FIN435 Class Web Page, Spring '24

Jacksonville University

Instructor: Maggie Foley

Exit Exam Questions (will be posted in week 10 on blackboard)

Term Project (on efficient frontier, updated, due with final)

Weekly SCHEDULE, LINKS, FILES and Questions

Week

Coverage, HW, Supplements

- Required

Reading Materials

Week

Marketwatch Stock Trading Game (Pass code: havefun)

Risk Tolerance Test https://jufinance.com/risk_tolerance.html

Use the information and directions below to join the game.

1. URL for your game:
https://www.marketwatch.com/game/jufin435-24s

2. Password for this private game: havefun.

3. Click on the 'Join Now' button to get started.

4. If you are an existing MarketWatch member, login. If you are a new user, follow the link for a Free account - it's easy!

5. Follow the instructions and start trading!

6. Game will be over on 4/22/2022

How to Use Finviz Stock Screener (youtube, FYI)

How To Win The MarketWatch Stock Market Game (youtube, FYI)

How Short Selling Works (Short Selling for Beginners) (youtube, FYI)

Chapter 6 Interest rate

Chapter summary

1) Shape of Yield Curve

i) Inverted Yield Curve Indicates Recession: The shape of the yield curve, particularly when inverted, serves as a significant indicator of an impending recession.

2) Expectation Theory

3) Interest Rate Breakdown

i) Breaking down interest rates involves considering various components:

Real Interest Rate

Inflation Premium:

Default Premium:

Liquidity Premium:

Maturity Premium:

For class discussion:

Interest Rate Volatility:

· What factors could explain the recent spike in interest rates compared to a year ago?

Economic Conditions and Rates:

· How do economic indicators like inflation, unemployment, and GDP growth contribute to the determination of interest rates?

Central Banks' Role:

· What role do central banks play in setting and adjusting interest rates, and how does their decision-making impact the economy?

Global Economic Influence:

· How do international economic conditions and events contribute to fluctuations in domestic interest rates?

Impact on Borrowers and Savers:

· Discuss the effects of high interest rates on borrowers and savers, both at the individual and business levels.

Investor Behavior:

· How does investor behavior respond to changes in interest rates, and what role does sentiment play in influencing rate movements?

Part I: Who determines interest rates in the US?

ppt

Market data website:

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

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

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

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

`The yield curve (Video, Khan academy)`

Daily Treasury Par Yield Curve Rates

https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value=2024

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
01/02/2024	5.55	5.54	5.46	5.41	5.24	4.80	4.33	4.09	3.93	3.95	3.95	4.25	4.08
01/03/2024	5.54	5.54	5.48	5.41	5.25	4.81	4.33	4.07	3.90	3.92	3.91	4.21	4.05
01/04/2024	5.56	5.48	5.48	5.41	5.25	4.85	4.38	4.14	3.97	3.99	3.99	4.30	4.13
01/05/2024	5.54	5.48	5.47	5.41	5.24	4.84	4.40	4.17	4.02	4.04	4.05	4.37	4.21
01/08/2024	5.54	5.48	5.49	5.39	5.24	4.82	4.36	4.11	3.97	3.99	4.01	4.33	4.17
01/09/2024	5.53	5.46	5.47	5.38	5.24	4.82	4.36	4.09	3.97	4.00	4.02	4.33	4.18

In class exercise – based on the above table,

· Draw yield curve on 1/2/2024, and 1/9/2024.

· Why do interest rates change on a daily basis?

1. What is the term structure of interest rates based on the provided yield curve data?

A) Inverted

B) Flat

C) Normal

Answer: A

Explanation: An inverted yield curve often suggests market expectations of economic downturn.

2. Which maturity shows the highest interest rate in the data?

A) 1 month

B) 10 Years

C) 30 Years

Answer: A

Explanation: The yield for the 1-month maturity is 5.5%, the highest among the options.

3. What does a downward-sloping yield curve suggest about market expectations?

A) Economic expansion

B) Economic contraction

C) Stable economic conditions

Answer: B

Explanation: An inverted yield curve often indicates expectations of economic downturn.

4. How does the yield for the 10-year maturity compare to the 1-year maturity on 01/05/2024?

A) Higher

B) Lower

C) Equal

Answer: B

Explanation: The yield for the 10-year maturity (4.05%) is lower than the 1-year maturity (4.84%).

5. Based on the data, what can be inferred about market confidence in the short term?

A) High confidence

B) Low confidence

C) Stable confidence

Answer: B

Explanation: Short-term yields are relatively high, indicating potential uncertainty or risk. Remember: Price and yield tend to move in opposite direction.

6. If the yield for the 3-month maturity decreases significantly, what might this signal about short-term economic expectations?

A) Economic expansion

B) Economic contraction

C) Stable economic conditions

Answer: A

Explanation: A decrease in short-term yields could suggest increased confidence in economic growth.

Treasury Inflation Protected Securities (TIPS)

NAME	COUPON	PRICE	YIELD	1 MONTH	1 YEAR	TIME (EST)
GTII5:GOV 5 Year	2.38	102.79	1.76%	-32	+25	2:46 AM
GTII10:GOV 10 Year	1.38	96.48	1.78%	-21	+40	2:46 AM
GTII20:GOV 20 Year	0.75	80.63	2.03%	-8	+48	2:46 AM
GTII30:GOV 30 Year	1.50	89.28	1.99%	-3	+51	2:46 AM

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

· Expected Inflation=5-year Treasury yield rate − 5-year TIPS rate

In this formula, the 10-year Treasury yield rate is indeed expected to be higher than the 10-year TIPS rate. The rationale is that the nominal Treasury yield includes both the real interest rate and the market's expectation for inflation, while the TIPS rate provides the real interest rate. Therefore, subtracting the TIPS rate from the Treasury yield gives an estimate of the market's expectation for inflation over the specified period.

In Class Exercise:

· What is TIPs?

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.

In class exercise:

1. Who is responsible for determining short-term interest rates in a centralized banking model?

A) Commercial Banks

B) Central Banks

C) Government Agencies

Answer: B

Explanation: In countries with a centralized banking model, short-term interest rates are determined by central banks.

2. What committee in the U.S. is responsible for setting interest rates and monetary policy?

A) Federal Trade Commission (FTC)

B) Federal Reserve Act Committee (FRAC)

C) Federal Open Market Committee (FOMC)

Answer: C

Explanation: The FOMC, consisting of governors of the Federal Reserve Board and Federal Reserve Bank presidents, determines the near-term direction of monetary policy and interest rates in the U.S.

3. How does a central bank decrease the money supply in the economy?

A) Increasing interest rates

B) Lowering interest rates

C) Printing more money

Answer: A

Explanation: Raising interest rates makes it more attractive to deposit funds, reducing borrowing and decreasing the money supply.

4. Which factor primarily influences the yields of 10- or 30-year Treasury notes?

A) Federal Reserve decisions

B) Market demand

C) Commercial bank policies

Answer: B

Explanation: The yields of Treasury notes depend on demand in the market after auctions by the U.S. Treasury Department.

5. What happens to interest rates when there is high demand for Treasury notes?

A) Rates increase

B) Rates decrease

C) Rates remain unchanged

Answer: B

Explanation: High demand for Treasury notes tends to push interest rates down.

6. Who determines interest rates on loans and mortgages offered by retail banks?

A) Government agencies

B) Central banks

C) Retail banks

Answer: C

Explanation: Retail banks control the interest rates on the loans and mortgages they offer.

7. Why might an individual with a lower credit score be charged a higher interest rate?

A) Higher credit risk

B) Lower credit risk

C) Government regulations

Answer: A

Explanation: Individuals with lower credit scores are considered higher risk, leading to higher interest rates.

Part II: Shapes of Yield Curve

For class discussion: What factors contributed to the shifts in yield curve shapes in 2023?

Data:

Date	1 Mo	2 Mo	3 Mo	6 Mo	1 Yr	2 Yr	3 Yr	5 Yr	7 Yr	10 Yr	20 Yr	30 Yr
1/6/2020	1.54	1.54	1.56	1.56	1.54	1.54	1.56	1.61	1.72	1.81	2.13	2.28
1/6/2021	0.09	0.09	0.09	0.09	0.11	0.14	0.2	0.43	0.74	1.04	1.6	1.81
1/6/2022	0.04	0.05	0.1	0.23	0.45	0.88	1.15	1.47	1.66	1.73	2.12	2.09
1/6/2023	4.32	4.55	4.67	4.79	4.71	4.24	3.96	3.69	3.63	3.55	3.84	3.67
1/5/2024	5.54	5.48	5.47	5.24	4.84	4.4	4.17	4.02	4.04	4.05	4.37	4.21

https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value=2023

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)

Understanding the yield curve: Why economists use it to predict recessions

BYTRINA PAUL October 23, 2023 at 1:03 PM EDT

https://fortune.com/recommends/investing/the-inverted-yield-curve-recession/

The inverted yield curve has predicted nearly every recession in the past few decades. It’s been inverted since last year but where’s the recession?

For the past year, you’ve probably heard that a recession is on the horizon. Though economists have been predicting a downturn for months, a recession seems nowhere in sight: the labor market is strong, the stock market is thriving, and inflation has cooled since last year. So, where is the recession, and why do people still think it will happen?

To predict a recession, economists look at certain indicators with a solid track record of signaling a downturn. One of those indicators is the yield curve. And right now, the yield curve is flashing red.

What is the yield curve?

The yield curve is a line that plots yields, or interest rates, of bonds with different maturities and equal credit quality. Though yield curves can be plotted with bonds of any maturity, some of the most common yield curves used are the spreads between either the three-month treasury bill or two-year and ten-year Treasury notes, which are used to indicate the spread between short-term and long-term Treasury securities.

Generally, a yield curve is upward-sloping, with short-term bonds offering lower yields and long-term bonds providing higher yields. In other words, you should be compensated with a higher yield when you tie up your money for longer periods.

Sometimes a yield curve can invert and start sloping downward. When this happens, short-term bonds have higher yields than long-term bonds, and investors are not rewarded for parting with their money for longer periods.

Why is the yield curve used to predict recessions?

When the yield curve inverts, investors expect the Fed to reduce its benchmark rate—the federal funds rate—in the future, which drives down yields for longer-term bonds.

According to Jeanette Garretty, chief economist and managing director at Robertson Stephens, a wealth-management company based in California, an inverted yield curve is used to predict recessions because it indicates what investors think the Fed will do with its benchmark rate in the future.

“What tends to happen before recessions is the Fed is raising interest rates, [or] setting that policy rate at the short end, and you have market participants getting more pessimistic, and they’re betting that interest rates are going to fall in the future,” says Andrew Patterson, senior international economist at Vanguard. “So you have a situation where you could have the short end of the yield curve having higher yields than longer-dated maturities.”

If the economy is currently experiencing high inflation and low unemployment rates, the Fed will raise interest rates to reduce demand and tamp down on inflation. Once rate hikes affect the economy—by cooling inflation and causing unemployment to rise—the Fed may need to cut rates to encourage consumers and businesses to spend again.

So how long does it take after the yield curve inverts for a recession to occur? Both Garretty and Patterson estimate that it takes around six to 12 months before a downturn happens.

Even though economists frequently rely on the yield curve to predict recessions, it’s not always a fool-proof indicator.

“Every recession that we’ve seen has been preceded by an inverted yield curve,” says Garretty. “That’s not to say that every inverted yield curve has pointed to a recession.”

The yield curve has only had one false positive since 1955: In 1966, there was an inversion of the yield curve that was not followed by a recession, according to a 2018 San Francisco Federal Reserve Bank report from 2018.

What is the yield curve telling us right now?

On July 5, 2022, the yield curve between the two-year and ten-year Treasury notes inverted, and it’s stayed that way since then. It’s been more than one year since the yield curve inverted, and the economy is still humming along—unemployment is at 3.8%, inflation has cooled to 3.7% year-over-year, and consumers are still spending.

“The U.S. is not in a recession,” says Garretty. “The labor market is generating a lot of income for people—they are getting real gains in their wages…Nobody's happy with these price increases, but they have the income that allows them to manage it.”

Though it seems like the economy and consumers have yet to feel the impact of the Fed’s rate hikes—which have risen from near-zero to more than 5% in the past 18 months—Patterson doesn’t rule out the possibility of a recession occurring just yet.

“Even though a yield curve of this duration has typically resulted in a recession in the past, there's good reason to believe a recession has been delayed for reasons like the housing market remaining resilient and the strength of the labor market,” says Patterson. “Recession remains our base case. Sometime in 2024.”

Only time will tell whether the recent yield curve inversion accurately predicts a recession.

“If forecasting recessions was as easy as looking at the yield curve…you would see a lot more economists saying things like on November 16 at two o'clock, there will be a recession—it’s clearly not that easy,” says Garretty.

The takeaway

The current inverted yield curve tells us what investors think will happen to the economy in the future: The Fed will need to cut interest rates because of a recession. However, when the yield curve inverts, it’s not always an indicator of an economic downturn—even if it has been in the past.

Regardless of whether a recession occurs, it never hurts to be ready for one, whether it’s by adding to your emergency fund or paying off high-interest rate debt.

In class exercise:

1. Why is an inverted yield curve considered a predictor of a future recession?

A) It suggests future interest rate cuts by the Fed

B) It indicates high inflation rates

C) It reflects strong labor market conditions

Answer: A

2. What is the current status of the yield curve between the two-year and ten-year Treasury notes?

A) It is upward-sloping

B) It is flat

C) It is inverted

Answer: C

Explanation: As of July 5, 2022, the yield curve between the two-year and ten-year Treasury notes is inverted.

3. What has been the trend in the U.S. labor market despite the inverted yield curve?

A) High unemployment rates

B) Stagnant wages

C) Strong job market and income gains

Answer: C

Explanation: The labor market is strong, and people are experiencing real gains in their wages.

4. How long does it typically take, according to Garretty and Patterson, for a recession to occur after the yield curve inverts?

A) 1-3 months

B) 6-12 months

C) 18-24 months

Answer: B

Explanation: Both Garretty and Patterson estimate it takes around six to 12 months for a downturn to happen after the yield curve inverts.

5. What happened in 1966 that is discussed as an exception egarding the yield curve and recessions?

A) The yield curve remained inverted without a recession

B) The yield curve accurately predicted a recession

C) The yield curve did not invert despite a recession

Answer: A

Explanation: In 1966, there was an inversion of the yield curve that was not followed by a recession.

6. Why does Patterson mention a potential delay in the occurrence of a recession despite the inverted yield curve?

A) Due to a resilient housing market

B) Due to low inflation

C) Due to stock market performance

Answer: A

Explanation: Patterson suggests that factors like the resilient housing market and the strength of the labor market may delay a recession.

7. What has been the trend in the Fed's benchmark interest rate in the past 18 months, as mentioned in the text?

A) Decreased to near-zero

B) Remained unchanged

C) Increased to more than 5%

Answer: C

Explanation: The article notes that the Fed's benchmark interest rate has risen from near-zero to more than 5% in the past 18 months.

8. What is the current stance of the U.S. economy, according to Garretty?

A) In a recession

B) Generating a lot of income and experiencing wage gains

C) Experiencing high inflation and unemployment

Answer: B

Explanation: Garretty mentions that the U.S. is not in a recession and that the labor market is generating income for people.

9. What does the articel suggest about using the yield curve to predict recessions?

A) It is foolproof and always accurate

B) It is unreliable and never accurate

C) It has been a reliable indicator, but not without exceptions.

Answer: C

Explanation: While the yield curve has historically predicted recessions, there has been one false positive in 1966.

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

Untitled-modified (4).png

Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Ave
2023	6.4	6	5	4.9	4	3	3.2	3.7	3.7	3.2	3.1	3	4
2022	7.5	7.9	8.5	8.3	8.6	9.1	8.5	8.3	8.2	7.7	7.1	6.5	8
2021	1.4	1.7	2.6	4.2	5	5.4	5.4	5.3	5.4	6.2	6.8	7	4.7
2020	2.5	2.3	1.5	0.3	0.1	0.6	1	1.3	1.4	1.2	1.2	1.4	1.2
2019	1.6	1.5	1.9	2	1.8	1.6	1.8	1.7	1.7	1.8	2.1	2.3	1.8
2018	2.1	2.2	2.4	2.5	2.8	2.9	2.9	2.7	2.3	2.5	2.2	1.9	2.4
2017	2.5	2.7	2.4	2.2	1.9	1.6	1.7	1.9	2.2	2	2.2	2.1	2.1
2016	1.4	1	0.9	1.1	1	1	0.8	1.1	1.5	1.6	1.7	2.1	1.3
2015	-0.1	0	-0.1	-0.2	0	0.1	0.2	0.2	0	0.2	0.5	0.7	0.1
2014	1.6	1.1	1.5	2	2.1	2.1	2	1.7	1.7	1.7	1.3	0.8	1.6
2013	1.6	2	1.5	1.1	1.4	1.8	2	1.5	1.2	1	1.2	1.5	1.5
2012	2.9	2.9	2.7	2.3	1.7	1.7	1.4	1.7	2	2.2	1.8	1.7	2.1
2011	1.6	2.1	2.7	3.2	3.6	3.6	3.6	3.8	3.9	3.5	3.4	3	3.2
2010	2.6	2.1	2.3	2.2	2	1.1	1.2	1.1	1.1	1.2	1.1	1.5	1.6
2009	0	0.2	-0.4	-0.7	-1.3	-1.4	-2.1	-1.5	-1.3	-0.2	1.8	2.7	-0.4
2008	4.3	4	4	3.9	4.2	5	5.6	5.4	4.9	3.7	1.1	0.1	3.8
2007	2.1	2.4	2.8	2.6	2.7	2.7	2.4	2	2.8	3.5	4.3	4.1	2.8
2006	4	3.6	3.4	3.5	4.2	4.3	4.1	3.8	2.1	1.3	2	2.5	3.2
2005	3	3	3.1	3.5	2.8	2.5	3.2	3.6	4.7	4.3	3.5	3.4	3.4
2004	1.9	1.7	1.7	2.3	3.1	3.3	3	2.7	2.5	3.2	3.5	3.3	2.7
2003	2.6	3	3	2.2	2.1	2.1	2.1	2.2	2.3	2	1.8	1.9	2.3
2002	1.1	1.1	1.5	1.6	1.2	1.1	1.5	1.8	1.5	2	2.2	2.4	1.6
2001	3.7	3.5	2.9	3.3	3.6	3.2	2.7	2.7	2.6	2.1	1.9	1.6	2.8
2000	2.7	3.2	3.8	3.1	3.2	3.7	3.7	3.4	3.5	3.4	3.4	3.4	3.4

https://www.usinflationcalculator.com/inflation/current-inflation-rates/#google_vignette

Chapter 6 – Assignments –

(FYI: Videos: 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))

· Chapter six case study (due with first mid term exam)

· Critical thinking question 1: What factors contributed to the shifts in yield curve shapes in 2023?

· Critical thinking question 2: Do you think we will enter a recession as predicted by the inverted yield curve?

· Critical thinking question 3: Do you endorse the notion of the Federal Reserve lowering interest rates in 2024? Why or why not?

Chapter 7 Bond Valuation

ppt

https://investor.vanguard.com/investor-resources-education/article/are-bonds-a-good-investment-right-now

For discussion: https://jufinance.com/risk_tolerance.html

Bond Type	Characteristics	Suitability	Risk
Short-Term Bonds	Quick maturity, Low risk, Lower returns	Conservative, Need liquidity	Reinvestment Risk
Long-Term Bonds	Higher returns, High risk	Long-term, High risk tolerance	Default Risk; Market interest rate risk
Corporate Bonds	Higher yields, Higher risk, Company influence	Seeking returns, Accepting higher risk	Default Risk; Market interest rate risk (assuming long maturity)
Treasury Securities	Low risk, Steady income, Different maturities	Conservative, Stable income requirement	Market interest rate risk (assuming long maturity)
Municipal Bonds	Tax advantages, Credit risk	Tax-efficient income, Higher tax bracket	Default Risk; Market interest rate risk (assuming long maturity)

· Among the aforementioned bonds, do you have a preference? If so, what factors influence your choice?

Untitled-modified (1).jpg

Outlook for Investing in Bonds in 2024

After starting the year recommending that investors focus on the middle of the yield curve, we began to advise investors to lengthen their duration in our midyear bond market update. According to our forecasts, we continue to think investors will be best served in longer-duration bonds and locking in the currently high interest rates. https://www.morningstar.com/markets/where-invest-bonds-2024

Market data website:

FINRA: https://www.finra.org/finra-data/fixed-income (FINRA bond market data)

Relationship between bond prices and interest rates (Khan academy)

In class exercise

1) What is the face value (par value) of the bond?

a. $500

b. $1,000

c. $1,500

2) How often are coupon payments made on the bond?

a. Annually

b. Semi-annually

c. Quarterly

3) If the bond has a two-year maturity, what is the total number of coupon payments made over its life?

a. 2

b. 4

c. 6

4) If interest rates rise after the bond is purchased, what happens to its price?

a. Increases

b. Decreases

c. Remains unchanged

5) If interest rates go down, what is the likely impact on the bond's price?

a. Increases

b. Decreases

c. Remains unchanged

6) For a zero-coupon bond with a face value of $1,000 and a two-year maturity, what is the price if the expected return is 10% per year?

a. $823

b. $1,000

c. $1,100

7) In the scenario of increased expectations, if the expected return is now 15% for the same zero-coupon bond, what happens to its price?

a. Increases

b. Decreases

c. Remains unchanged

8) If the expected return decreases to 5% for the same zero-coupon bond, what is the new price?

a. $822

b. $905

c. $1,000

9) What does a bond trading at a premium mean?

a. Its price is below par

b. Its price is above par

c. Its price is equal to par

10) What does a bond trading at a discount mean?

a. Its price is below par

b. Its price is above par

c. Its price is equal to par

11) If interest rates are lower than expected, how does it affect the price of a bond?

a. Increases

b. Decreases

c. Increases

12) What is the primary reason for a bond trading at a discount?

a. High coupon rate

b. Low market interest rates

c. Low coupon rate

13) In the context of bond pricing, what is the present value?

a. Future value of cash flows

b. Current value of future cash flows

c. Face value of the bond

14) Why does the price of a bond decrease when interest rates rise?

a. Increase in coupon payments

b. Decrease in market expectations

c. Decrease in present value of future cash flows

15) What does a bond trading at par mean?

a. Its price is below par

b. Its price is above par

c. Its price is equal to par

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

· Higher market interest rates è lower fixed-rate bond prices è higher fixed-rate bond yields

· Lower fixed-rate bond coupon rates è higher interest rate risk

· Higher fixed-rate bond coupon rates è lower interest rate risk

· Lower market interest rates è higher fixed-rate bond prices è lower fixed-rate bond yields èhigher interest rate risk to rising market interest rates

· Longer maturity è higher interest rate risk è higher coupon rate

· Shorter maturity è lower interest rate risk è lower coupon rate

From https://www.sec.gov/files/ib_interestraterisk.pdf

In class exercise: True / False

1) Higher market interest rates lead to higher fixed-rate bond yields.

True

Explanation: Higher market interest rates result in lower fixed-rate bond prices and, consequently, higher fixed-rate bond yields.

2) Lower fixed-rate bond coupon rates decrease interest rate risk.

False

Explanation: When a bond has a lower fixed-rate coupon, the bondholder receives less interest income. In a rising interest rate environment, new bonds with higher coupon rates become more attractive to investors, leading to a decrease in the market value of existing bonds with lower coupon rates. Therefore, lower fixed-rate bond coupon rates make the bond more sensitive to changes in interest rates, resulting in higher interest rate risk.

3) Higher fixed-rate bond coupon rates lead to higher interest rate risk.

False

Explanation: Higher coupon rates lower interest rate risk for fixed-rate bonds. See above for further explanation.

4) Lower market interest rates result in higher fixed-rate bond yields.

False

Explanation: Lower market interest rates lead to higher fixed-rate bond prices and lower fixed-rate bond yields.

5) Longer maturity is associated with lower interest rate risk and a lower coupon rate.

False

Explanation: Longer maturity is associated with higher interest rate risk and a higher coupon rate. In terms of coupon rates, there is a general tendency for longer-maturity bonds to have higher coupon rates. This is because investors typically demand higher compensation for the increased interest rate risk associated with longer-term investments.

6) Shorter maturity reduces interest rate risk and increases the coupon rate.

False

Explanation: Shorter maturity is associated with lower interest rate risk and a lower coupon rate.

7) Rising market interest rates decrease fixed-rate bond prices and increase interest rate risk.

True

Explanation: Rising market interest rates lead to lower fixed-rate bond prices and higher interest rate risk.

8) Lower fixed-rate bond coupon rates result in higher fixed-rate bond prices.

False

Explanation: Lower fixed-rate bond coupon rates generally result in lower demand and, consequently, lower bond prices, since when a bond has a lower coupon rate, it becomes less attractive to investors seeking higher yields. As a result, the bond's market price tends to decrease.

9) Shorter maturity is associated with higher interest rate risk and a higher coupon rate.

False.

Explanation: Shorter maturity is associated with lower interest rate risk, not higher. When a bond has a shorter maturity, it means that the time until the bond's principal is repaid is shorter. In such cases, changes in interest rates have a lesser impact on the bond's price. The correct statement should be “Shorter maturity is associated with lower interest rate risk and a lower coupon rate”.

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

In Class Exercise (could be used to prepare for the first midterm exam)

Excel Solution Video-Part 1 Video-Part 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))

Assignments of Chapter 7:

1) Chapter 7 Case Study – Due with first midterm exam (updated)

Case study video in class 1/30/2024 (video. Thanks, Chris)

2) Critical Thinking Challenge – Just choose one of the two questions as follows from https://www.cnbc.com/2023/11/01/fixed-income-back-in-the-spotlight-how-investors-can-take-advantage.html:

Option 1 - The Impact of Rising Interest Rates on Bond Investments:

a. Describe the recent shift in interest rates and its impact on bond investments.

b. Discuss the reasons behind the dramatic increase in interest rates and how this shift has affected the bond market.

Option 2 - The Role of Active Fixed-Income Management in Volatile Markets:

a. Discuss the importance of adopting an active approach to fixed-income management in the current volatile market.

b. Explore how an active approach allows for better returns and the flexibility to navigate challenging market conditions.

3) A quick quiz on the conceptual comprehension of the bond chapter (FYI only, not required):

www.jufinance.com/bond.html

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/

Op-ed: Fixed income is back in the spotlight. Here’s how investors can take advantage

PUBLISHED WED, NOV 1 2023 9:00 AM EDT Christopher Gunster, head of fixed income at Fidelis Capital

https://www.cnbc.com/2023/11/01/fixed-income-back-in-the-spotlight-how-investors-can-take-advantage.html

KEY POINTS

· In recent quarters, we have witnessed a dramatic shift higher in interest rates, a move that investors should not fear but embrace. Bonds are now all the rage.

· The current real yield on a 10-year Treasury is approaching 2.5%, a level that should excite bond investors.

· Return expectations are the highest in years and, although markets could remain volatile, now is the appropriate time to reassess your portfolio and consider an increase in your fixed-income allocation.

Fixed-income investing is entering an exciting new era, and investors should take notice. Decades of low interest rates, engineered by global central banks, have suppressed the bond market’s ability to generate attractive and reliable returns.

But in recent quarters, we have witnessed a dramatic shift higher in interest rates, a move that investors should not fear but embrace. Bonds are now all the rage in investing circles and, although not as trendy as Taylor Swift, their popularity has certainly risen in recent months alongside interest rates.

Interest rates have increased dramatically since the beginning of 2022. As an example, the yield-to-maturity on the benchmark U.S. 10-year Treasury

is now nearing 5%, up over 3.30%.

The yield on the 10-year and other Treasury bonds is now the highest since the onset of the Great Financial Crisis in 2007. In addition to the rise in nominal interest rates, we have also experienced a similar increase in real interest rates (rates adjusted for inflation).

If we use market-derived, forward-looking expectations of inflation to adjust nominal yields, the current real yield on a 10-year Treasury is approaching 2.5%, a level that should excite bond investors.

Granted, the journey to higher yields has been painful to bond investors. In 2022, the total return of the Bloomberg Aggregate Bond Index, a broad universe of U.S. taxable bonds, posted a return of -13.01% (according to Bloomberg as of Dec. 31, 2022), the worst calendar year performance for this index since its inception in 1976.

Other bond market sectors experienced similar distress, but with the pain comes the gain. Higher rates can now provide more total return and more stability in returns going forward.

When calculating fixed-income returns for most bonds, there are two components: price return and income return.

First time seeing Treasury yield move like this in 20-year career, says Exante Data’s Jens Nordvig

At the start of 2022, there was little income being generated from high-quality bonds. The negative total returns for the year were driven by large price declines with a small positive contribution from income.

As an example, the Bloomberg Aggregate Bond Index posted a price return of -15.3% and an income return of +2.3%. However, the yield-to-maturity on the Bloomberg Aggregate Index is now 5.64% (according to Bloomberg as of Oct. 17, 2023), over 3.5% higher than the beginning of 2022.

As a result, we would expect a much larger positive contribution to future returns from income and a less negative contribution from price return.

How can an investor take advantage of the higher-yield environment?

We would suggest that investors reassess their current bond allocation and marginally increase their exposure in a manner consistent with their portfolio’s current position, investment objectives and risk tolerance.

While we are not calling the top in near-term rate movements, we do believe we are entering more of a range-bound yield market for longer maturity bonds. This is consistent with our expectations of no additional rate hikes from the Federal Reserve this cycle and a continued decline in near-term inflation.

To efficiently capture the higher yields, we would advise a modest increase in longer-dated maturity bonds as well as an allocation to shorter maturity bonds in a barbell approach, while avoiding intermediate maturity where possible.

Given the inverted shape of the yield curve, a barbell approach can help maximize the overall yield of the portfolio and provide additional return should long-end rates move lower.

For non-taxable or investors that are not tax-sensitive, we would prefer the use of higher-quality corporate bonds, as we believe the market has not appropriately priced the risk of a potential recession in lower-quality bonds.

Additionally, the agency mortgage-backed securities market is a high-quality sector for investors to consider. Year to date, this sector has underperformed other investment grade sectors and now offers an attractive risk-return profile.

For those investors in high-income tax brackets, municipal bonds are attractive. Similar to our view on taxable bonds, we would recommend a bias toward higher-quality bonds as a potential recession could negatively impact lower-rated municipalities.

While we currently favor municipal bonds for those high-tax investors, we would not eliminate corporate bonds or other taxable securities from consideration. Certain market conditions can favor taxable bonds on an after-tax, risk-adjusted basis.

It’s important that investors select a manager who can take advantage of those opportunities when they arise to create a tax-efficient portfolio.

To the extent that interest rates move significantly higher, counter to our expectations, we would view this as an opportunity for investors to lock in even higher yields for longer. Under such a scenario, we would not expect a repeat of 2022 bond market returns.

We estimate that interest rates would have to increase by 0.70% to 1.00% before forward-looking 12-month total returns would turn negative for the major bond indexes.

We have little doubt that the heightened level of market volatility will continue into 2024. Opportunities present themselves when market volatility increases.

To that end, we recommend an active approach to fixed-income management. Having the flexibility to successfully navigate and benefit during challenging markets allows for better returns.

It is a new dawn for bonds and fixed-income investors. Return expectations are the highest in years and, although markets could remain volatile, now is the appropriate time to reassess your portfolio and consider an increase in your fixed-income allocation.

— By Christopher Gunster, head of fixed income at Fidelis Capital

In class exercise

1. What is the key point emphasized in the op-ed regarding fixed income?

a. Fixed income is losing popularity

b. Investors should fear the recent shift in interest rates

c. Fixed income is back in the spotlight

Answer: c.

Explanation: The op-ed highlights the resurgence of fixed income in recent quarters.

2. What is the current real yield on a 10-year Treasury, as mentioned in the op-ed?

a. 3.5%

b. 2.5%

c. 5.64%

Answer: b.

Explanation: The op-ed states that the current real yield on a 10-year Treasury is approaching 2.5%.

3. How did the Bloomberg Aggregate Bond Index perform in 2022, according to the op-ed?

a. Positive return

b. -15.3% return

c. -13.01% return

Answer: c.

Explanation: The op-ed mentions a negative total return of -13.01% for the Bloomberg Aggregate Bond Index in 2022.

4. What is suggested as a strategy to take advantage of the higher-yield environment?

a. Increase bond exposure

b. Reduce bond exposure

c. Maintain the current bond allocation

Answer: a.

Explanation: The op-ed suggests reassessing and marginally increasing bond exposure.

5. What type of bond allocation is recommended for non-taxable or tax-insensitive investors?

a. Corporate bonds

b. Municipal bonds

c. Agency mortgage-backed securities

Answer: a.

Explanation: Higher-quality corporate bonds are preferred for non-taxable or tax-insensitive investors.

6. What does the op-ed recommend for investors in high-income tax brackets?

a. Municipal bonds

b. Corporate bonds

c. Agency mortgage-backed securities

Answer: a.

Explanation: Municipal bonds are recommended for investors in high-income tax brackets.

7. What does the op-ed suggest about the agency mortgage-backed securities market?

a. It is not recommended for investment

b. It has outperformed other investment grade sectors

c. It is a high-risk sector

Answer: b.

Explanation: The op-ed mentions that this sector has underperformed other investment grade sectors.

8. What is the recommended approach for capturing higher yields in a portfolio?

a. Focus on intermediate maturity bonds

b. Invest only in longer-dated maturity bonds

c. Use a barbell approach with longer and shorter maturity bonds

Answer: c.

Explanation: A barbell approach is advised to maximize overall portfolio yield.

9. What is recommended for investors to consider in response to market volatility, according to the op-ed?

a. Adopt a passive approach

b. Increase exposure to stocks

c. Take an active approach to fixed-income management

Answer: c.

Explanation: The op-ed recommends an active approach to benefit during challenging markets.

10. What is described as the current state of return expectations for bonds and fixed-income investors?

a. The highest in years

b. The lowest in years

c. Stable and predictable

Answer: a.

Explanation: The op-ed suggests that return expectations are the highest in years.

11. What is the op-ed's suggestion regarding reassessing portfolios in the current environment?

a. It is not necessary to reassess portfolios

b. Portfolios should be reassessed and fixed-income allocation increased

c. Portfolios should be reassessed, but fixed-income allocation should be decreased

Answer: b.

Explanation: The op-ed suggests reassessing portfolios and considering an increase in fixed-income allocation.

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 Video

1. How to achieve the best investment results (low risk, high return) (SOLUTION, updated FYI)
- Modern Portfolio Theory
Three stock portfolio: A, B, C
Year	A	B	C
1	10%	4%	12%
2	5%	6%	5%
3	4%	8%	7%
4	7%	10%	8%
5	1%	5%	14%

Assuming you have $10,000, how should you allocate funds among the three stocks to create an optimal portfolio with the highest return and lowest risk?

Steps

1. Mean, risk for each stock

2. Correlation between stocks: 3 correlations

3. Set it up as a portfolio and get portfolio's mean and risk

Portfolio Return = w₁*r₁ + w₂*r₂ + w₃*r₃

where: w₁, w₂, w₃ are the weights of each stock in the portfolio, and r₁, r₂, r₃ are the returns of each stock in the portfolio.

Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃)

where: σ_1,σ_2,σ₃are the standard deviations of each stock in the portfolio. ρ_12,ρ_13,ρ₂₃are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

For example, ρ₁₂ represents the correlation coefficient between the returns of stock 1 and stock 2, ρ₂₃ represents the correlation coefficient between the returns of stock 2 and stock.

4. Use solver to find lowest risk (standard deviation) for any given return.

2. 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)

3. 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).

1. What is the value of A? 2%

Solution: This is the intercept of the SML

2. What is the value of B? 10%

Solution:

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

3. 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)

4. 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

5. 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=300000

New portfolio beta = 1.2*200000/300000 + X*(100000/300000) = 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, or refer to https://www.jufinance.com/portfolio/

8. Practice Quiz - FYI only

9. Another practice quiz – FYI only

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 (FYI)

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 (FYI)

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 (FYI only)

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).

Term project – efficient frontier (group project, due with final)

· Term project word file, class video 2 13 2024, class video 2 15 2024 Graph Video

· Sample outcome (from 2023) In class exercise 2-14-2024 (Excel)

· Efficient Frontier template (FYI) (based on Modern Portfolio Theory, or Markowitz Portfolio Theory)

· Efficient Frontier Sample Report (word file)

Summary

Data Collection:

· Gather monthly closing prices for eight securities (CSG, HD, C, LUV, TXN, JNJ, IBM, BA) from January 31, 2019, to January 31, 2024, from Yahoo Finance.

· Calculate monthly returns for each security using the formula:

Statistical Analysis:

· Calculate the average monthly return and standard deviation for each security.

· Annualize the average monthly return and standard deviation.

Correlation Analysis:

· Use the correlation function in Excel to calculate pairwise correlation coefficients between the eight securities.

· Construct a correlation matrix.

Covariance Matrix:

· Calculate the covariance matrix for the securities using the correlation coefficients and standard deviations.

Equally Weighted Portfolio:

· Formulate an equally weighted portfolio with 1/8th investment in each security.

· Calculate the bordered covariance matrix for the equally weighted portfolio.

· Determine the variance of the portfolio and its expected return.

Solver Analysis:

· Use Excel Solver to find optimal portfolio weights that minimize the portfolio's standard deviation.

· Define constraints for the weights and the portfolio's expected return.

· Iterate the solver process to obtain solutions for various target portfolio returns.

Efficient Frontier:

· Graph the portfolio expected returns and standard deviations along with those of individual securities and the equally weighted portfolio.

· Plot the efficient frontier, showing the trade-off between expected return and risk for different portfolio compositions.

By following these steps, you can construct the efficient frontier and determine optimal portfolio allocations based on the risk-return trade-off.

Explanation:

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.

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, r₈are the returns of each stock in the portfolio.

Portfolio Standard Deviation:

Portfolio Standard Deviation = sqrt(w₁²*σ₁²+ w₂²*σ₂²+ w₃²*σ₃² + w₄²*σ₄²+ w₅²*σ₅²+ w₆²*σ₆²+ w₇²*σ₇²+ w₈²*σ₈²+ 2*w₁*w₂*ρ₁₂*σ₁*σ₂ + 2*w₁*w₃*ρ₁₃*σ₁*σ₃ + 2*w₁*w₄*ρ₁₄*σ₁*σ₄ + 2*w₁*w₅*ρ₁₅*σ₁*σ₅ + 2*w₁*w₆*ρ₁₆*σ₁*σ₆ + 2*w₁*w₇*ρ₁₇*σ₁*σ₇ + 2*w₁*w₈*ρ₁₈*σ₁*σ₈ + 2*w₂*w₃*ρ₂₃*σ₂*σ₃ + 2*w₂*w₄*ρ₂₄*σ₂*σ₄ + 2*w₂*w₅*ρ₂₅*σ₂*σ₅ + 2*w₂*w₆*ρ₂₆*σ₂*σ₆ + 2*w₂*w₇*ρ₂₇*σ₂*σ₇ + 2*w₂*w₈*ρ₂₈*σ₂*σ₈ + 2*w₃*w₄*ρ₃₄*σ₃*σ₄ + 2*w₃*w₅*ρ₃₅*σ₃σ₅ + 2*w₃*w₆*ρ₃₆*σ₃*σ₆ + 2*w₃*w₇*ρ₃₇*σ₃*σ₇ + 2*w₃*w₈*ρ₃₈*σ₃*σ₈ + 2*w₄*w₅*ρ₄₅*σ₄σ₅ + 2*w₄*w₆*ρ₄₆*σ₄*σ₆ + 2*w₄*w₇*ρ₄₇*σ₄*σ₇ + 2*w₄*w₈*ρ₄₈*σ₄*σ₈ + 2*w₅*w₆*ρ₅₆*σ₅*σ₆ + 2*w₅*w₇*ρ₅₇*σ₅*σ₇ + 2*w₅*w₈*ρ₅₈*σ₅*σ₈ + 2*w₆*w₇*ρ₆₇*σ₆*σ₇ + 2*w₆*w₈*ρ₆₈*σ₆*σ₈ + 2*w₇*w₈*ρ₇₈*σ₇*σ₈ )

where: σ_1,σ_2,σ_3,σ_4,σ_5,σ_6,σ_7,σ₈are the standard deviations of each stock in the portfolio. ρ_12,ρ_13,ρ_14,ρ_15,ρ_16,ρ_17,ρ_18,ρ_23,ρ_24,ρ_25,ρ_26,ρ_27,ρ_28,ρ_34,ρ_35,ρ_36,ρ_37,ρ_38,ρ_45,ρ_46,ρ_75,ρ_48,ρ_56,ρ_57,ρ_58,ρ_67,ρ_68,ρ₇₈are correlation coefficients between the stock returns. They represent the pairwise correlations between the stocks in the portfolio.

For example, ρ₁₂ represents the correlation coefficient between the returns of stock 1 and stock 2, ρ₂₃ represents the correlation coefficient between the returns of stock 2 and stock.

About the CML (Capital market line, optional)

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.

FYI only:

https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html

Chapter 9 Stock Return Evaluation

ppt

For class discussion:

· What is the dividend growth model, and why do we use dividends to estimate a company's true value?

· Can we reliably predict future dividend payments?

· Why do we require returns estimated based on risk factors to determine stock prices?

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 12/07/2023

· DIVIDEND YIELD 1.31%

· ANNUAL DIVIDEND $2.28

· P/E RATIO 30.26

Ex/EFF Date	Type	Cash Amount	Declaration Date	Record Date	Payment Date
05/09/2024	Cash	$0.2075	02/20/2024	05/10/2024	05/28/2024
03/14/2024	Cash	$0.2075	02/20/2024	03/15/2024	04/01/2024
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

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 chapter8)

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

In class exercise

2. 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

(hint: terminal value in year 5 = 120*(1+6%)/(15%-6%))

(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 3 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)

Case Study chapter 9 (due with the Second Midterm Exam)

Class Video 2-27-2024 (Thanks, Levi)

Stock Quiz (FYI only)

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

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

(FYI: Hertz Global Holdings Inc (NYSE:HTZ) WACC %:5.21% As of 2/21/2024

As of today (2024-02-21), Hertz Global Holdings's weighted average cost of capital is 5.21%%. Hertz Global Holdings's ROIC % is 7.05% (calculated using TTM income statement data). Hertz Global Holdings 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.

*Note: The beta of this company cannot be obtained because it has a price history shorter than 3 years. It will thus be set to 1 as default to calculate WACC. https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc

Hertz Global Holdings WACC % Calculation

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Generally speaking, a company's assets are financed by debt and equity. WACC is the average of the costs of these sources of financing, each of which is weighted by its respective use in the given situation. By taking a weighted average, we can see how much interest the company has to pay for every dollar it finances.

WACC

(E + D)

Cost of Equity

(E + D)

Cost of Debt

(1 - Tax Rate)

1. Weights:
Generally speaking, a company's assets are financed by debt and equity. We need to calculate the weight of equity and the weight of debt.
The market value of equity (E) is also called "Market Cap". As of today, Hertz Global Holdings's market capitalization (E) is $2219.504 Mil.
The market value of debt is typically difficult to calculate, therefore, GuruFocus uses book value of debt (D) to do the calculation. It is simplified by adding the latest one-year quarterly average Short-Term Debt & Capital Lease Obligation and Long-Term Debt & Capital Lease Obligation together. As of Dec. 2023, Hertz Global Holdings's latest one-year quarterly average Book Value of Debt (D) is $17397.6 Mil.
a) weight of equity = E / (E + D) = 2219.504 / (2219.504 + 17397.6) = 0.1131
b) weight of debt = D / (E + D) = 17397.6 / (2219.504 + 17397.6) = 0.8869

2. Cost of Equity:
GuruFocus uses Capital Asset Pricing Model (CAPM) to calculate the required rate of return. The formula is:
Cost of Equity = Risk-Free Rate of Return + Beta of Asset * (Expected Return of the Market - Risk-Free Rate of Return)
a) GuruFocus uses 10-Year Treasury Constant Maturity Rate as the risk-free rate. It is updated daily. The current risk-free rate is 4.307%. Please go to Economic Indicators page for more information. Please note that we use the 10-Year Treasury Constant Maturity Rate of the country/region where the company is headquartered. If the data for that country/region is not available, then we will use the 10-Year Treasury Constant Maturity Rate of the United States as default.
b) Beta is the sensitivity of the expected excess asset returns to the expected excess market returns. Hertz Global Holdings's beta cannot be obtained because it has a price history shorter than 3 years. It will thus be set to 1 as default to calculate WACC.
c) (Expected Return of the Market - Risk-Free Rate of Return) is also called market premium. GuruFocus requires market premium to be 6%.
Cost of Equity = 4.307% + 1 * 6% = 10.307%

3. Cost of Debt:
GuruFocus uses latest TTM Interest Expense divided by the latest one-year quarterly average debt to get the simplified cost of debt.
As of Dec. 2023, Hertz Global Holdings's interest expense (positive number) was $793 Mil. Its total Book Value of Debt (D) is $17397.6 Mil.
Cost of Debt = 793 / 17397.6 = 4.5581%.

4. Multiply by one minus TTM Tax Rate:
GuruFocus uses the most recent TTM Tax Expense divided by the most recent TTM Pre-Tax Income to calculate the tax rate. The calculated TTM tax rate is limited to between 0% and 100%. If the calculated tax rate is higher than 100%, it is set to 100%. If the calculated tax rate is less than 0%, it is set to 0%.
The latest calculated TTM Tax Rate = -330 / 286 = -115.38%, which is less than 0%. Therefore it's set to 0%.

Hertz Global Holdings's Weighted Average Cost Of Capital (WACC) for Today is calculated as:

WACC	=	E / (E + D)	*	Cost of Equity	+	D / (E + D)	*	Cost of Debt	*	(1 - Tax Rate)
	=	0.1131	*	10.307%	+	0.8869	*	4.5581%	*	(1 - 0%)
	=	5.21%

HERTZ WACC in 2017

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

In Class Exercise (https://www.jufinance.com/fin435_24s/wacc_in_class_exercise.html)

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%) = 3.98%------ after tax cost of debt

· Ke = 5/(50 – 0) + 5% =15% -------- cost of equity

· WACC = Wd*Kd +We*Ke = (1/3)*3.98% + (2/3)*15% =11.33%

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% (=rate(20, 8%*1000, -1050, 1000)

A-T cost of debt 4.51% (= rate(20, 8%*1000, -1050, 1000)*(1-40%)

Cost of equity, r_s= r_RF + b(RP_M) 11.10% (=4.5% + 1.2*5.5%)

WACC = w_d(r_d)(1 – T) + w_c(r_s) = 8.79% (=35%*4.51% + 65% * 11.1%)

· WACC Case study (due with the 2^nd midterm exam)

· Case Study In Class Video (3/5/2024)

· WACC quiz (FYI only)

· Critical Thinking Challenge:

When comparing the WACC for Apple from the two provided sources (as shown in the tables below), which source do you consider to provide a more reliable WACC estimation? Additionally, could you calculate the market value of equity based on the WACC determined by each method?

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

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

Shares outstanding = 15.44B (https://ycharts.com/companies/AAPL/shares_outstanding)

FCF of 2023 = 106.9B (https://www.alphaspread.com/security/nasdaq/aapl/financials/cash-flow-statement/free-cash-flow)

For FCF growth rate, let's simplify the calculation by using a 7% discount rate.

Refer to https://www.stock-analysis-on.net/NASDAQ/Company/Apple-Inc/DCF/Present-Value-of-FCFF for a more appropriate growth rate.

gurufocus.com:

Step	Calculation	Value
Market Value of Equity (E)	$2,805,094.894 Billion	-
Book Value of Debt (D)	$109,826.6 Million	-
Weight of Equity	E/(E+D)	0.9623
Weight of Debt	D/(E+D)	0.0377
Risk-Free Rate	4.30%	-
Beta	1.21	-
Expected Market Premium	6%	-
Cost of Equity	( Risk-Free Rate + Beta * Expected Market Premium )	11.56%
Interest Expense	$2,930 Million	-
Cost of Debt	(Interest Expense)/(Book Value of Debt)	2.67%
Tax Rate	14.80%	-
WACC	Weight of Equity * Cost of Equity + Weight of Debt * Cost of Debt * (1 - Tax Rate) )	11.21%

Valueinvesting.io

Component	Low Range	High Range	Selected Value
Long-term bond rate	3.90%	4.40%	-
Equity market risk premium	4.60%	5.60%	-
Adjusted beta	0.8	0.95	- (????)
Additional risk adjustments	0.00%	0.50%	-
Cost of equity	7.60%	10.20%	8.90%
Tax rate	14.60%	15.20%	14.90%
Debt/Equity ratio	0.04	0.04	-
Cost of debt	4.00%	4.60%	4.30%
After-tax WACC	7.40%	9.90%	-
Selected WACC			8.70%
Low	High

Unlevered beta	0.71	0.94
Relevered beta	0.73	0.97
Adjusted relevered beta	0.82	0.98

Beta (β)

Unlevered Beta (β_u):

· Definition: Unlevered beta represents the systematic risk of a company's assets without taking into account the effects of financial leverage (debt).

· Calculation: It is calculated based on the company's business risk and industry risk, excluding the influence of financial structure.

· Use: Unlevered beta is commonly used in the context of valuing a company's operations or core business, as it reflects the inherent riskiness of the company's underlying business activities.

Relevered Beta (β_L):

· Definition: Relevered beta represents the systematic risk of a company's equity after accounting for the effects of financial leverage (debt).

· Calculation: It is calculated by unlevering the beta (removing the effects of financial leverage), adjusting it for the company's capital structure (using the debt-to-equity ratio), and then relevering it to reflect the company's actual financial structure.

· Use: Relevered beta is often used in the context of determining the required rate of return for a company's equity or estimating the company's cost of equity capital, taking into account its specific financial structure.

https://www.wallstreetprep.com/knowledge/beta-levered-unlevered/

Hint:

Compare the reliability of Apple's Weighted Average Cost of Capital (WACC) between the two websites by calculating the market value of equity based on each method using Apple's Free Cash Flow (FCF) in 2023 and a growth rate of 5% with the Dividend Growth Model approach. Then, you'll calculate the stock price using the equity value and the number of outstanding shares.

Here's the step-by-step process:

1) Calculate Equity Value:

Based on each website's WACC, you'll calculate the firm value using the FCF and growth rate, subtract the book value of debt to get the equity value.

· Calculate firm value using the formula:

Firm Value = FCF 2023 × (1 + growth rate)/ (WACC − growth rate)

· Calculate equity value:

Equity Value = Firm Value − Book Value of Debt

2) Calculate Stock Price: Divide the equity value by the number of outstanding shares to get the stock price.

· Calculate stock price:

Stock Price = Equity Value / Number of Outstanding Shares

Once you have the equity values from both methods, you'll compare the differences in the calculated stock prices.

Hint:

Corporate Bond Data is available at FINRA.ORG: https://www.finra.org/finra-data/fixed-income/corp-and-agency

Muni Bond Data is available at EMMA: https://emma.msrb.org/

Treasury Securities Data is available at Treasury Direct: https://www.treasurydirect.gov/

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%

***** How much does Amazon worth in 2019?”

FYI: 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%

Recommended websites for WACC

Hertz

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

https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc

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

Amazon

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

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

Apple

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

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

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.

Summary:

Method	Equation	Ease of Use	Potential Problems	Popularity
Net Present Value (NPV)	NPV = ∑(Cash flows / (1 + Discount Rate)^n) - Initial Investment	Relatively easy to calculate in Excel using the NPV function	Difficulty in estimating future cash flows accurately. Sensitivity to changes in discount rate	Very popular due to its focus on absolute value and consideration of the time value of money
Internal Rate of Return (IRR)	NPV = 0, where NPV = ∑(Cash flows / (1 + IRR)^n) - Initial Investment	Can be calculated in Excel using the IRR function	IRR assumes reinvestment at the same rate, which might not be realistic. It can give misleading results if cash flows change sign multiple times	Widely used due to its intuitive appeal and ability to represent project profitability as a percentage
Modified Internal Rate of Return (MIRR)	Reflects the reinvestment rate for positive cash flows and the borrowing rate for negative cash flows, and considers the timing of cash flows	Requires additional steps to calculate in Excel compared to IRR or NPV	MIRR provides a different perspective than traditional IRR, potentially leading to confusion in interpretation	Less commonly used compared to NPV and IRR, but can provide valuable insights, especially in certain scenarios
Payback Period	The time it takes for initial investment to be recovered. Calculated by summing the cash flows until they equal or exceed the initial investment	Relatively easy to calculate in Excel using simple addition and comparison	Ignores cash flows occurring after the payback period, potentially leading to suboptimal decisions	Commonly used due to its simplicity, especially in smaller businesses or for quick assessments
Profitability Index (PI)	PI = Present Value of Cash Inflows / Initial Investment	Fairly straightforward to calculate in Excel using division	It's a relative measure, so it may not provide a clear indication of project profitability	Used less frequently compared to NPV and IRR, but still relevant for comparing projects with varying initial investments

In Class Exercise – 1

1. What is the primary advantage of using Net Present Value (NPV) in capital budgeting?

A) It considers the timing of cash flows.

B) It provides a percentage-based measure of profitability.

C) It is easy to calculate in Excel.

Answer: A

Explanation: NPV considers the time value of money by discounting cash flows to their present value, thereby providing a more accurate measure of project profitability.

2. Which potential problem is associated with the Internal Rate of Return (IRR) method?

A) It ignores cash flows occurring after the payback period.

B) It assumes reinvestment at the same rate.

C) It is difficult to estimate future cash flows accurately.

Answer: B

Explanation: IRR assumes reinvestment at the same rate, which might not be realistic and can lead to misleading results.

3. What distinguishes the Modified Internal Rate of Return (MIRR) from traditional IRR?

A) It reflects the reinvestment rate for positive cash flows and the borrowing rate for negative cash flows.

B) It considers the timing of cash flows.

C) It is calculated by summing the cash flows until they equal or exceed the initial investment.

Answer: A

Explanation: MIRR reflects different rates for reinvestment and borrowing, providing a more realistic measure of project profitability.

4. What is a common criticism of the Payback Period method?

A) It is difficult to calculate in Excel.

B) It considers the timing of cash flows.

C) It ignores cash flows occurring after the payback period.

Answer: C

Explanation: Payback Period ignores cash flows occurring after the payback period, potentially leading to suboptimal decisions.

5. What does the Profitability Index (PI) measure?

A) The percentage-based profitability of a project.

B) The present value of cash inflows.

C) The ratio of present value of cash inflows to initial investment.

Answer: C

Explanation: PI measures the efficiency of an investment by comparing the present value of cash inflows to the initial investment.

6. Which characteristic makes the Internal Rate of Return (IRR) method popular in capital budgeting?

A) It provides a percentage-based measure of profitability.

B) It considers the timing of cash flows.

C) It is easy to calculate in Excel.

Answer: A

Explanation: IRR provides a percentage-based measure of project profitability, making it popular among investors and analysts.

In class exercise - 2

Part I: Single project

1. How much is MIRR? IRR? Payback period? Discounted payback period? NPV?

WACC: 11.00%

Year 0 1 2 3

Cash flows -$800 $350 $350 $350

Answer:

1) NPV:

NPV = -800 + 350/(1+11%) + 350/(1+11%)²+ 350/(1+11%)³ = 55.30

Or in excel: = npv(11%, 350, 350, 350)-800 = 55.30

2) IRR:

So NPV = 0 = -800 + 350/(1+IRR) + 350/(1+IRR)²+ 350/(1+IRR)³, use Solver, can get IRR = 14.93%

Or in excel:

3) PI: profitable index

SO, PI= (350/(1+11%) + 350/(1+11%)²+ 350/(1+11%)³) / 800 = 1.069

Or PI = NPV/800 + 1 = 55.30/800 + 1 = 1.069

4) Payback period:

A portion of the third year = (800-350-350)/350 = 100/350 = 0.2857

So it takes 2 + 0.2857 = 2.2857 years to pay off the debt of $800.

5) Discounted payback period:

Note: All the cash flows in the above equation should be the present values.

A portion of the third year = (800-318.18-289.26)/262.96 = 0.72

So it takes 2 + 0.72 = 2.72 years to pay off the debt of $800.

A portion of the third year = (800-318.18-289.26)/262.96 = 0.72

So it takes 2 + 0.72 = 2.72 years to pay off the debt of $800.

Or use the calculator at https://www.jufinance.com/capital/

Part II: Multi-Projects

1. Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) “true value” is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will have no effect on the value gained or lost.

WACC: 7.50%

Year 0 1 2 3 4

CFS -$1,100 $550 $600 $100 $100

CFL -$2,700 $650 $725 $800 $1,400

Answer:

Question 2:

Period	Project A	Project B
0	-500	-400
1	325	325
2	325	200
IRR
NPV

If the required rate of return is 10%. Which project shall you choose?

1) How much is the cross over rate? (answer: 11.8%)

2) How is your decision if the required rate of return is 13%? (answer: NPV of B>NPV of A)

· Rule for mutually exclusive projects: (answer: Choose B)

· What about the two projects are independent? (answer: Choose both)

Solution:

Part III More on IRR – (non-conventional cash flow)

Suppose an investment will cost $90,000 initially and will generate the following cash flows:

– Year 1: 132,000

– Year 2: 100,000

– Year 3: -150,000

The required return is 15%. Should we accept or reject the project?

1) How does the NPV profile look like? (Answer: Inverted NPV profile)

2) IRR1= 10.11% -- answer

3) IRR2= 42.66% -- answer

Solution:

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

Class Video of Chapter 11’s Case Study

NPV Quiz (FYI)

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.

In Class Exercise (FYI) MIRR Quiz here

1. What does MIRR improve upon compared to IRR?

A) Multiple solutions for the same project

B) Reinvestment rate assumption

C) Discount rate calculation

Answer: B

Explanation: MIRR improves upon IRR by addressing the unrealistic assumption of reinvesting cash flows at the IRR itself.

2. What does MIRR allow project managers to do?

A) Change reinvestment rate assumptions

B) Assume reinvestment rate at IRR

C) Use NPV calculations exclusively

Answer: A

Explanation: MIRR allows project managers to adjust the assumed reinvestment rate, providing flexibility in modeling different scenarios.

3. How does IRR tend to overstate project profitability?

A) By assuming reinvestment at cost of capital

B) By discounting future cash flows

C) By considering multiple reinvestment rates

D) None of the above

Answer: D

Explanation: IRR tends to overstate project profitability due to unrealistic assumptions about reinvestment rates.

4. When is MIRR particularly useful?

A) When project cash flows are unpredictable

B) When all projects have the same reinvestment rate

C) When comparing projects of unequal size

Answer: C

Explanation: MIRR is particularly useful when evaluating projects with different sizes and cash flow patterns.

5. What is the key difference between MIRR and IRR?

A) MIRR accounts for project size

B) MIRR assumes reinvestment at cost of capital

C) MIRR eliminates the issue of multiple solutions

Answer: B

Explanation: MIRR assumes reinvestment of positive cash flows at the cost of capital, while IRR assumes reinvestment at the IRR itself.

6. Which metric is more likely to lead to capital budgeting mistakes based on overly optimistic estimates?

A) MIRR

B) NPV

C) IRR

Answer: C

Explanation: IRR tends to overstate project profitability and can lead to capital budgeting mistakes based on overly optimistic estimates.

7. What problem does MIRR solve related to IRR when a project has different periods of positive and negative cash flows?

A) Inconsistent reinvestment rates

B) Multiple IRRs

C) Overstated profitability

Answer: B

Explanation: MIRR generates one solution for a given project, eliminating the issue of multiple IRRs.

8. Which metric is more effective in selecting mutually exclusive investments?

A) MIRR

B) NPV

C) IRR

Answer: B

Explanation: NPV often provides a more effective theoretical basis for selecting mutually exclusive investments.

Second Midterm Exam (3.21, in class exam)

· Chapters 9, 10, 11

· similar to in class exercises and case studies

What is DCF?

Video – Amazon – DCF Example (self-made video in spring 2023)

Evaluation of Amazon based on DCF – ChatGPT done in Spring 2023

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.

Step one of DCF: FCF - Chapter 3 Financial Statement

ppt

Balance Sheet Template https://www.jufinance.com/10k/bs

Income Statement Template https://www.jufinance.com/10k/is

Cash flow template https://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 debt holders) 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 non-operating assets (e.g., marketable securities, investments in other companies, etc.)

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 on Cash Flow Statement and FCF only (due with final)

Case video on 3/26/2024

A review of Cash Flow Statement (FIN301): https://www.jufinance.com/10k/cf/

Excel Template

Cash Flow Statement		Notes
Cash at the beginning of the year		Cash, last year's balance sheet; "=Cash in 2022"
Cash From operation
net income		Income statement of 2023
plus depreciation		Income statement of 2023
-/+ AR		Changes of AR between this year and last year - balance sheet. CHANGE SIGN! use 2023 - 2022
-/+ Inventory		Changes of Inventory between this year and last year /// balance sheet. CHANGE SIGN! use 2023 - 2022
+/- AP		Changes of AP between this year and last year /// balance sheet. use 2023 - 2022
net change in cash from operation	--
Cash From investment
-/+ (NFA+depreciation)		Changes of NFA between this year & last year, add back depreciation//balance sheet. CHANGE SIGN!
net change in cash from investment	--
Cash From Financing
+/- long term debt		Changes of LD between this year and last year /// balance sheet. use 2023 - 2022
Common stock		Changes of CS between this year and last year /// balance sheet. use 2023 - 2022
- dividend		Income statement of 2023; Do not add negative sign to subtract dividend
net change in cash from financing	--

Total net change of cash	--

Cash at the end of the year	--	Should match Cash on current year's balance sheet; if not, go back and check; "=2023's cash"

Step 2 of DCF - Chapter 12: Cash Flow Estimation and Monte Carlo Method in Excel

ppt

Chapter 12 case study (due with final. Monte Carol is required.)

Case Video in Class on 3/28/2024

Monte Carlo In Class 4/2/2024

Monte Carlo Demonstration Based on Case in Class (FYI, Video)

Critical thinking challenge (due with final):

· Recalculate 100 times of the NPV based on the Monte Carlo simulation method by randomly changing the tax rate and the WACC (or any two factors)

· 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:

Instructions on Monte Carlo Simulation Process (using Tax Rate and WACC as example):

· Pick two variables, such as tax rate and WACC.

· Parameter Definition:

You defined the parameters for the two variables, such as tax rate and WACC, including their means and standard deviations.

· Random Sample Generation: Using the norminv function, you generated 100 sets of random samples for tax rate and WACC, ensuring they follow normal distributions based on the provided mean and standard deviation.

· NPV Calculation: For each set of randomly generated tax rate and WACC, you calculated the Net Present Value (NPV) using the appropriate formula.

· Statistical Analysis: You reported statistical results including the mean, standard deviation, minimum, and maximum NPV values obtained from the Monte Carlo simulation.

· Histogram Visualization: You visualized the probability distribution of NPV values by creating a histogram.

· Summary of Results:

Mean NPV: The average NPV across the 100 iterations.

Standard Deviation of NPV: The measure of dispersion of NPV values around the mean.

Minimum NPV: The lowest NPV value obtained.

Maximum NPV: The highest NPV value obtained.

Histogram: The histogram provides a visual representation of the distribution of NPV values, showing the frequency of NPV occurrences within different ranges.

· Conclusion:

Your Monte Carlo simulation approach effectively captured the variability and uncertainty in NPV outcomes resulting from fluctuations in tax rates and WACC. The statistical analysis and histogram visualization offer insights into the range of potential NPV values and their likelihood of occurrence, aiding in decision-making processes related to financial planning and investment evaluation.

About norminv function in excel: =norminv(RAND(), mean, standard_deviation)

· RAND() generates a random number between 0 and 1.

· For example, to generate a random tax rate with a mean of 25% and a standard deviation of 2.5%, you can use:

=norminv(RAND(), 25%, 2.5%)

Monte Carlo Simulation Demonstration (FYI， 2023 video)

Introduction to Monte Carlo Simulation in Excel 2016 (youtube)

Structure

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

The Monte Carlo Simulation: Understanding the Basics (FYI)

By KUSHAL AGARWAL Updated June 19, 2023

https://www.investopedia.com/articles/investing/112514/monte-carlo-simulation-basics.asp#:~:text=Monte%20Carlo%20is%20used%20in,under%20analysis%20and%20its%20volatility.https://www.investopedia.com/articles/investing/112514/monte-carlo-simulation-basics.asp#:~:text=Monte%20Carlo%20is%20used%20in,under%20analysis%20and%20its%20volatility.

What Is a Monte Carlo Simulation?

Analysts can assess possible portfolio returns in many ways. The historical approach, which is the most popular, considers all the possibilities that have already happened. However, investors shouldn't stop at this. The Monte Carlo method is a stochastic (random sampling of inputs) method to solve a statistical problem, and a simulation is a virtual representation of a problem. The Monte Carlo simulation combines the two to give us a powerful tool that allows us to obtain a distribution (array) of results for any statistical problem with numerous inputs sampled over and over again.

KEY TAKEAWAYS

· The Monte Carlo method uses a random sampling of information to solve a statistical problem; while a simulation is a way to virtually demonstrate a strategy.

· Combined, the Monte Carlo simulation enables a user to come up with a bevy of results for a statistical problem with numerous data points sampled repeatedly.

· The Monte Carlo simulation can be used in corporate finance, options pricing, and especially portfolio management and personal finance planning.

· On the downside, the simulation is limited in that it can't account for bear markets, recessions, or any other kind of financial crisis that might impact potential results.

Monte Carlo Simulation Demystified

Monte Carlo simulations can be best understood by thinking about a person throwing dice. A novice gambler who plays craps for the first time will have no clue what the odds are to roll a six in any combination (for example, four and two, three and three, one and five). What are the odds of rolling two threes, also known as a "hard six?" Throwing the dice many times, ideally several million times, would provide a representative distribution of results, which will tell us how likely a roll of six will be a hard six. Ideally, we should run these tests efficiently and quickly, which is exactly what a Monte Carlo simulation offers.

The problem with looking to history alone is that it represents, in effect, just one roll, or probable outcome, which may or may not be applicable in the future. A Monte Carlo simulation considers a wide range of possibilities and helps us reduce uncertainty. A Monte Carlo simulation is very flexible; it allows us to vary risk assumptions under all parameters and thus model a range of possible outcomes. One can compare multiple future outcomes and customize the model to various assets and portfolios under review.

A Monte Carlo simulation can accommodate a variety of risk assumptions in many scenarios and is therefore applicable to all kinds of investments and portfolios.

Applying the Monte Carlo Simulation

The Monte Carlo simulation has numerous applications in finance and other fields. Monte Carlo is used in corporate finance to model components of project cash flow, which are impacted by uncertainty. The result is a range of net present values (NPVs) along with observations on the average NPV of the investment under analysis and its volatility. The investor can, thus, estimate the probability that NPV will be greater than zero. Monte Carlo is used for option pricing where numerous random paths for the price of an underlying asset are generated, each having an associated payoff. These payoffs are then discounted back to the present and averaged to get the option price. It is similarly used for pricing fixed income securities and interest rate derivatives. But the Monte Carlo simulation is used most extensively in portfolio management and personal financial planning.

Uses in Portfolio Management

A Monte Carlo simulation allows an analyst to determine the size of the portfolio a client would need at retirement to support their desired retirement lifestyle and other desired gifts and bequests. She factors into a distribution of reinvestment rates, inflation rates, asset class returns, tax rates, and even possible lifespans. The result is a distribution of portfolio sizes with the probabilities of supporting the client's desired spending needs.

The analyst next uses the Monte Carlo simulation to determine the expected value and distribution of a portfolio at the owner's retirement date. The simulation allows the analyst to take a multi-period view and factor in path dependency; the portfolio value and asset allocation at every period depend on the returns and volatility in the preceding period. The analyst uses various asset allocations with varying degrees of risk, different correlations between assets, and distribution of a large number of factors – including the savings in each period and the retirement date – to arrive at a distribution of portfolios along with the probability of arriving at the desired portfolio value at retirement. The client's different spending rates and lifespan can be factored in to determine the probability that the client will run out of funds (the probability of ruin or longevity risk) before their death.

A client's risk and return profile is the most important factor influencing portfolio management decisions. The client's required returns are a function of her retirement and spending goals; her risk profile is determined by her ability and willingness to take risks. More often than not, the desired return and the risk profile of a client are not in sync with each other. For example, the level of risk acceptable to a client may make it impossible or very difficult to attain the desired return. Moreover, a minimum amount may be needed before retirement to achieve the client's goals, but the client's lifestyle would not allow for the savings or the client may be reluctant to change it.

Monte Carlo Simulation Example

Let's consider an example of a young working couple who works very hard and has a lavish lifestyle including expensive holidays every year. They have a retirement objective of spending $170,000 per year (approx. $14,000/month) and leaving a $1 million estate to their children. An analyst runs a simulation and finds that their savings-per-period is insufficient to build the desired portfolio value at retirement; however, it is achievable if the allocation to small-cap stocks is doubled (up to 50 to 70% from 25 to 35%), which will increase their risk considerably. None of the above alternatives (higher savings or increased risk) are acceptable to the client. Thus, the analyst factors in other adjustments before running the simulation again. the analyst delays their retirement by two years and decreases their monthly spend post-retirement to $12,500. The resulting distribution shows that the desired portfolio value is achievable by increasing allocation to small-cap stock by only 8 percent. With the available insight, the analyst advises the clients to delay retirement and decrease their spending marginally, to which the couple agrees.

The Bottom line

A Monte Carlo simulation allows analysts and advisors to convert investment chances into choices. The advantage of Monte Carlo is its ability to factor in a range of values for various inputs; this is also its greatest disadvantage in the sense that assumptions need to be fair because the output is only as good as the inputs. Another great disadvantage is that the Monte Carlo simulation tends to underestimate the probability of extreme bear events like a financial crisis. In fact, experts argue that a simulation like the Monte Carlo is unable to factor in the behavioral aspects of finance and the irrationality exhibited by market participants. It is, however, a useful tool for advisors.

In Class Exercise (FYI)

1. What does the Monte Carlo simulation involve?

a) Generating random paths for the price of an underlying asset

b) Analyzing historical data only

c) Calculating deterministic outcomes

Answer: a

Explanation: The Monte Carlo simulation involves generating random paths for the price of an underlying asset to analyze a range of possible outcomes.

2. In finance, Monte Carlo simulation is primarily used for:

a) Analyzing historical trends

b) Predicting deterministic outcomes

c) Portfolio management and personal financial planning

Answer: c

Explanation: Monte Carlo simulation is extensively used in portfolio management and personal financial planning to assess various outcomes and risks.

3. What does the Monte Carlo simulation allow an analyst to determine in portfolio management?

a) The exact portfolio size needed at retirement

b) The expected value and distribution of a portfolio at a specific date

c) The precise returns of individual assets

Answer: b

Explanation: In portfolio management, the Monte Carlo simulation allows an analyst to determine the expected value and distribution of a portfolio at a specific date.

4. What is the key factor influencing portfolio management decisions in Monte Carlo simulations?

a) Inflation rates

b) Risk and return profile of the client

c) Tax rates

Answer: b

Explanation: The risk and return profile of the client is the key factor influencing portfolio management decisions in Monte Carlo simulations.

5. What is the greatest disadvantage of Monte Carlo simulation?

a) Inability to factor in market irrationality

b) Overestimation of extreme bear events

c) Underestimation of extreme bear events

Answer: c

Explanation: The greatest disadvantage of Monte Carlo simulation is its tendency to underestimate the probability of extreme bear events like a financial crisis.

6. How does a Monte Carlo simulation help convert investment chances into choices?

a) By eliminating all risks

b) By considering a range of values for various inputs

c) By providing deterministic outcomes

Answer: b

Explanation: A Monte Carlo simulation helps convert investment chances into choices by considering a range of values for various inputs, allowing for better decision-making.

7. What is the main advantage of Monte Carlo simulation?

a) It provides deterministic outcomes

b) It factors in market irrationality

c) It considers a range of values for various inputs

Answer: c

Explanation: The main advantage of Monte Carlo simulation is its ability to consider a range of values for various inputs, allowing for comprehensive analysis.

8. What is the primary application of Monte Carlo simulation in corporate finance?

a) Analyzing historical trends

b) Pricing fixed income securities

c) Portfolio management and personal financial planning

d) Modeling components of project cash flow in corporate finance

Answer: d

Explanation: In addition to portfolio management and personal financial planning, Monte Carlo simulation is widely used in corporate finance for modeling components of project cash flow, especially those impacted by uncertainty.

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 (4.9.2024) – Black-Schools-Merton Option Pricing Model

Case video in class part II (4.11.2024) – Binomial Option Pricing Model

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-Merton Option Calculator

https://www.mystockoptions.com/black-scholes.cfm

Black-Scholes-Merton Option Calculator by ChatGPT (at jufinance.com)

www.jufinance.com/https://www.jufinance.com/option_chatgpt/

(Just Ask ChatGPT for the Black Scholes Option pricing model code in JavaScript and HTML. Then, copy the code, open Notepad, paste it, and save the file as an HTML file, like option.html. Easy!)

Black-Scholes-Merton Model Illustration Excel

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*t - d)/(u-d)

where r is the risk-free rate and t is the time until expiration; u is the up factor and d is the down factor.

In our example, the risk-neutral probability is approximately:

Pu = (1+0.08*1 - 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-Merton 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.

Seminar one – Is it possible for Samsung to acquire Nvidia?

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)

Final Offer from Amazon: $42/share; a total of $13.4 billions

Why does Amazon's Bezos want Whole Foods? (video)

Mergers and Acquisitions Explained: A Crash Course on M&A (youtube, FYI)

Is it possible for Samsung to acquire Nvidia?

Samsung vs. NVIDIA Video produced by invideo.ai and Dr. Foley

IN Class Exercise

1. During the due diligence phase, Samsung's team primarily focuses on:

a) Assessing financial health

b) Finalizing integration plans

c) Conducting shareholder meetings

Answer: a

Explanation: Due diligence involves analyzing NVIDIA's financial health, technology portfolio, market position, and potential synergies with Samsung's existing businesses.

2. Which of the following is a potential defense mechanism that NVIDIA's board might employ to deter Samsung's acquisition attempt?

a) Poison Pill

b) Shareholder approval

c) Regulatory approval

Answer: a

Explanation: Poison Pill is a defense mechanism used by companies to dilute the acquirer's stake if it surpasses a certain threshold, making the acquisition more costly and less attractive.

3. What could be a consequence of NVIDIA implementing a "poison pill" defense mechanism?

a) Faster acquisition process

b) Shareholder dilution

c) Increased shareholder approval

Answer: b

Explanation: Implementing a poison pill defense mechanism could result in diluting the acquirer's stake by issuing additional shares to existing shareholders.

4. What is one of the strategies NVIDIA's board could use to counter Samsung's acquisition attempt?

a) Conducting extensive due diligence

b) Offering incentives to key employees

c) Engaging in proxy contests

Answer: c

Explanation: Proxy contests involve seeking support from shareholders to vote against the proposed acquisition, highlighting potential risks or drawbacks associated with Samsung's offer.

5. What regulatory approval might Samsung need to secure for the acquisition?

a) Shareholder approval

b) Due diligence approval

c) Antitrust approval

Answer: c

Explanation: Given the size and scope of the two companies, regulatory approval from various antitrust authorities would be necessary to ensure the acquisition does not substantially lessen competition in relevant markets.

6. What action could NVIDIA take if it believes Samsung's acquisition attempt is unlawful?

a) Shareholder dilution

b) Engaging in litigation

c) Conducting shareholder meetings

Answer: b

Explanation: NVIDIA could resort to legal action if it believes Samsung's acquisition attempt is unlawful or not in the best interests of shareholders.

7. Which of the following is NOT a potential defense mechanism that NVIDIA's board might employ?

a) Litigation

b) Corporate restructuring

c) Shareholder approval

Answer: c

Explanation: Shareholder approval is a step in the acquisition process and not a defense mechanism used by the target company.

8. What role does shareholder approval play in the acquisition process?

a) It influences the success of the acquisition

b) It determines the integration timeline

c) It impacts regulatory approval

Answer: a

Explanation: Shareholder approval is crucial as it ensures that the acquisition is supported by the company's shareholders, increasing the likelihood of success.

9. Which defense mechanism involves seeking out alternative buyers?

a) Poison Pill

b) White Knight

c) Litigation

Answer: b

Explanation: A white knight is an alternative buyer sought by the target company to potentially offer a better deal for shareholders or align more closely with the company's strategic objectives.

10. What could be a consequence of NVIDIA engaging in litigation against Samsung's acquisition attempt?

a) Delay in regulatory approval

b) Faster integration process

c) Higher shareholder approval

Answer: a

Explanation: Litigation could lead to delays in the acquisition process as legal proceedings unfold, potentially delaying regulatory approval.

11. What could be a consequence of NVIDIA spinning off certain divisions or assets?

a) Increased shareholder value

b) Delay in shareholder approval

c) Making itself less attractive for acquisition

Answer: c

Explanation: Spinning off certain divisions or assets could make NVIDIA less attractive for acquisition by reducing its overall value or strategic relevance to the acquirer.

12. What could prolong the process of replacing NVIDIA's entire board with directors more amenable to the acquisition?

a) Due diligence

b) Proxy Contest

c) Shareholder approval

Answer: b

Explanation: Proxy contests involve seeking support from shareholders to vote against the proposed acquisition, potentially prolonging the process of replacing the board.

13. What is the primary focus of NVIDIA's board during a proxy contest?

a) Finalizing integration plans

b) Engaging in litigation

c) Swaying shareholder opinion against the acquisition

Answer: c

Explanation: The primary focus of a proxy contest is to sway shareholder opinion against the acquisition by highlighting potential risks or drawbacks associated with the offer.

14. What action could Samsung take to ensure the support and retention of key NVIDIA employees post-acquisition?

a) Offering incentives

b) Engaging in litigation

c) Conducting shareholder meetings

Answer: a

Explanation: Samsung could offer incentives to key NVIDIA employees to ensure their support and retention post-acquisition, aligning their interests with the success of the combined entity.

15. Which defense mechanism involves making the acquisition more costly and less attractive for the acquirer?

a) White Knight

b) Poison Pill

c) Proxy Contest

Answer: b

Explanation: Poison Pill defense mechanism aims to make the acquisition more costly and less attractive for the acquirer by diluting their stake if certain thresholds are exceeded.

Self-Test on Merger Knowledge (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, FYI)

· 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

Seminar Two – Which option should NVIDIA choose: paying dividends or engaging in share repurchases?

Chapter 15 Distributions to Shareholders

· This chapter will not be covered in the final exam

Ppt

Should NVIDIA Pay Dividends? | Exploring Financial Strategies with Dr. Foley - Made by InVideo.ai

Theory	Explanation	Alignment with NVIDIA
Residual Theory of Dividends	Companies should pay dividends only when they have excess funds after financing all positive NPV projects.	NVIDIA might not align with this theory as it is a high-growth technology company that may prioritize reinvesting profits into research and development, acquisitions, or other growth opportunities over paying dividends.
Bird-in-Hand Theory	Investors prefer dividends because they provide a certain return, while capital gains are uncertain.	NVIDIA might not align with this theory as it might prioritize reinvestment to capitalize on growth opportunities, especially considering its position in the dynamic technology sector.
Clientele Effect	Companies tend to attract investors with similar preferences to their dividend policies.	NVIDIA may align with this theory if it has a significant portion of investors who prefer capital appreciation over dividends and therefore chooses not to pay dividends to maintain this investor base.
Signaling Theory	Paying dividends can signal to investors that a company is financially healthy and confident about its future prospects.	NVIDIA might not align with this theory as it might prefer to reinvest profits rather than signal financial health through dividend payments, especially considering its growth potential and position in the technology sector.
Tax Considerations	Dividends are typically taxed differently than capital gains. Companies might consider the tax implications of paying dividends on their investors and themselves.	NVIDIA might align with this theory as it could consider the tax implications of paying dividends, both for its investors and for the company itself, in making its dividend policy decisions.

In Class Exercise

1. According to the Residual Theory of Dividends, when should companies pay dividends?

A) When they have positive NPV projects.

B) When they have excess funds after financing all positive NPV projects.

C) When they have low debt-to-equity ratios.

Answer: B

Explanation: The Residual Theory suggests that dividends should be paid only when there are excess funds after financing all positive NPV projects.

2. What does the Bird-in-Hand Theory propose about investor preferences?

A) Investors prefer risky investments over stable returns.

B) Investors prefer companies with high debt-to-equity ratios.

C) Investors prefer dividends due to their certainty compared to uncertain capital gains.

Answer: C

Explanation: The Bird-in-Hand Theory suggests that investors prefer dividends because they provide a certain return compared to uncertain capital gains.

3. How does the Clientele Effect influence a company's dividend policy?

A) It suggests that companies attract investors with similar dividend preferences.

B) It encourages companies to pay dividends regardless of investor preferences.

C) It advises companies to pay dividends only when they have excess funds.

Answer: A

Explanation: The Clientele Effect suggests that companies tend to attract investors with similar preferences to their dividend policies.

4. What does the Signaling Theory propose about the impact of dividend payments?

A) Dividends have no impact on investor perceptions.

B) Dividends signal financial health and confidence about future prospects.

C) Dividends indicate that a company is struggling financially.

Answer: B

Explanation: The Signaling Theory suggests that paying dividends can signal to investors that a company is financially healthy and confident about its future prospects.

5. How might tax considerations influence a company's dividend policy?

A) They have no impact on dividend decisions.

B) They might encourage companies to pay dividends to attract investors.

C) They might lead companies to consider the tax implications of dividends for investors and themselves.

Answer: C

Explanation: Tax considerations might influence a company's dividend policy by leading them to consider the tax implications of dividends for investors and themselves.

6. What type of investors might prefer dividends over capital appreciation?

A) Investors seeking high-risk investments.

B) Investors with a preference for stable income streams.

C) Investors focused solely on short-term gains.

Answer: B

Explanation: Investors who prefer stable income streams are likely to prefer dividends over capital appreciation.

7. Why might a high-growth technology company like NVIDIA prioritize reinvesting profits?

A) To capitalize on growth opportunities in research, development, and acquisitions.

B) To attract investors with similar dividend preferences.

C) To signal financial health to investors.

Answer: A

Explanation: High-growth technology companies like NVIDIA might prioritize reinvesting profits to capitalize on growth opportunities rather than paying dividends.

Should NVIDIA Pursue Stock Repurchases?

Nvidia's $25 billion buyback 'a head-scratcher' for some shareholders

https://www.reuters.com/technology/nvidias-25-billion-buyback-a-head-scratcher-some-shareholders-2023-08-25/

By Lewis Krauskopf, Chibuike Oguh and Lance Tupper

August 25, 202310:42 AM

NEW YORK, Aug 25 (Reuters) - Nvidia's (NVDA.O), opens new tab move to buy back $25 billion of its shares after its stock has more than tripled this year caught some investors off-guard, even as they cheered a stellar second-quarter report.

Shares of Nvidia touched a record high on Thursday, a day after the company blew past expectations with its quarterly revenue forecast as an artificial-intelligence boom fueled demand for its chips. Nvidia shares, which had run up in the days leading up to its report, climbed more than 6% on Thursday but pared gains to end the day little changed.

However, Nvidia's stock buyback - the fifth-biggest repurchase announcement among U.S.-based companies this year, according to EPFR - surprised some investors.

Companies commonly repurchase their stock as a way to return capital to shareholders. Such buybacks can benefit a stock's price by reducing the supply of shares and increasing demand, and can boost earnings per share, a closely watched investor metric.

But while shareholders often see buybacks as an encouraging sign when a company’s stock appears cheap, Nvidia’s shares have shot up some 220% in 2023, leaving investors searching for the reasons behind the company’s move.

"It's a little bit of a head-scratcher," said King Lip, chief strategist at Baker Avenue Wealth Management, which has $2.5 billion in assets under management and counts Nvidia as a top-10 holding.

"As a shareholder, we like to see stock buybacks, but for a company like Nvidia that is growing so fast, you kind of want to see their earnings being plowed back in to the company,” Lip added.

As opposed to companies with sluggish financial performance growth that turn to buybacks to help prop up earnings per share, the announcement from Nvidia "comes as a surprise" given that they are "a hot growth tech name," said Daniel Morgan, senior portfolio manager at Synovus Trust, which owns Nvidia shares.

"The message seems to be that (Nvidia's) management believes that their stock is undervalued," Morgan said.

For some investors, an "undervalued" Nvidia might be a difficult message to stomach. Nvidia shares traded at 45 times forward 12-month earnings estimates as of Wednesday compared with about 19 times for the overall S&P 500 (.SPX), opens new tab, according to Refinitiv

A smartphone with a displayed NVIDIA logo is placed on a computer motherboard in this illustration taken March 6, 2023.

"Historically, you'd love it when a company is able to buy their stock back when it is depressed, but I don't think anybody can make the case that it is at a depressed place right now," said Tom Plumb, CEO and lead portfolio manager at Plumb Funds, which has Nvidia as one of its largest holdings.

However, Plumb said, the company might be limited in how it can deploy its resources after its deal to buy semiconductor designer Arm Holdings Ltd collapsed last year amid regulatory concerns.

"They're generating incredible amounts of cash, more than they need for their current investment strategy, and they're prohibited from buying significant complementary businesses," Plumb said. "So what are they going to do with their cash?"

Nvidia spent about 27% of revenue on research and development last year, in line with rival chip companies.

The company did not immediately respond to a request for comment….

Meanwhile, several other megacap tech and growth companies have announced even bigger buybacks this year: Apple (AAPL.O), opens new tab at $90 billion, Alphabet (GOOGL.O), opens new tab at $70 billion and Meta Platforms (META.O), opens new tab at $40 billion.

Tech companies tend to prefer using cash for buybacks over dividends, because "if they are on the hook for a dividend every quarter that may hinder their ability to take advantage of growth opportunities," said Daniel Klausner, head of U.S. public equity advisory at Houlihan Lokey.

Indeed, some investors welcomed Nvidia's buyback decision.

"It’s a show of confidence," said Francisco Bido, senior portfolio manager for F/M Investments' large cap focused fund, which holds Nvidia shares. "If they had better use for (the cash), I am pretty sure they would have done it."

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.

Will Nvidia Stock Split In 2024? https://www.forbes.com/sites/investor-hub/article/will-nvidia-stock-split-2024/?sh=7c6e16b049ec

· Based on Nvidia's split history and its current price, a 2024 split is likely. Analyst Ken Mahoney, president and CEO of Mahoney Asset Management, agrees, although with a slightly longer timeline. Mahoney recently told Bloomberg News that he predicts Nvidia will split within 12 months.

· The split ratio will depend on how the stock performs over the next few months. If NVDA has another standout earnings release that drives the price higher, we could see a six-for-one exchange before year-end. That would give shareholders of record an extra five shares for each one they own on the split date.

· Bottom Line

With a high stock price, good momentum and an optimistic outlook, Nvidia is poised for a stock split in 2024. A split doesn't change the stock's potential for volatility, so do your research to ensure the move is right before you buy.

What is a 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.

Major Dividend Policy Theory Explained (FYI only)

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.

Self-Test on Dividend Knowledge (FYI)

Final Exam (during final week, in class, non-cumulative, similar to case study and in class exercise)

4/22-25, from 1pm to 5 pm, in office 118A
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)

Happy Graduation!

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

What Is Expectations Theory (video)

Understanding Expectations Theory

Expectations Theory

Example of Calculating Expectations Theory

Disadvantages of Expectations Theory

· 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

***** How much does Amazon worth in 2019?”

FYI: 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)

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

Introduction to Monte Carlo Simulation in Excel 2016 (youtube)

Mergers rules of SEC

Nvidia's $25 billion buyback 'a head-scratcher' for some shareholders

What Is Expectations Theory `(video`)