash flows as CF1, CF2, ..., CFn.

· Determine the discount rate: The discount rate is the rate of return that an investor requires to invest in the firm. This rate should reflect the risk associated with the investment, with higher-risk investments requiring a higher rate of return. Let's denote the discount rate as r.

· Calculate the present value of future cash flows: Once the future cash flows and discount rate have been determined, we can calculate the present value of each cash flow using the following formula:

PV = CF / (1 + r)^n

where PV is the present value of the cash flow, CF is the cash flow for a given year, r is the discount rate, and n is the number of years into the future that the cash flow occurs.

· Calculate the terminal value: After estimating cash flows for a number of years, we need to estimate the value of the firm beyond the forecast period. Let's denote the terminal value as TV.

· Calculate the total present value: Once we have calculated the present value of each cash flow and the terminal value, we can sum them up to get the total present value (PV) of the firm:

PV = PV1 + PV2 + ... + PVn + PV of TV

· Subtract the firm's debt: Finally, we need to subtract the firm's outstanding debt from the total present value to arrive at the firm's equity value:

· Equity value = PV - Debt

· Overall, the DCF analysis provides an estimate of the intrinsic value of the firm based on its expected future cash flows and the WACC. However, it should be noted that the accuracy of the analysis is highly dependent on the accuracy of the cash flow and discount rate estimates. --- ChatGPT

DCF - An Example – ChatGPT (FYI)

XYZ Corp. DCF Analysis Report

Introduction:

This report is a DCF analysis of XYZ Corp., a publicly traded company with a current market capitalization of $10 billion. The purpose of this report is to estimate the intrinsic value of the company using a discounted cash flow (DCF) model. Assuming that the company’s funding is entirely based on equity.

Step 1: Forecast Future Cash Flows

To forecast future cash flows, we have assumed that the company's cash flows will grow at a rate of 5% per year for the next five years. The forecasted cash flows are as follows:

Year 0: $1.00 billion

Year 1: $1.05 billion

Year 2: $1.10 billion

Year 3: $1.16 billion

Year 4: $1.22 billion

Year 5: $1.28 billion

Step 2: Estimate the Terminal Value

To estimate the terminal value, we have assumed that the cash flows beyond Year 5 will grow at a rate of 2% per year, which is lower than the growth rate assumed for the forecasted cash flows. The terminal value is calculated as follows:

Terminal Value = Year 6 Cash Flow / (Discount Rate - Growth Rate)

Year 6 Cash Flow = $1.28 billion *(1+ 2%) = $1.30 billion

Discount Rate = 10%

Growth Rate = 2%

Therefore, Terminal Value = $1.30 billion / ( cost of equity - 2%)

Step 3: Determine the Discount Rate

To determine the discount rate, we have used the Capital Asset Pricing Model (CAPM) to estimate the company's cost of equity. The CAPM formula is:

Cost of Equity = Risk-Free Rate + Beta * (Market Risk Premium)

where:

Risk-Free Rate = 2%

Beta = 1.2 (estimated based on industry comparables)

Market Risk Premium = 7% (historical average)

Therefore, Cost of Equity = 2% + 1.2 * 7% = 10.4%

Terminal Value = $1.30 billion / (cost of equity - 2%) = $1.30 billion / (10.4% - 2%) = $15.50 billion

Step 4: Calculate the Present Value of Future Cash Flows

To calculate the present value of each cash flow, we have used the following formula:

Present Value = Cash Flow / (1 + Discount Rate) ^ Year

Using this formula, we can calculate the present value of each cash flow as follows:

Year 1: $1.05 billion / (1 + 10.4%)^1 = $951 million

Year 2: $1.10 billion / (1 + 10.4%)^2 = $905 million

Year 3: $1.16 billion / (1 + 10.4%)^3 = $860 million

Year 4: $1.22 billion / (1 + 10.4%)^4 = $818 million

Year 5: $1.28 billion / (1 + 10.4%)^5 = $778 million

Terminal Value: $15.50 billion / (1 + 10.4%)^5 = $9.45 billion

Step 5: Sum the present value of cash flows and terminal value

We can now sum up the present value of each cash flow and the terminal value to get the total intrinsic value of XYZ Corp.

Total Intrinsic Value = Present Value of Cash Flows + Terminal Value

= $951 million + $905 million + $860 million + $818 million + $778 million + $9.45 billion

= $13.76 billion

Step 6: Compare the intrinsic value with the market capitalization

Finally, we need to compare the intrinsic value of XYZ Corp. with its market capitalization to determine whether the stock is undervalued, overvalued, or fairly valued. In this case, the intrinsic value of XYZ Corp. is $13.76 billion, while its market capitalization is $10 billion. This suggests that the stock is undervalued and may be a good investment opportunity.

Note that this example is simplified and does not take into account other factors such as changes in working capital or debt payments. Also, it's important to keep in mind that DCF analysis is only one of several methods used to value a company and should be used in conjunction with other valuation techniques.

Overall, based on the DCF analysis, XYZ Corp. appears to be undervalued relative to its intrinsic value. However, investors should conduct further research and analysis before making any investment decisions.

Step 7: Sensitivity Analysis (Monte Carlo Analysis is a method used for conducting sensitivity analysis)

Sensitivity analysis is an important tool in determining the robustness of our valuation. It helps us understand how changes in assumptions can affect the estimated intrinsic value. In our DCF analysis of XYZ Corp., we assumed a 5% growth rate for the next five years and a 2% growth rate beyond that. Let's see how our intrinsic value would change if we vary these assumptions.

Assumption 1: Growth Rate

If we assume a lower growth rate of 4% for the next five years, the intrinsic value of XYZ Corp. decreases to $13.20 billion. On the other hand, if we assume a higher growth rate of 6%, the intrinsic value increases to $14.34 billion. This tells us that our estimate is sensitive to changes in the growth rate assumption.

Assumption 2: Terminal Growth Rate

If we assume a lower terminal growth rate of 1%, the intrinsic value of XYZ Corp. decreases to $12.67 billion. Conversely, if we assume a higher terminal growth rate of 3%, the intrinsic value increases to $15.14 billion. Again, this tells us that our estimate is sensitive to changes in the terminal growth rate assumption.

Overall, our DCF analysis suggests that XYZ Corp. is undervalued, with an intrinsic value of $13.76 billion compared to its market capitalization of $10 billion. However, we must keep in mind that this is just one method of valuation and there are many other factors that can affect the stock price. As always, investors should conduct their own due diligence and consult with financial professionals before making any investment decisions.

Video – Amazon – DCF

Evaluation of Amazon based on DCF - ChatGPT

DCF (Discounted Cash Flow) analysis is a commonly used method for evaluating the intrinsic value of a company. It is based on the idea that the value of a company is determined by the present value of its expected future cash flows.

Here are the steps to evaluate Amazon using DCF:

Step 1: Estimate Amazon's Free Cash Flow (FCF)

FCF is the cash generated by a company after accounting for all capital expenditures needed to maintain or grow the business. To calculate Amazon's FCF, we can start with its operating cash flow and subtract its capital expenditures.

Operating cash flow for the last 12 months (as of September 2021) was $92.5 billion, and capital expenditures were $24.5 billion. Therefore, Amazon's FCF is:

FCF = Operating cash flow - Capital expenditures

FCF = $92.5 billion - $24.5 billion

FCF = $68 billion

Step 2: Estimate Amazon's growth rate

Next, we need to estimate the rate at which Amazon's FCF is likely to grow in the future. One way to do this is to look at the historical growth rates and make an educated guess about future growth.

Amazon's FCF has grown at an average rate of 25% over the past five years. Assuming a conservative growth rate of 15% for the next five years, and then a terminal growth rate of 3% after that, we can estimate Amazon's future FCF as follows:

Year 1 FCF = $68 billion x (1 + 15%) = $78.2 billion

Year 2 FCF = $78.2 billion x (1 + 15%) = $89.9 billion

Year 3 FCF = $89.9 billion x (1 + 15%) = $103.4 billion

Year 4 FCF = $103.4 billion x (1 + 15%) = $119 billion

Year 5 FCF = $119 billion x (1 + 15%) = $137 billion

Terminal FCF = $137 billion x (1 + 3%) / (11% - 3%) = $1760.94 billion (11% is the WACC)

Step 3: Determine Amazon's Discount Rate

The discount rate is the rate of return required by investors to compensate for the risk of investing in a company. A higher discount rate indicates a higher level of risk. To determine Amazon's discount rate, we can use the CAPM (Capital Asset Pricing Model), which takes into account the risk-free rate, market risk premium, and Amazon's beta.

Assuming a risk-free rate of 2%, a market risk premium of 6%, and Amazon's beta of 1.5, we can calculate Amazon's discount rate as follows:

Discount rate = Risk-free rate + Beta x Market risk premium

Discount rate = 2% + 1.5 x 6%

Discount rate = 11%

Step 4: Calculate Amazon's Intrinsic Value

Finally, we can calculate Amazon's intrinsic value using the discounted cash flow formula, which is the sum of the present value of all future cash flows.

Intrinsic value = (Year 1 FCF / (1 + Discount rate)^1) + (Year 2 FCF / (1 + Discount rate)^2) + ... + (Terminal FCF / (1 + Discount rate)^5)

Intrinsic value = ($78.2 billion / (1 + 11%)^1) + ($89.9 billion / (1 + 11%)^2) + ($103.4 billion / (1 + 11%)^3) + ($119 billion / (1 + 11%)^4) + ($137 billion / (1 +11%)^5) + ($1.76 trillion / (1 + 11%)^5)

Intrinsic value = $1,423 billion

We made the assumption that AMAZON's cost of equity is roughly equivalent to its WACC for the purpose of simplifying the calculation. However, according to gurufocus.com, as of the end of March 2023, AMAZON's WACC is 9.65%.

Step 5: Compare Intrinsic Value with Market Value

The last step is to compare the intrinsic value we calculated with the current market value of Amazon. As of March 2023, Amazon's market capitalization is around $2.4 trillion.

Comparing the intrinsic value of $1,423 billion with the market capitalization of $2.4 trillion, we can see that the market value is higher than the intrinsic value, which suggests that the stock may be overvalued. However, it's important to keep in mind that the DCF analysis is based on various assumptions and estimates, and the actual value of a company may differ from the calculated intrinsic value.

Therefore, it's important to use multiple valuation methods and take into account other factors such as industry trends, competitive landscape, and management quality to make an informed investment decision.

To calculate the estimated per-share stock price based on the DCF analysis, we can divide the intrinsic value by the total number of shares outstanding. As of December 2021, Amazon had around 500 million shares outstanding.

Estimated Per-Share Stock Price = Intrinsic Value / Shares Outstanding

Estimated Per-Share Stock Price = $1,423 billion / 500 million

Estimated Per-Share Stock Price = $2,847

Therefore, based on this DCF analysis, the estimated per-share stock price for Amazon is $2,847. However, it's important to note that this is just an estimate based on certain assumptions and estimates, and the actual stock price may differ based on various factors such as market sentiment, company performance, and global economic conditions.

How much does Amazon worth?” --- FYI only: Amazon.com Inc. (AMZN)

https://www.stock-analysis-on.net/NASDAQ/Company/Amazoncom-Inc/DCF/Present-Value-of-FCFF

Present Value of Free Cash Flow to the Firm (FCFF)

In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Free cash flow to the firm (FCFF) is generally described as cash flows after direct costs and before any payments to capital suppliers.

Intrinsic Stock Value (Valuation Summary)

Amazon.com Inc., free cash flow to the firm (FCFF) forecast

Year	Value	FCFF_t or Terminal value (TV_t)	Calculation	Present value at 16.17%
0¹	FCFF₀	(4,286)
1	FCFF₁	–	= (4,286) × (1 + 0.00%)	–
2	FCFF₂	–	= – × (1 + 0.00%)	–
3	FCFF₃	–	= – × (1 + 0.00%)	–
4	FCFF₄	–	= – × (1 + 0.00%)	–
5	FCFF₅	–	= – × (1 + 0.00%)	–
5	Terminal value (TV₅)	–	= – × (1 + 0.00%) ÷ (16.17% – 0.00%)	–
Intrinsic value of Amazon.com's capital				–
Less: Debt (fair value)				45,696
Intrinsic value of Amazon.com's common stock				–

Intrinsic value of Amazon.com's common stock (per share)				$–
Current share price				$1,642.81

Weighted Average Cost of Capital (WACC)

Amazon.com Inc., cost of capital

	Value¹	Weight	Required rate of return²	Calculation
Equity (fair value)	803,283	0.95	16.97%
Debt (fair value)	45,696	0.05	2.10%	= 2.99% × (1 – 29.84%)

¹ USD $ in millions

Equity (fair value) = No. shares of common stock outstanding × Current share price
= 488,968,628 × $1,642.81 = $803,282,551,764.68

Debt (fair value). See Details »

² Required rate of return on equity is estimated by using CAPM. See Details »

Required rate of return on debt. See Details »

Required rate of return on debt is after tax.

Estimated (average) effective income tax rate
= (20.20% + 36.61% + 60.59% + 0.00% + 31.80%) ÷ 5 = 29.84%

WACC = 16.17%

FCFF Growth Rate (g)

FCFF growth rate (g) implied by PRAT model

Amazon.com Inc., PRAT model

	Average	Dec 31, 2017	Dec 31, 2016	Dec 31, 2015	Dec 31, 2014	Dec 31, 2013
*Selected Financial Data (USD $ in millions)*
Interest expense		848	484	459	210	141
Net income (loss)		3,033	2,371	596	(241)	274

Effective income tax rate (EITR)¹		20.20%	36.61%	60.59%	0.00%	31.80%

Interest expense, after tax²		677	307	181	210	96
Interest expense (after tax) and dividends		677	307	181	210	96

EBIT(1 – EITR)³		3,710	2,678	777	(31)	370

Current portion of long-term debt		100	1,056	238	1,520	753
Current portion of capital lease obligation		5,839	3,997	3,027	2,013	955
Current portion of finance lease obligations		282	144	99	67	28
Long-term debt, excluding current portion		24,743	7,694	8,235	8,265	3,191
Long-term capital lease obligations, excluding current portion		8,438	5,080	4,212	3,026	1,435
Long-term finance lease obligations, excluding current portion		4,745	2,439	1,736	1,198	555
Total stockholders' equity		27,709	19,285	13,384	10,741	9,746
Total capital		71,856	39,695	30,931	26,830	16,663
*Ratios*
Retention rate (RR)⁴		0.82	0.89	0.77	–	0.74
Return on invested capital (ROIC)⁵		5.16%	6.75%	2.51%	-0.12%	2.22%
*Averages*
RR	0.80
ROIC	3.31%

Growth rate of FCFF (g)⁶	0.00%

¹ See Details »

2017 Calculations

² Interest expense, after tax = Interest expense × (1 – EITR)
= 848 × (1 – 20.20%) = 677

³ EBIT(1 – EITR) = Net income (loss) + Interest expense, after tax
= 3,033 + 677 = 3,710

⁴ RR = [EBIT(1 – EITR) – Interest expense (after tax) and dividends] ÷ EBIT(1 – EITR)
= [3,710 – 677] ÷ 3,710 = 0.82

⁵ ROIC = 100 × EBIT(1 – EITR) ÷ Total capital
= 100 × 3,710 ÷ 71,856 = 5.16%

⁶ g = RR × ROIC
= 0.80 × 3.31% = 0.00%

FCFF growth rate (g) forecast

Amazon.com Inc., H-model

Year	Value	g_t
1	g₁	0.00%
2	g₂	0.00%
3	g₃	0.00%
4	g₄	0.00%
5 and thereafter	g₅	0.00%

where:
g₁ is implied by PRAT model
g₅ is implied by single-stage model
g₂, g₃ and g₄ are calculated using linear interpoltion between g₁ and g₅

Calculations

g₂ = g₁ + (g₅ – g₁) × (2 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (2 – 1) ÷ (5 – 1) = 0.00%

g₃ = g₁ + (g₅ – g₁) × (3 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (3 – 1) ÷ (5 – 1) = 0.00%

g₄ = g₁ + (g₅ – g₁) × (4 – 1) ÷ (5 – 1)
= 0.00% + (0.00% – 0.00%) × (4 – 1) ÷ (5 – 1) = 0.00%

Chapter 3 Financial Statement (Step one of the DCF approach)

ppt

Using a Balance Sheet to Analyze a Company (VIDEO)

What is an Income Statement? (Video)

How Do You Read a Cash Flow Statement? | (VIDEO)

Balance Sheet Template

http://www.jufinance.com/10k/bs

Income Statement Template

http://www.jufinance.com/10k/is

Cash flow template

http://www.jufinance.com/10k/cf

Note: All companies, foreign and domestic, are required to file registration statements, periodic reports, and other forms electronically through EDGAR.

************ What is Free Cash Flow **************

What is free cash flow (video)

What is free cash flow (FCF)? Why is it important?

• FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debtholders) after making the necessary investments to support operations.

• A company’s value depends on the amount of FCF it can generate.

What are the five uses of FCF?

o Pay interest on debt.

o Pay back principal on debt.

o Pay dividends.

o Buy back stock.

o Buy nonoperating assets (e.g., marketable securities, investments in other companies, etc.)

Capital expenditure = increases in NFA + depreciation

Or, capital expenditure = increases in GFA

What are operating current assets?

• Operating current assets are the CA needed to support operations.

• Op CA include: cash, inventory, receivables.

• Op CA exclude: short-term investments, because these are not a part of operations.

What are operating current liabilities?

• Operating current liabilities are the CL resulting as a normal part of operations.

• Op CL include: accounts payable and accruals.

• Op CL exclude: notes payable, because this is a source of financing, not a part of operations.

Note: All companies, foreign and domestic, are required to file registration statements, periodic reports, and other forms electronically through EDGAR. https://www.sec.gov/edgar/searchedgar/companysearch.html

FCF calculator

https://www.jufinance.com/fcf

In class exercise

Firm AAA has EBIT (operating income) of $3 million, depreciation of $1 million. Firm AAA’s expenditures on fixed assets = $1 million. Its net operating working capital = $0.6 million. Calculate for free cash flow. Imagine that the tax rate =40%.

FCF = EBIT(1 – T) + Deprec. – (Capex + NOWC)

answer:

EBIT $3

Tax rate 40%

Depreciation $1

Capex + NOWC $1.60

So, FCF = 3*(1-40%) + 1 –(1+0.6) = 1.2

Case study of chapter 3

· FCF

· MVA: How to calculate market value added | MVA calculation | FIN-Ed (video)

· EVA: Economic Value Added: EVA Explained (video)

· Balance Sheet

· Income Statement

In Class Video (4/3/2023)

· Excel File here (due with the final exam,) ‘

*Industry name*	*Number of firms*	*Dividends*	*Net Income*	*Dividends + Buybacks - Stock Issuances*	*FCFE (before debt cash flows)*	*FCFE (after debt cash flows)*
Advertising	58	$1,053.13	$1,557.12	$2,099.32	$701.92	$1,441.35
Aerospace/Defense	77	$10,261.13	$14,514.28	$26,339.72	$11,777.55	$7,574.30
Air Transport	21	$0.00	($3,270.31)	($143.96)	($7,598.89)	($21,052.22)
Apparel	39	$1,985.68	$3,655.80	$7,841.46	($2,499.16)	($1,233.15)
Auto & Truck	31	$2,124.50	$20,137.80	($7,894.97)	$2,434.31	($3,779.69)
Auto Parts	37	$694.40	$1,869.70	$1,567.87	($1,796.70)	($246.25)
Bank (Money Center)	7	$29,107.12	$102,625.92	$40,338.00	$141,352.92	$280,520.92
Banks (Regional)	557	$19,659.99	$67,543.37	$32,945.14	$58,434.71	$192,772.18
Beverage (Alcoholic)	23	$1,270.60	$1,608.29	$2,592.31	($195.71)	($105.87)
Beverage (Soft)	31	$12,915.35	$22,852.32	$15,024.79	$21,780.18	$25,887.17
Broadcasting	26	$1,266.31	$8,817.25	$3,464.83	($5,822.60)	($7,578.38)
Brokerage & Investment Banking	30	$11,022.99	$38,423.51	$23,872.69	$100,348.33	$171,525.17
Building Materials	45	$1,861.54	$14,370.39	$11,720.67	$9,419.22	$13,041.20
Business & Consumer Services	164	$3,112.87	$11,028.56	$8,943.99	$11,231.01	$16,410.59
Cable TV	10	$5,128.40	$17,653.30	$36,833.00	$18,830.08	$28,294.38
Chemical (Basic)	38	$4,333.80	$15,819.51	$9,182.00	$9,847.05	$6,877.91
Chemical (Diversified)	4	$330.00	$2,259.24	$1,683.10	$1,824.07	$1,901.91
Chemical (Specialty)	76	$7,557.41	$18,677.57	$19,090.45	$5,618.06	$25,052.17
Coal & Related Energy	19	$513.96	$2,515.23	($345.25)	$2,307.19	$1,255.10
Computer Services	80	$7,172.66	$7,664.51	$12,895.07	$7,927.03	$13,115.96
Computers/Peripherals	42	$18,124.95	$106,948.54	$123,564.50	$107,732.42	$105,646.15
Construction Supplies	49	$4,538.96	$14,115.59	$12,082.06	$4,323.04	$10,297.31
Diversified	23	$6,865.35	$4,556.31	$23,473.13	($8,333.02)	($28,355.90)
Drugs (Biotechnology)	598	$17,685.00	$1,336.62	$13,735.23	$6,456.49	$513.27
Drugs (Pharmaceutical)	281	$37,183.45	$72,397.57	$50,169.94	$75,076.60	$72,293.14
Education	33	$90.00	$516.08	$2,104.63	$407.23	($685.19)
Electrical Equipment	110	$2,409.19	$6,991.17	$3,687.43	($116.23)	$10,494.28
Electronics (Consumer & Office)	16	$0.00	$39.39	$230.06	($353.91)	($344.21)
Electronics (General)	138	$916.43	$8,638.31	$4,921.24	$486.37	$7,877.66
Engineering/Construction	43	$432.10	$2,558.96	$2,727.69	($1,888.01)	$3,697.80
Entertainment	110	$959.84	$1,903.67	$2,560.07	$5,417.98	($1,283.68)
Environmental & Waste Services	62	$2,146.70	$4,640.61	$3,975.31	$3,314.61	$8,304.54
Farming/Agriculture	39	$3,015.71	$14,341.24	$8,068.02	($4,214.13)	$4,957.79
Financial Svcs. (Non-bank & Insurance)	223	$13,017.30	$95,373.69	$60,726.69	$86,528.70	($162,222.92)
Food Processing	92	$10,574.62	$19,663.08	$15,571.88	$11,098.26	$9,624.51
Food Wholesalers	14	$1,021.60	$2,343.41	$1,699.52	($1,201.28)	($540.28)
Furn/Home Furnishings	32	$796.43	$1,170.87	$3,857.91	($1,718.25)	$507.55
Green & Renewable Energy	19	$657.02	$1,155.76	$196.87	($392.33)	$2,042.75
Healthcare Products	254	$6,570.31	$14,242.60	$14,559.38	$8,342.26	$21,726.15
Healthcare Support Services	131	$13,557.74	$41,031.69	$44,679.36	$39,997.55	$35,170.62
Heathcare Information and Technology	138	$1,581.92	($529.78)	$8,491.10	($3,101.06)	$4,235.22
Homebuilding	32	$1,361.39	$24,986.04	$7,894.75	$9,262.75	$10,501.21
Hospitals/Healthcare Facilities	34	$949.00	$6,999.96	$9,476.79	$2,703.89	$9,327.11
Hotel/Gaming	69	$793.83	$1,606.13	$15,579.42	$4,108.84	$1,538.00
Household Products	127	$14,431.34	$22,657.09	$19,606.34	$17,895.42	$24,106.84
Information Services	73	$10,475.09	$37,313.93	$46,377.01	$41,679.42	$56,500.60
Insurance (General)	21	$3,403.41	$20,197.72	$13,417.34	$11,622.09	$16,243.71
Insurance (Life)	27	$5,853.45	$15,306.23	$18,439.95	$15,021.27	$10,250.87
Insurance (Prop/Cas.)	51	$7,922.51	$10,805.47	$16,179.26	$7,392.63	$8,226.39
Investments & Asset Management	600	$15,100.19	$35,375.45	($17,337.91)	$32,624.12	$62,520.16
Machinery	116	$5,613.08	$15,291.50	$13,889.15	$8,070.20	$26,845.63
Metals & Mining	68	$4,009.40	$6,414.92	$6,402.72	$3,994.43	$5,889.08
Office Equipment & Services	16	$392.50	$473.13	$576.86	($167.91)	$929.15
Oil/Gas (Integrated)	4	$26,119.36	$99,099.30	$40,345.10	$111,781.80	$75,992.90
Oil/Gas (Production and Exploration)	174	$20,127.07	$86,953.77	$41,719.95	$59,398.57	$46,696.46
Oil/Gas Distribution	23	$8,450.90	$2,683.10	$9,512.83	($192.46)	$1,748.88
Oilfield Svcs/Equip.	101	$7,323.11	$41,659.69	$25,266.85	$34,325.07	$24,456.82
Packaging & Container	25	$2,718.41	$9,491.27	$8,916.47	$2,669.65	$2,600.74
Paper/Forest Products	7	$99.00	$1,255.70	$1,313.61	$921.51	$905.06
Power	48	$21,251.45	$35,093.37	$13,635.40	($35,714.94)	$17,634.52
Precious Metals	74	$1,943.35	$1,211.84	$1,658.21	$243.93	$1,104.43
Publishing & Newspapers	20	$407.90	$778.84	$989.17	$715.58	$1,365.97
R.E.I.T.	223	$51,601.83	$47,868.79	$1,818.52	$88,400.76	$150,282.44
Real Estate (Development)	18	$0.00	$538.86	$469.87	$787.35	$879.40
Real Estate (General/Diversified)	12	$48.10	$144.88	$89.51	$60.37	$160.86
Real Estate (Operations & Services)	60	$229.56	($830.15)	$4,494.01	$2,587.49	$2,975.10
Recreation	57	$1,069.82	$784.68	$1,160.86	($4,087.93)	($1,988.65)
Reinsurance	1	$201.00	$575.00	$306.00	$533.30	$1,264.30
Restaurant/Dining	70	$8,430.28	$13,628.14	$20,501.45	$10,248.10	$15,970.87
Retail (Automotive)	30	$738.77	$11,025.24	$12,507.54	$7,563.78	$22,789.96
Retail (Building Supply)	15	$10,186.13	$24,750.59	$37,174.05	$12,747.23	$25,674.25
Retail (Distributors)	69	$3,130.07	$14,460.39	$8,006.13	($3,931.77)	$3,217.19
Retail (General)	15	$10,568.63	$26,032.60	$33,456.72	($5,214.18)	$12,954.65
Retail (Grocery and Food)	13	$1,013.25	$5,113.51	$2,585.48	$2,892.69	$1,299.14
Retail (Online)	63	$513.40	$3,688.55	$12,759.24	($51,160.77)	($39,972.87)
Retail (Special Lines)	78	$5,685.91	$17,547.91	$22,107.18	$3,438.49	$8,185.60
Rubber& Tires	3	$0.00	$864.12	($1.46)	($352.39)	$295.70
Semiconductor	68	$23,911.23	$72,801.99	$62,269.76	$36,738.16	$41,487.00
Semiconductor Equip	30	$2,591.80	$18,191.87	$16,041.22	$8,840.69	$20,856.58
Shipbuilding & Marine	8	$256.30	$2,071.70	$629.34	$2,064.45	$1,634.49
Shoe	13	$2,072.05	$7,698.70	$1,090.41	$6,060.83	$8,598.47
Software (Entertainment)	91	$60.03	$91,628.19	$103,663.72	$56,468.04	$67,774.87
Software (Internet)	33	$0.34	($5,178.90)	$3,398.96	($7,707.22)	($6,077.91)
Software (System & Application)	390	$24,238.73	$71,266.94	$64,479.06	$48,833.83	$71,160.04
Steel	28	$1,342.77	$25,593.54	$9,591.24	$18,329.90	$16,980.17
Telecom (Wireless)	16	$145.71	$2,321.21	$1,011.06	($3,333.42)	($1,972.90)
Telecom. Equipment	79	$7,183.58	$14,067.43	$19,482.92	$9,251.85	$11,450.13
Telecom. Services	49	$21,546.93	$41,509.34	$13,044.09	$38,803.38	($4,787.07)
Tobacco	15	$14,569.30	$13,594.15	$17,637.73	$12,523.43	$11,467.92
Transportation	18	$6,209.10	$18,562.94	$13,749.07	$10,682.41	$10,330.74
Transportation (Railroads)	4	$5,115.98	$14,258.80	$19,545.00	$11,470.98	$18,925.38
Trucking	35	$729.19	$2,048.54	$9,226.79	($11,721.86)	($3,931.09)
Utility (General)	15	$9,711.00	$16,381.30	$8,442.10	($12,850.02)	($2,207.72)
Utility (Water)	16	$937.33	$2,065.11	$677.24	($1,100.09)	$656.97
Total Market	7165	$636,300.29	$1,834,489.12	$1,464,406.32	$1,330,007.52	$1,727,349.81
Total Market (without financials)	5649	$531,213.34	$1,448,837.76	$1,275,825.16	$876,682.75	$1,147,513.33

Note: Dividends and Free Cash Flows to Equity, i.e., cash flows left over after taxes, reinvestment needs and debt payments (FCFE), by industry

https://pages.stern.nyu.edu/~adamodar/

FYI: Market Value Added (MVA)

By JAMES CHEN Updated May 26, 2021, Reviewed by DAVID KINDNESS, Fact checked by HANS DANIEL JASPERSON

https://www.investopedia.com/terms/m/mva.asp#:~:text=Market%20value%20added%20(MVA)%20is,claims%20held%20against%20the%20company.

What Is Market Value Added?

Market value added (MVA) is a calculation that shows the difference between the market value of a company and the capital contributed by all investors, both bondholders and shareholders. In other words, it is the market value of debt and equity minus all capital claims held against the company. It is calculated as:

MVA = V - K

where MVA is the market value added of the firm, V is the market value of the firm, including the value of the firm's equity and debt (its enterprise value), and K is the total amount of capital invested in the firm.

MVA is closely related to the concept of economic value added (EVA), representing the net present value (NPV) of a series of EVA values.

Understanding Market Value Added (MVA)

When investors want to look under the hood to see how a company performs for its shareholders, they first look at MVA. A company’s MVA is an indication of its capacity to increase shareholder value over time. A high MVA is evidence of effective management and strong operational capabilities. A low MVA can mean the value of management’s actions and investments is less than the value of the capital contributed by shareholders. A negative MVA means the management's actions and investments have diminished and reversed the value of capital contributed by shareholders.

FYI: Economic Value Added (EVA)

By JAMES CHEN Updated March 22, 2022, Reviewed by JANET BERRY-JOHNSON, Fact checked by KIRSTEN ROHRS SCHMITT

https://www.investopedia.com/terms/e/eva.asp

What Is Economic Value Added (EVA)?

Economic value added (EVA) is a measure of a company's financial performance based on the residual wealth calculated by deducting its cost of capital from its operating profit, adjusted for taxes on a cash basis. EVA can also be referred to as economic profit, as it attempts to capture the true economic profit of a company. This measure was devised by management consulting firm Stern Value Management, originally incorporated as Stern Stewart & Co.

Understanding Economic Value Added (EVA)

EVA is the incremental difference in the rate of return (RoR) over a company's cost of capital. Essentially, it is used to measure the value a company generates from funds invested in it. If a company's EVA is negative, it means the company is not generating value from the funds invested into the business. Conversely, a positive EVA shows a company is producing value from the funds invested in it.

The formula for calculating EVA is:

EVA = NOPAT - (Invested Capital * WACC)

Where:

NOPAT = Net operating profit after taxes

Invested capital = Debt + capital leases + shareholders' equity

WACC = Weighted average cost of capital2

Chapter 12: Cash Flow Estimation (2^nd step of DCF)

ppt

Chapter 12 case study (due with final. Monte Carol is not required. FYI only)

Case Video in Class

Monte Carlo Demonstration Based on Case in Class (FYI, Video)

Critical thinking challenge (due with final, optional for extra credits):

· Recalculate 100 times of the NPV based on the Monte Carlo simulation method by randomly changing the tax rate and the WACC

· Report statistical results: Mean, Standard Deviation, Min, Max of the NPV.

· Report the Histogram of the NPV, or the probability distribution of the NPV, such as the following:

Monte Carlo Simulation Demonstration (FYI)

Using Microsoft Excel to generate random normal numbers (FYI)

Introduction to Monte Carlo Simulation in Excel 2016 (FYI)

Structure or template:

Years

Investment Outlay

Equipment cost

$(----------)

Installation

(--------)

Increase in inventory

(-------)

Increase in A/P

-------

Initial net investment

$(-------)

Operating Cash Flows

Units sales

-------

Price per unit

* $ ---

$ ---

Total revenues

-------

Operating costs (w/o deprn)

-------

Depreciation

-------

Total costs

-------

Operating income

-------

Taxes on operating income

-------

A-T operating income

-------

Depreciation

-------

Operating cash flow

-------

Terminal Year Cash Flows

Recovery of net working capital -------

Salvage value

-------

Tax on salvage value

(-------)

Total termination cash flow

-------

Project Cash Flows

Net cash flows

$(-------)

$ -------

In class exercise (self-study)

1. What is the project's Year 1 cash flow?

Sales revenues $22,250

Depreciation $8,000

Other operating costs $12,000

Tax rate 35.0%

Answer:

Sales revenues $22,250

− Operating costs (excl. deprec.) 12,000

− Depreciation 8,000

Operating income (EBIT) $ 2,250

− Taxes Rate = 35% 788

After-tax EBIT $ 1,463

+ Depreciation 8,000

Cash flow, Year 1 $ 9,463

2. The required equipment has a 3-year tax life, and it will be depreciated by the straight-line method over 3 years. What is the project's Year 1 cash flow?

Equipment cost (depreciable basis) $65,000

Straight-line depreciation rate 33.333%

Sales revenues, each year $60,000

Operating costs (excl. deprec.) $25,000

Tax rate 35.0%

Answer:

Equipment life, years 3

Equipment cost $65,000

Depreciation: rate = 33.333% $21,667

Sales revenues $60,000

− Basis x rate = depreciation 21,667

− Operating costs (excl. deprec.) 25,000

Operating income (EBIT) $13,333

− Taxes Rate = 35.0% 4,667

After-tax EBIT $ 8,667

+ Depreciation 21,667

Cash flow, Year 1 $30,333

3. The equipment that would be used has a 3-year tax life, and the allowed depreciation rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10-year expected life. What is the Year 1 cash flow?

Equipment cost (depreciable basis) $65,000

Sales revenues, each year $60,000

Operating costs (excl. deprec.) $25,000

Tax rate 35.0%

Answer:

Equipment cost $65,000

Depreciation rate 33.0%

Sales revenues $60,000

− Operating costs (excl. deprec.) 25,000

− Depreciation 21,450

Operating income (EBIT) $13,550

− Taxes Rate = 35% 4,743

After-tax EBIT $ 8,808

+ Depreciation 21,450

Cash flow, Year 1 $30,258

4. The equipment that would be used has a 3-year tax life, would be depreciated by the straight-line method over its 3-year life, and would have a zero salvage value. No new working capital would be required. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's NPV?

Risk-adjusted WACC 10.0%

Net investment cost (depreciable basis) $65,000

Straight-line deprec. rate 33.3333%

Sales revenues, each year $65,500

Operating costs (excl. deprec.), each year $25,000

Tax rate 35.0%

Answer:

WACC 10.0% Years 0 1 2 3

Investment cost -$65,000

Sales revenues $65,500 $65,500 $65,500

− Operating costs (excl. deprec.) 25,000 25,000 25,000

− Depreciation rate = 33.333% 21,667 21,667 21,667

Operating income (EBIT) $18,833 $18,833 $18,833

− Taxes Rate = 35% 6,592 6,592 6,592

After-tax EBIT $12,242 $12,242 $12,242

+ Depreciation 21,667 21,667 21,667

Cash flow -$65,000 $33,908 $33,908 $33,908

NPV $19,325

5. The equipment originally cost $22,500, of which 75% has been depreciated. The firm can sell the used equipment today for $6,000, and its tax rate is 40%. What is the equipment’s after-tax salvage value for use in a capital budgeting analysis? Note that if the equipment's final market value is less than its book value, the firm will receive a tax credit as a result of the sale.

Answer:

% depreciated on equip. 75%

Tax rate 40%

Equipment cost $22,500

− Accumulated deprec. 16,875

Current book value of equipment $ 5,625

Market value of equipment 6,000

Gain (or loss): Market value − Book value $ 375

Taxes paid on gain (−) or credited (+) on loss -150

AT salvage value = market value +/− taxes $ 5,850

FYI: Analyzing Business Performance through Monte Carlo Sensitivity Analysis – ChatGPT

Introduction to Monte Carlo Simulation in Excel 2016 (FYI, Video)

Let's consider an example of a coffee shop that sells coffee and baked goods. The coffee shop has historical data for the past year, which shows that the average daily revenue is $1000 with a standard deviation of $100, and the average daily cost is $600 with a standard deviation of $50.

To use Monte Carlo simulation to simulate the profits, we can follow the following steps:

Determine the distribution of the revenue and costs data:

Based on the historical data, we can assume that revenue and costs follow a normal distribution. We can estimate the distribution parameters (mean and standard deviation) for each variable as follows:

Revenue: Mean = $1000, Standard Deviation = $100

Costs: Mean = $600, Standard Deviation = $50

Generate random values for revenue and costs based on their respective distributions:

We can use a Monte Carlo simulation software like Excel or Python to generate random values. Let's say we want to simulate 1000 days of operation for the coffee shop. We can use the following formulas in Excel to generate random values for revenue and costs:

Revenue: =NORM.INV(RAND(), 1000, 100)

Costs: =NORM.INV(RAND(), 600, 50)

We can copy these formulas down for 1000 rows to generate 1000 random values for revenue and costs.

Calculate the profit for each set of random values:

We can use the following formula in Excel to calculate the profit for each set of random values:

Profit: = Revenue - Costs

We can copy this formula down for 1000 rows to calculate the profit for each set of random values.

Repeat steps 2 and 3 thousands of times:

We can repeat steps 2 and 3 thousands of times to get a large sample size of profits.

In Excel, we can use the data table feature to simulate profits for thousands of iterations.

We can set up the data table as follows:

Column A: Iteration number (1 to 1000)

Column B: Random revenue (generated using the formula above)

Column C: Random costs (generated using the formula above)

Column D: Profit (calculated using the formula above)

We can then select columns B, C, and D and go to Data > What-If Analysis > Data Table. In the "Column Input Cell" box, we can enter a reference to a cell that contains a random number (e.g., =RAND()). Excel will then simulate profits for thousands of iterations.

Analyze the simulated profit distribution:

We can use the simulation results to analyze the profit distribution. In Excel, we can calculate the mean, standard deviation, and other statistical measures for the profit column. We can also create a histogram or probability density plot to visualize the distribution.

Use the simulation results to make business decisions:

We can use the simulation results to estimate the probability of different profit outcomes.

For example, we can use the following formulas in Excel to estimate the probability of making a profit of at least $500 or at least $600:

Probability of profit >= $500: =1-COUNTIF(D2:D1001,"<500")/1000

Probability of profit >= $600: =1-COUNTIF(D2:D1001,"<600")/1000

Based on the simulation results, we can estimate that the probability of making a profit of at least $500 is around 76%, and the probability of making a profit of at least $600 is around 50%. We can use these probabilities to make decisions such as setting pricing strategies, reducing costs, or investing in new products or services.

Overall, Monte Carlo simulation is a powerful tool for analyzing uncertainty and risk in business operations. By simulating different scenarios, we can estimate the probability of different outcomes and make informed decisions based on the simulation results. However, it's important to note that the accuracy of the simulation depends on the quality of the input data and assumptions made about the distribution of revenue and costs. Therefore, it's important to carefully analyze the input data and assumptions to ensure that the simulation results are reliable. However, the accuracy of the simulation depends on the quality of the input data and assumptions made about the distribution of revenue and costs. It's crucial to carefully analyze the input data and assumptions to ensure that the simulation results are reliable. Monte Carlo simulation is not a crystal ball and cannot predict future outcomes with certainty, but it can help businesses analyze uncertainty and risk.

Chapter 19 Derivatives

Chapter 19 PPT

Chapter 19 Case Study Part I - due with final

Chapter 19 Case Study part II – due with final

Case video in class Part I (4.10.2023)

Case video in class part II (4.12.2023)

Case video in class ----- Part I Part II

1^st, understand what is call and put option

2^nd, understand the pay off of call and put option

3^rd, can draw payoff profile of call and put option

Call and Put Option Calculator

www.jufinance.com/option

Call and Put Option Diagram Illustration Excel

(Thanks to Dr. Greence at UAH)

4^th, can calculate call option pricing using binomial model

Binomial Calculator by ChatGPT

Instruction on Binomial model - in class exercise - case study

· In the first step, you are calculating the range of values at expiration by considering the two possible ending stock prices of $30 and $50. You then calculate the ending option and portfolio values for each of these stock prices.

· Next, in step 2, you are equalizing the range of payoffs for the stock and the option by buying 0.75 shares and selling 1 option. This allows you to create a riskless hedged investment in step 3, where you calculate the ending values of the portfolio for the two possible ending stock prices.

· Finally, in step 4, you are pricing the call option by calculating the present value of the portfolio using the risk-free rate of 8%. The calculated present value of the portfolio is $20.83, which can be used to calculate the call option value.

^5th, can calculate call option price using black-scholes model

Black-Scholes Option Calculator

https://www.mystockoptions.com/black-scholes.cfm

Black Scholes Option Calculator (at jufinance.com)

www.jufinance.com/https://www.jufinance.com/option_chatgpt/

Black-Scholes Model Illustration Excel

(Thanks to Dr. Greence at UAH)

Binomial Tree (FYI)

A binomial tree is a representation of the intrinsic values an option may take at different time periods. The value of the option at any node depends on the probability that the price of the underlying asset will either decrease or increase at any given node.

https://www.investopedia.com/terms/b/binomial_tree.asp#:~:text=A%20binomial%20tree%20is%20a%20representation%20of%20the%20intrinsic%20values,increase%20at%20any%20given%20node.

Black-Scholes model (reference only)

Puts and Calls - How to Make Money When Stocks are Going Up or Down (FYI)

https://www.youtube.com/watch?v=D9-_Jar2UpQ

Call Options Trading for Beginners in 9 min. - Put and Call Options Explained (FYI)

https://www.youtube.com/watch?v=q_z1Zx_BALo

Binomial Option Pricing Model Explained ----

using In Class Case Study as an example (FYI only)

The binomial option pricing model is a mathematical formula that allows us to calculate the fair value of an option by modeling the possible future prices of the underlying asset, and calculating the probability of each price occurring.

The model works by creating a binomial tree that represents the possible future prices of the asset, and then working backward through the tree to calculate the expected value of the option at each node.

Here are the steps to use the binomial option pricing model:

Step 1: Determine the Inputs

The first step is to gather the inputs needed for the model. These include:

· The current price of the underlying asset

· The range of possible future prices of the asset

· The exercise price of the option

· The risk-free rate of interest

· The time until expiration of the option

Let’s try to work on the same question as we did in class. A stock that is currently trading at $40, and two possible future prices at the end of one year are: $30 and $50. The exercise price of the option is $35, the risk-free rate is 8%, and the time until expiration is one year --- our case study example

Step 2: Calculate the Up and Down Factors

The next step is to calculate the up and down factors, which represent the expected percentage increase and decrease in the stock price over one period. These factors are calculated as:

· Up factor (u) = Future price if stock goes up / Current stock price

· Down factor (d) = Future price if stock goes down / Current stock price

In our example, the up factor is $50 / $40 = 1.25, and the down factor is $30 / $40 = 0.75.

Step 3: Create the Binomial Tree

This step involves creating the binomial tree as below.

Binomial Tree

$40

/ \

$50 $30

Step 4: Calculate the Risk-Neutral Probability

The next step is to calculate the probability of each future price occurring, using the risk-neutral probability. The risk-neutral probability is the probability of the stock going up or down, assuming that the market is risk-neutral and the expected return of the stock is equal to the risk-free rate.

The risk-neutral probability is calculated as:

Risk-neutral probability (p) = (1+r-d)/(u-d)

where r is the risk-free rate and t is the time until expiration.

In our example, the risk-neutral probability is approximately:

Pu = (1+0.08-0.75)/(1.25-0.75)= 0.66

Or use the more accurate model:

Risk-neutral probability Pu = (e^((r * t)/n) - d) / (u - d)

where r is the risk-free rate and t is the time until expiration, and n is the height of the binomial tree. In our example, n=1.

In our example, the risk-neutral probability is:

Pu = (e^(0.08 * 1) - 0.75) / (1.25 - 0.75) = 0.6666

Step 5: Calculate the Option Value at Each Node of the Tree

To get the value of the option at each node of the tree, we should work backward from the end of the tree to the current price of the stock.

Simply speaking, at the end of the tree, the option value = difference between the stock price and the exercise price, or zero if the stock price is below the exercise price.

For example, we need to calculate the value of the option if the stock price goes up to $50, and if it goes down to $30. The results are as follows.

Vu = Max($50 - $35, 0) = $15

Vd = $0

Working backward up the tree, we can calculate the option value at each node as the discounted expected value of the option at the next period:

Option value = v = (Pu * Vu + Pd * Vd) / (1 + r)^t;

Option Value at $40 = (0.66 x $15 + (1 - 0.66) x $0) / (1 + 0.08)^1 = $9.17

Therefore, the value of the option is approximately $9.17 if the stock price is $40.

Black-Scholes Option Pricing Model Explained ----

using In Class Case Study as an example (FYI only)

C = SN(d1) – X*exp(-r*t)*N(d2)

where:

· S = the current stock price

· X = the option strike price

· r = the risk-free interest rate

· t = time until expiration, expressed as a fraction of a year

V =	P[ N (d₁) ] − Xe^{-rRF t} [ N (d₂) ]
d₁ =	{ ln (P/X) + [r_RF + s² /2) ] t } / s (t^1/2)
d₂ =	d₁ − s (t ^{1 / 2})

d1 = [ln(S/X) + (r + σ^2/2)t] / [σsqrt(t)]

d2 = d1 - σ*sqrt(t)

σ = the annualized standard deviation of stock returns

Using the values used in the case study in class:

· S = X = 21

· r = 0.05

· σ = 0.3

· t = 0.36

First, we calculate d1 and d2:

d1 = ln(21/21)+(0.05+0.3^2/2)*0.36)/(0.3*sqrt(0.36)) =0.19

d2 = 0.19 - 0.3*sqrt(0.36) = 0.01

Next, we calculate the call option price using the Black-Scholes formula:

C = SN(d1) – X*exp(-r*t)*N(d2)

C = 21*normdist(0.19, 0, 1, true) - 21*exp(-0.05*0.36)*normdist(0.01, 0, 1, true) = 1.687 (rounded to three decimal places)

Therefore, the expected result for the call option price using the Black-Scholes formula with the given inputs is approximately 1.687.

By the way, based on Put - Call Parity, the put option price (P) is the following:

P = C - S + Xe^(-rt)

= 1.687 - 21 + 21*exp(-0.05*0.36) = 1.3124

FYI – normdist function in Excel

The normdist function is used in Excel to calculate the probability density function of a normally distributed random variable. This function takes four arguments: x, mean, standard_dev, and cumulative.

Here is a brief explanation of each argument:

· x: This is the value for which you want to calculate the probability density function. It must be a numeric value.

· mean: This is the mean of the distribution. It must be a numeric value.

· standard_dev: This is the standard deviation of the distribution. It must be a numeric value.

· cumulative: This is an optional argument that specifies whether you want to calculate the cumulative distribution function or the probability density function. If this argument is omitted or set to TRUE, the function will calculate the cumulative distribution function. If it is set to FALSE, the function will calculate the probability density function.

To use the normdist function in Excel, follow these steps:

· In a cell, type =NORMDIST(x, mean, standard_dev, cumulative) and replace the values of x, mean, standard_dev, and cumulative with the values you want to use.

· Press Enter. Excel will calculate the probability density function or the cumulative distribution function of the normally distributed random variable, depending on the value of the cumulative argument.

For example,

1) if you want to calculate the probability density function of a normally distributed random variable with a mean of 10 and a standard deviation of 2 at the value of 12, use the following: =NORMDIST(12, 10, 2, FALSE) = probability density at that point.

2) =NORMDIST(12, 10, 2, true) calculates the cumulative distribution function (CDF) of a normally distributed random variable with a mean of 10 and a standard deviation of 2, evaluated at the value of 12.

· The true value of the fourth argument - calculate the CDF.

Chapter 15 Distributions to Shareholders

· This chapter will not be covered in the final exam

Ppt

Theory one: Indifference theory

Do Dividends even matter? - Dividend Irrelevance theory (video)

n Assuming:

– No transactions costs to buy and sell securities

– No flotation costs on new issues

– No taxes

– Perfect information

– Dividend policy does not affect k_e

n Dividend policy is irrelevant. If dividends are too high, investors may use some of the funds to buy more of the firm’s stock. If dividends are too low, investors may sell off some of the stock to generate additional funds.

Theory two: bird in hand theory – High dividend can increase firm value

Warren Buffett and the first investment primer: a bird in the hand equals two in the bush (Aesop) (video)

Dividends are less risky. Therefore, high dividend payout ratios will lower k_e (reducing the cost of capital), and increase stock price

Theory three: Tax effect theory – Low dividend can increase firm value

Dividend Clienteles | Business Finance (FINC101)

1) Dividends received are taxable in the current period. Taxes on capital gains, however, are deferred into the future when the stock is actually sold.

2) The maximum tax rate on capital gains is usually lower than the tax rate on ordinary income. Therefore, low dividend payout ratios will lower k_e (reducing the cost of capital), raise g, and increase stock price.

Which theory is most correct? – again, results are mixed.

1) Some research suggests that high payout companies have high required return on stock, supporting the tax effect hypothesis.

2) But other research using an international sample shows that in countries with poor investor protection (where agency costs are most severe), high payout companies are valued more highly than low payout companies.

Stock Repurchase: Buying own stock back from stockholders.

Reasons for repurchases:

· As an alternative to distributing cash as dividends.

· To dispose of one-time cash from an asset sale.

· To make a large capital structure change.

· May be viewed as a negative signal (firm has poor investment opportunities).

· IRS could impose penalties if repurchases were primarily to avoid taxes on dividends.

· Selling stockholders may not be well informed, hence be treated unfairly.

· Firm may have to bid up price to complete purchase, thus paying too much for its own stock.

Stock Split: Firm increases the number of shares outstanding, say 2:1. Sends shareholders more shares.

Reasons for stock split:

· There’s a widespread belief that the optimal price range for stocks is $20 to $80.

· Stock splits can be used to keep the price in the optimal range.

· Stock splits generally occur when management is confident, so are interpreted as positive signals.

Chapter 21 Mergers and Divestitures

· This chapter will not be covered in the final exam

· watch TV series Succession and gain insights of the dynamics of such corporate fights

ppt

Mergers rules of SEC

Mergers are business combination transactions involving the combination of two or more companies into a single entity. Most state laws require that mergers be approved by at least a majority of a company's shareholders if the merger will have a significant impact on either the acquiring or target company.

If the company you've invested in is involved in a merger and is subject to the SEC disclosure rules, you will receive information about the merger in the form of either a proxy statement on Schedule 14A or an information statement on Schedule 14C.

The proxy or information statement will describe the terms of the merger, including what you will receive if the merger proceeds. If you believe the amount you will receive is not fair, check the statement for information on appraisal or dissenter's rights under state law. You must follow the procedures precisely or your rights may be lost.

You can obtain a copy of a company's proxy or information statement by using the SEC's EDGAR database.

Summary of key M&A documents for finding deal terms of public targets

(www.wsp.com)

Acquisition type	Document	Date filed	Best place to find it
Mergers	Press release	Announcement date	1. Target (likely also acquirer) will file SEC form 8K (could be in an 8K exhibit)
Mergers	Press release	Announcement date	2. Target (likely also acquirer) website
Mergers	Definitive agreement	Announcement date	1. Target 8K (often the same 8K that contains press release)
Mergers	Merger proxy	Several weeks after the announcement date	1. Target PREM14A and DEFM14A
Tender/exchange offers	Tender offer (or exchange offer)	Upon initiation of tender offer	1. Target Schedule TO (attached as exhibit)
Tender/exchange offers	Tender offer (or exchange offer)	Upon initiation of tender offer
Tender/exchange offers	Schedule 14D-9	Within 10 days of filing of Schedule TO	1. Target Schedule 14D-9
Mergers and exchange offers	Registration statement/prospectus	Several weeks after the announcement date	1. Acquirer Form S-4

******* Whole Foods SEC Filing (FYI)********

Whole foods form 8k filed with SEC on 8/23/2017

“As a result of the Merger, each share of common stock……was converted into the right to receive $42.00 in cash, without interest (the “Merger Consideration”).”

Whole Foods DEFA 14A 8k form with SEC 6/14/2017

Whole foods DEFA 14A 8k form with SEC 6/16/2017

Whole foods is providing materials for the upcoming shareholder voting.

Whole foods DEFA 14A 8k with SEC 7/21/2017

Has law suit documents

Whole foods DEFA 14A 8k with SEC 7/21/2017

Notifying shareholders for upcoming special shareholder meeting

********* Amazon SEC filing *********

Amazon Form 8k with SEC on 6/15/2017

Financing of the Merger

The Company expects to finance the Merger with debt financing ……

Amazon Whole Foods Merger Agreement on 6/15/2017

For the term project, if you work on this M&A case, you should be able to find most of the information in this agreement.

Amazon 8k form Completion of acquisition or disposition of assets 8/28/2018

********** Miscellaneous **********

7 potential bidders, a call to Amazon, and an ultimatum: How the Whole Foods deal went down (from business insider.com)

********** SDC Amazon Whole Foods Deal Record (For this class only)*****

Tear Sheet (SDC) (on blackboard)

Why does Amazon's Bezos want Whole Foods? (video)

Mergers and Acquisitions Explained: A Crash Course on M&A (youtube, FYI)

Elon Musk vs. Twitter: Inside the 6-Month Battle | Timeline | WSJ (youtube, FYI)

For discussion:

· Why does Amazon want to buy Whole Foods?

· Did Whole Foods want to be acquired? What can Whole Foods do to defend itself? (poison pill, white knight, classified board, golden parachute, etc.)

· What can Amazon do to persuade Whole Foods shareholders to sell their stocks?

· Why does Elon Musk want to acquire Twitter?

· Did Twitter want to be acquired? What can Twitter do to defend itself? (poison pill, white knight, classified board, golden parachute, etc.)

Twitter Serves Elon Musk a POISON PILL - What It Is and How It Works (youtube, FYI)

For your knowledge (FYI):

· In reality, dividends are more predictable than earnings .

· You own around 100 shares of the stock of AAA, which is currently being sold for around $120 per share. A 2-for-1 stock split is about to be declared by the company. After the split has taken place, which of the following describes your probable position? You own 200 shares of AAA’s stock. Meanwhile, the AAA stock price will be near $60 per share.

· Alice Gordan and Alex Roy believe that when the dividend payout ratio is lowered, the required return on equity tends to increase. On which of the following assumptions is their argument based? dividends are viewed as less risky than future capital gains.

· A strict residual dividend policy is followed by your firm. Everything remains constant, which of the factors mentioned below are most probably going to result in an increase in the dividend per share of a firm? when a company’s profit (net income) rises

· Horizontal merger would be an example of The Home Depot and Lowe’s getting merged.

· When the merger of two companies in a similar industry takes place in order to develop products that are needed at various stages of the production cycle, it is referred to as: integration vertically

· A rights offering that provides the existing target shareholders with the rights to purchase shares in the acquirer of the target at an extremely discounted price after particular conditions are met is referred to as a: poison pill

(Twitter POISON Pill Explained by a Lawyer (youtube), FYI)

· A scenario where each and every director gets a three-year term to provide their services and the terms are arranged in a staggered manner so that just one-third of the directors are eligible for the election every year is referred to as a: classified board

· In a situation where it becomes inevitable that a hostile takeover may take place, and a target company may at times search for another friendlier company in order to acquire it, is referred to as a: white knight

Can Twitter find a white knight to fend off Elon Musk? (youtube)

· When a firm is being taken over and the senior managers of that firm are let go, a very lucrative severance package is offered to those senior managers. It is referred to as a: golden parachute

Final Exam (during final week, in class, non-cumulative, similar to case study)

4/24 Monday, Room 288, 11:30 - 2 PM (with SPO301 students)
4/26 Wednesday, our classroom, 3-5:30 PM (with FIN415 class)
You may also arrange to meet and take the final exam at a different time by appointment

Finance Exit Exam (with final, in class, close book close notes, 40 multiple choice questions)

__ _ _ __ __ _ __| |_ _ __ _| |_(_) ___ _ __

/ _` | '__/ _` |/ _` | | | |/ _` | __| |/ _ \| '_ \

| (_| | | | (_| | (_| | |_| | (_| | |_| | (_) | | | |

\__, |_| \__,_|\__,_|\__,_|\__,_|\__|_|\___/|_| |_|

|___/

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║╚╣╬║║║║╬║╔╣╬╚╣╔╣║║╚╣╬╚╣╔╣║╬║║║║
╚═╩═╩╩═╬╗╠╝╚══╩═╩═╩═╩══╩═╩╩═╩╩═╝
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How To Win The MarketWatch Stock Market Game (youtube, FYI)

How Short Selling Works (Short Selling for Beginners) (youtube, FYI)

Who Determines Interest Rates?

Short-Term Interest Rates: Central Banks

Long-Term Interest Rates: Demand for Treasury Notes

Other Rates: Retail Banks

Gerald Celente: Low Interest Rates are Building the Biggest Bubble in Modern History - 9/21/14

What Is the Relationship Between Inflation and Interest Rates?

By JEAN FOLGER Updated Dec 6, 2019

The Inverse Correlation Between Interest Rates and Inflation

Quantity Theory of Money

Interest Rates, Savings, Loans, and Inflation

The Federal Open Market Committee

What Is Expectations Theory (video)

Understanding Expectations Theory

Expectations Theory

Example of Calculating Expectations Theory

Disadvantages of Expectations Theory

Computing Duration Excel (video, FYI)

How "Convexity" Impacts Bond Yields (youtube)

Despite record profits in 2021, many corporations are paying barely any taxes

· What Is the Capital Asset Pricing Model?

What Is the Capital Asset Pricing Model?

The Importance of Diversification

Understanding Diversification in Stock Trading to Avoid Losses

How to Build a Portfolio | by Wall Street Survivor

WMT Dividend History

Deriving the Gordon Growth Model Equation

Stock Splits

How much does Amazon worth?” --- FYI only: Amazon.com Inc. (AMZN)

Present Value of Free Cash Flow to the Firm (FCFF)

Intrinsic Stock Value (Valuation Summary)

Weighted Average Cost of Capital (WACC)

FCFF Growth Rate (g)

FCFF growth rate (g) implied by PRAT model

FCFF growth rate (g) forecast

Using Microsoft Excel to generate random normal numbers (FYI)

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