FIN435 Class Web
Page, Spring '23
Jacksonville
University
Instructor:
Maggie Foley
Exit Exam Questions (will be posted
in week 10 on blackboard)
How to find a
good job? (video; Thanks to Dr. Simak)
Weekly SCHEDULE, LINKS, FILES and Questions
Week |
Coverage, HW, Supplements -
Required |
|
Reading Materials |
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Week 1 |
Marketwatch Stock Trading Game (Pass code: havefun) 1. URL for your game: 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)
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Chapter 6 Interest rate Part I: Who determines interest rates in the US? Market data website: Market watch on Wall Street Journal has daily yield curve and
interest rate information.
|
NAME |
COUPON |
PRICE |
YIELD |
1 MONTH |
1 YEAR |
TIME (EST) |
GB3:GOV 3 Month |
0.00 |
4.42 |
4.55% |
+33 |
+451 |
12:31 AM |
GB6:GOV 6 Month |
0.00 |
4.59 |
4.76% |
+11 |
+458 |
12:31 AM |
GB12:GOV 12 Month |
0.00 |
4.41 |
4.62% |
-2 |
+424 |
12:31 AM |
GT2:GOV 2 Year |
4.25 |
100.07 |
4.21% |
-13 |
+332 |
12:31 AM |
GT5:GOV 5 Year |
3.88 |
100.93 |
3.66% |
-10 |
+215 |
12:31 AM |
GT10:GOV 10 Year |
4.13 |
104.89 |
3.53% |
-5 |
+177 |
12:31 AM |
GT30:GOV 30 Year |
4.00 |
106.22 |
3.65% |
+10 |
+157 |
12:31 AM |
|
Treasury Inflation Protected Securities (TIPS)
(1/10/2023)
NAME |
COUPON |
PRICE |
YIELD |
1 MONTH |
1 YEAR |
TIME (EST) |
GTII5:GOV 5 Year |
1.63 |
100.66 |
1.48% |
+5 |
+280 |
1/9/2023 |
GTII10:GOV 10 Year |
0.63 |
93.91 |
1.31% |
+1 |
+209 |
1/9/2023 |
GTII20:GOV 20 Year |
0.75 |
87.82 |
1.48% |
+7 |
+179 |
1/9/2023 |
GTII30:GOV 30 Year |
0.13 |
69.44 |
1.41% |
+14 |
+160 |
1/9/2023 |
Federal Reserve Rates (1/10/2023)
RATE |
CURRENT |
1 YEAR PRIOR |
|
4.32 |
0.07 |
|
4.50 |
0.25 |
|
7.50 |
3.25 |
Municipal Bonds (1/10/2023)
NAME |
YIELD |
1 DAY |
1 MONTH |
1 YEAR |
TIME (EST) |
|
2.54% |
-4 |
+2 |
+222 |
1/9/2023 |
|
2.38% |
-4 |
-11 |
+199 |
1/9/2023 |
|
2.35% |
-5 |
-15 |
+159 |
1/9/2023 |
|
2.45% |
-4 |
-14 |
+126 |
1/9/2023 |
|
3.42% |
-4 |
-9 |
+174 |
1/9/2023 |
https://www.bloomberg.com/markets/rates-bonds/government-bonds/us
In
Class Exercise:
·
Please draw the yield curve based on the
above information;
·
What can be predicted from the current
yield curve?
·
What is TIPs? What is municipal bond? What
is Fed Fund Rate?
·
Why are the TIPS’ rates negative?
For
Daily Treasury rates such as the following, please visit
Date 1 Mo 2 Mo 3 Mo 4
Mo 6 Mo 1 Yr 2 Yr 3 Yr 5
Yr 7 Yr 10 Yr 20 Yr 30 Yr 01/03/2023 4.17 4.42 4.53 4.70 4.77 4.72 4.40 4.18 3.94 3.89 3.79 4.06 3.88 01/04/2023 4.20 4.42 4.55 4.69 4.77 4.71 4.36 4.11 3.85 3.79 3.69 3.97 3.81 01/05/2023 4.30 4.55 4.66 4.75 4.81 4.78 4.45 4.18 3.90 3.82 3.71 3.96 3.78 01/06/2023 4.32 4.55 4.67 4.74 4.79 4.71 4.24 3.96 3.69 3.63 3.55 3.84 3.67 01/09/2023 4.37 4.58 4.70 4.74 4.83 4.69 4.19 3.93 3.66 3.60 3.53 3.83 3.66 |
For class
discussion: Why do interest rates change daily? Interest rates are
determined by whom in the U.S.?
“ interest
rates are determined by
the Federal Open Market Committee (FOMC), which consists of seven governors
of the Federal Reserve Board and five Federal Reserve Bank presidents. The
FOMC meets eight times a year to determine the near-term direction of
monetary policy and interest rates.”
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
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%.
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.
Retail banks
are also partly responsible for controlling interest
rates. Loans and mortgages they offer
may have rates that change based on several factors including their needs,
the market, and the individual consumer.
For example, someone with a
lower credit score may be at a higher risk of default, so they pay a higher
interest rate. The same applies to credit cards. Banks will offer different
rates to different customers, and will also increase the rate if there is a
missed payment, bounced payment, or for other services like balance transfers
and foreign exchange.
Monday 1/15/2020
For daily yield curve, please visit https://www.gurufocus.com/yield_curve.php
Understanding the yield curve (video)
Introduction to the yield curve (khan academy)
Summary of Yield Curve Shapes and Explanations
Normal Yield Curve
When bond investors expect the economy to hum along at normal rates of growth
without significant changes in inflation rates or available capital, the
yield curve slopes gently upward. In the absence of economic disruptions,
investors who risk their money for longer periods expect to get a bigger
reward — in the form of higher interest — than those who risk their money for
shorter time periods. Thus, as maturities lengthen, interest rates get
progressively higher and the curve goes up.
Steep Curve –
Economy is improving
Typically the yield on 30-year Treasury bonds is three percentage points
above the yield on three-month Treasury bills. When it gets wider than that —
and the slope of the yield curve increases sharply — long-term bond holders
are sending a message that they think the economy will improve quickly in the
future.
Inverted Curve –
Recession is coming
At first glance an inverted yield curve seems like a paradox. Why would
long-term investors settle for lower yields while short-term investors take
so much less risk? The answer is that long-term investors will settle for
lower yields now if they think rates — and the economy — are going even lower
in the future. They're betting that this is their last chance to lock in
rates before the bottom falls out.
Flat
or Humped Curve
To become inverted, the yield curve
must pass through a period where long-term yields are the same as short-term rates.
When that happens the shape will appear to be flat or, more commonly, a
little raised in the middle.
Unfortunately, not all flat or humped curves
turn into fully inverted curves. Otherwise we'd all get rich plunking our
savings down on 30-year bonds the second we saw their yields start falling
toward short-term levels.
On the other hand, you shouldn't discount a
flat or humped curve just because it doesn't guarantee a coming recession.
The odds are still pretty good that economic slowdown and lower interest
rates will follow a period of flattening yields.
Formula --- Break down of interest rate
r = r* + IP + DRP + LP + MRP
r = required return on a debt security
r* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium
MRPt = 0.1% (t – 1)
DRPt + LPt = Corporate spread * (1.02)(t−1)
Assignments:
·
Chapter six case study
(due with first mid term exam) --- video
is available on blackboard under collaborate/recording,
as well as here www.jufinance.com/video/fin435_chapter_6_case_video_1.mp4
(1/18/2023)
www.jufinance.com/video/fin435_chapter_6_case_video_2.mp4
(1/23/2023)
·
Critical thinking question 1: Why are TIPS yields so
low? Shall you invest in TIPS? Why or why not? (optional for extra credits)
·
Critical thinking question 2: Do you think we will
enter a recession as predicted by the inverted yield curve? (optional for
extra credits)
What is interest rates
https://www.youtube.com/watch?v=Pod73wrvdSQ
https://www.youtube.com/watch?v=pTpK6Te6tYI
How interest rates are set
https://www.youtube.com/watch?v=Oz5hNemSdWc
What happens if Fed raise interest rates
https://www.youtube.com/watch?v=4OP-3Ui6K1s
JEAN
FOLGER
dated Dec 6, 2019Inflation and interest rates are often linked and frequently
referenced in macroeconomics
. Inflation refers to
the rate at which prices for goods and services rise. In the United
States, the interest rate, or the amount charged by a
lender to a borrower, is based on the federal funds rate
that is
determined by the Federal Reserve (sometimes called "the Fed").
By setting the target for the federal funds rate, the Fed has
at its disposal a powerful tool that it uses to influence the rate of
inflation. This tool enables the Fed to expand or contract the money supply as
needed to achieve target employment rates, stable prices, and stable economic growth
.
KEY TAKEAWAYS
Under a system of fractional reserve
banking, interest
rates and inflation tend to be inversely correlated. This relationship
forms one of the central tenets of contemporary monetary policy: Central
banks manipulate short-term interest rates to affect the rate of inflation in
the economy.
The below chart demonstrates the inverse correlation between
interest rates and inflation. In the chart, CPI refers to the Consumer Price Index
, a measurement that
tracks changes in prices. Changes in the CPI are used to identify periods of
inflation and deflation
.
In general, as interest rates are reduced, more people
are able to borrow more money. The result is that consumers have more money
to spend, causing the economy to grow and inflation to increase.
The opposite holds true for rising interest rates
. As interest rates are increased, consumers tend to save as returns from
savings are higher. With less disposable income
being spent as a result of the increase in the
interest rate, the economy slows and inflation decreases.
To better understand how the relationship between inflation
and interest rates works, it's important to understand the banking system,
the quantity theory of money
, and the role
interest rates play.
Fractional Reserve Banking
The world currently uses a fractional reserve banking system.
When someone deposits $100 into the bank, they maintain a claim on that
$100. The bank, however, can lend out those dollars based on the reserve ratio
set by the
central bank. If the reserve ratio is 10%, the bank can lend out the other
90%, which is $90 in this case. A 10% fraction of the money stays in the bank
vaults.
As long as the subsequent $90 loan is outstanding, there are
two claims totaling $190 in the economy. In other words, the supply of money
has increased from $100 to $190. This is a simple demonstration of how
banking grows the money supply.
In economics, the quantity theory of money states that
the supply and demand
for money
determines inflation. If the money supply grows, prices tend to rise, because
each individual piece of paper becomes less valuable.
Hyperinflation is an
economic term used to describe extreme inflation where price increases are
rapid and uncontrolled. While central banks generally target an annual inflation rate
of around 2% to 3% as an acceptable rate for a healthy economy,
hyperinflation goes well beyond this. Countries that experience
hyperinflation
have an inflation rate of 50% or more per month.
The interest rate acts as a price for holding or loaning
money. Banks pay an interest rate on savings in order to attract depositors.
Banks also receive an interest rate for money that is loaned from their
deposits.
When interest rates are low, individuals and businesses tend
to demand more loans. Each bank loan increases the money supply in a
fractional reserve banking system. According to the quantity theory of
money, a growing money supply
increases inflation.
Thus, low interest rates tend to result in more inflation. High interest
rates tend to lower inflation.
This is a very simplified version of the relationship, but it
highlights why interest rates and inflation tend to be inversely correlated.
The Federal Open Market Committee
(FOMC) meets
eight times each year to review economic and financial conditions and decide
on monetary policy
. Monetary policy
refers to the actions taken that affect the availability and cost of money
and credit. At these meetings, short-term interest rate targets are
determined.
Using economic indicators such as the Consumer Price Index
(CPI) and the Producer Price Indexes
(PPI), the Fed will establish interest rate
targets intended to keep the economy in balance. By moving interest rate
targets up or down, the Fed attempts to achieve target employment rates,
stable prices, and stable economic growth. The Fed will raise interest rates
to reduce inflation and decrease rates to spur economic growth.
Investors and traders keep a close eye on the FOMC rate
decisions. After each of the eight FOMC meetings, an announcement is made
regarding the Fed's decision to increase, decrease, or maintain key interest
rates. Certain markets may move in advance of the anticipated interest rate
changes and in response to the actual announcements. For example, the U.S.
dollar typically rallies in response to an interest rate increase, while
the bond market
falls in
reaction to rate hikes.
Here’s what the inverted yield curve means for your portfolio
https://www.cnbc.com/2022/10/31/what-an-inverted-yield-curve-means-for-the-economy.html
PUBLISHED MON, OCT 31 20223:29 PM
EDT
Kate Dore, CFP®
KEY POINTS
·
When shorter-term government bonds
have higher yields than long-term, which is known as yield curve inversions,
it’s one signal of a future recession.
·
“The yield curve is not perfect,
but it does better in general than standard forecasts,” said Robert Barbera,
director of Johns Hopkins Center for Financial Economics.
·
As investors brace for another
interest rate hike from the Federal Reserve, many are closely watching
signals about the future of the economy.
This week, investors are expecting
the fourth 0.75 percentage point increase, which may continue to affect
government bond yields.
As the Fed takes further action to
fight inflation, many are watching the so-called “inverted yield curve,” one
sign there’s an economic slump on the horizon.
The
“yield curve” is a snapshot of the bond market, showing the interest
investors may expect to earn from bonds with different maturities. These
expectations may change based on what’s happening in the economy.
What the inverted yield curve means
Generally, longer-term bonds pay more than bonds with shorter
maturities. Since longer-maturity bonds are more vulnerable to price changes,
investors expect a “premium,” explained Preston Caldwell, head of U.S.
economics for Morningstar Research Services.
“In normal times, the yield curve slopes upwards,” he said. But there’s
currently a downward sloping curve, also known as an “inverted yield,” with
the 2-year Treasury paying more than
the 10-year Treasury
We are positioning for a U.S. recession in
2023, says JPMorgan’s Elyse Ausenbaugh
While many experts believe the
inverted yield curve is one signal of a future recession, Caldwell said it’s
more “correlative,” showing how the markets expect the Federal Reserve to
respond in the near term.
What’s more, he said there’s “too
much focus” on the “will there or won’t there be recession” question, and not
enough attention on the severity of a possible recession, which the yield
curve doesn’t show, he said.
‘Real economic indicators are going
to suffer’
While a yield curve inversion is only one signal of a possible
recession, it shouldn’t be ignored, particularly at the lower end of the
curve, experts say.
“Economists have a very, very
consistent record of not forecasting recessions,” said Robert Barbera,
director of the Center for Financial Economics at Johns Hopkins University.
“The yield curve is not perfect, but it does better in general than standard
forecasts.”
However,
it “certainly looks like short rates are going up until that inflation rate
breaks in a big way,” he said. “And unfortunately, if we look at the
history of that dynamic, it’s likely that real economic indicators are going
to suffer alongside or ahead of that break for inflation.”
Videos (optional)
(optional)
https://ycharts.com/indicators/10_2_year_treasury_yield_spread
2-year Treasury yield tops 10-year
rate, a ‘yield curve’ inversion that could signal a recession
PUBLISHED THU, MAR 31 20225:09 PM
EDTUPDATED THU, MAR 31 20229:13 PM EDT
Patti Domm
The
2-year and 10-year Treasury yields inverted for the first time since
2019 on Thursday, sending a possible warning signal that a recession could be
on the horizon.
The bond market phenomenon means the rate of the 2-year note is now
higher than the 10-year note yield.
This part of the yield curve is the most closely watched and typically
given the most credence by investors that the economy could be heading for a
downturn when it inverts. The 2-year to 10-year spread was last in negative
territory in 2019, before pandemic lockdowns sent the global economy into a
steep recession in early 2020.
The yield on the 10-year Treasury
fell to 2.331%, while the yield on the 2-year Treasury was at 2.337% at one
point in late trading Thursday. After a brief inversion, both yields were
basically trading at the 2.34% level in the latest trading.
When the curve inverts, “there has been a better than two-thirds chance
of a recession at some point in the next year and a greater than 98% chance
of a recession at some point in the next two years,” according
to Bespoke.
Some data providers showed the 2-10
spread technically inverted for a few seconds earlier Tuesday, but CNBC data
did not confirm the inversion until now. And to be sure, many economists
believe the curve needs to stay inverted for a substantial amount of time
before it gives a valid signal.
In general, a simple way to look at
the importance of the yield curve is to think about what it means for a bank.
The yield curve measures the spread between a bank’s cost of money versus
what it will make by lending it out or investing it over a longer period of time.
If banks can’t make money, lending slows and so does economic activity.
While the yield curve has sent
somewhat reliable signals about pending recessions, there is often a long
time lag and analysts say there needs to be corroborating evidence before investors
need to fear a recession is around the corner.
Some of those other signals could include a slowdown in hiring and a
sudden increase in unemployment, or early warnings in ISM and other data that
manufacturing activity could be slowing. Analysts say
the yield curve’s inversion could also reverse should there be a resolution
to the war in Ukraine or the Federal Reserve pauses in its rate-hiking cycle.
According to MUFG Securities, the yield curve inverted 422 days ahead of
the 2001 recession, 571 days ahead of the 2007-to-2009 recession and 163 days
before the 2020 recession.
“Most of time, it is a recession
harbinger but not all the time,” said Julian Emanuel, head of equity,
derivatives and quantitative strategy at Evercore ISI. He noted one time when
the curve inverted but the economy avoided a recession was in 1998 during the
Russian debt crisis which was followed by the Long Term Capital Management
failure.
“The nice thing about the last 30-year
history is that there’s been so few recessions that you don’t want to say
something is a golden rule, particularly when there are not enough
observations and there’s one big standout to that rule,” he said.
Bespoke notes that after six
instances where the 2-year and 10-year yields inverted going back to 1978,
the stock market continued to perform positively. The S&P 500 was up an average 1.6% a month after the
inversions but was up an average 13.3% a year later.
“Basically what tends to happen is
over the long haul is that yes in most cases there is a recession, but many
times it is six- to 18-months in the distance and the stock market does not
tend to peak until between two and 12-months prior to the onset of a
recession,” said Emanuel. “Again, while the probability of a recession in
Europe has become a base case, that’s not the case for the U.S.”
Some bond pros do not believe the
yield curve inversion is as reliable a recession predictor as it once was
because the Federal Reserve has become such a big player in the market. The
Fed’s nearly $9 trillion balance sheet holds many Treasurys, and strategists
believe it has suppressed interest rates at the long end, meaning the yields
of the 10-year note and the 30-year bond should be higher.
In fact, Richard Bernstein
Associates notes that if the Fed had never engaged in quantitative easing,
the 10-year yield could be closer to 3.7%. Were it not for the central bank’s
bond-buying program, the yield curve for the 2-year and the 10-year would
then be more like 100 basis points apart, instead of inverted. (1 basis point
equals 0.01%.)
Strategists say the 2-year yield
has climbed most rapidly since it is the part of the curve most reflective of
Fed rate hikes. The 10-year has also moved higher on the Fed, but it has also
been held back by flight-to-quality trades as investors keep an eye on the
Ukraine war. Yields move opposite price.
Some market pros believe the 3-month yield to the 10-year yield is a
more accurate recession forecaster, and that curve has not flattened at all. That spread
has been widening, a signal for better economic growth.
Chapter 6 Interest rate Part II: Term Structure of Interest rate
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)č c = ((1+a)^N / (1+b)^m)^(1/(N-M))-1
Or
approximately,
N*a
= M*b +(N-M)*(c)č c = (N*a – M*b) /(N-M)
(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.”
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
)
By CHRIS B. MURPHY Updated Apr 21, 2019
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.
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 aims to help investors make decisions by
using long-term rates, typically from government bonds, to forecast the rate
for short-term bonds.
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:
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 č 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 č 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 č 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 č 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 č Default = liquidity = 0, maturity=?
2-year T-notes = 6.2% = r* + inflation + maturity = 3% + 3% +
maturity
5 One-year
Treasury securities yield 5%. The market anticipates that 1 year from now,
1-year Treasury securities will yield 6%. If the pure expectations theory is
correct, what is the yield today for 2-year Treasury securities? (answer: 5.5%)
Or,
Real Interest rate in the US from 2000-2022
https://fred.stlouisfed.org/series/REAINTRATREARAT1YE
Three Month
T-Bill rate (a proxy of the risk free rate)
https://www.cnbc.com/quotes/US3M
Chapter 7
Market data website:
1. FINRA
http://finra-markets.morningstar.com/BondCenter/Default.jsp
(FINRA bond market data)
2. WSJ
Market watch on Wall
Street Journal has daily yield curve and bond yield information.
http://www.marketwatch.com/tools/pftools/
http://www.youtube.com/watch?v=yph8TRldW6k
Simplified Balance Sheet of WalMart
Balance Sheet
of WalMart https://www.nasdaq.com/market-activity/stocks/wmt/financials
Period Ending: |
1/31/2022 |
1/31/2021 |
1/31/2020 |
1/31/2019 |
Current Assets |
||||
Cash and Cash Equivalents |
$14,760,000 |
$17,741,000 |
$9,465,000 |
$7,722,000 |
Short-Term Investments |
-- |
-- |
-- |
-- |
Net Receivables |
$8,280,000 |
$6,516,000 |
$6,284,000 |
$6,283,000 |
Inventory |
$56,511,000 |
$44,949,000 |
$44,435,000 |
$44,269,000 |
Other Current Assets |
$1,519,000 |
$20,861,000 |
$1,622,000 |
$3,623,000 |
Total Current Assets |
$81,070,000 |
$90,067,000 |
$61,806,000 |
$61,897,000 |
Long-Term Assets |
||||
Long-Term Investments |
-- |
-- |
-- |
-- |
Fixed Assets |
$112,624,000 |
$109,848,000 |
$127,049,000 |
$111,395,000 |
Goodwill |
$29,014,000 |
$28,983,000 |
$31,073,000 |
$31,181,000 |
Intangible Assets |
-- |
-- |
-- |
-- |
Other Assets |
$22,152,000 |
$23,598,000 |
$16,567,000 |
$14,822,000 |
Deferred Asset Charges |
-- |
-- |
-- |
-- |
Total Assets |
$244,860,000 |
$252,496,000 |
$236,495,000 |
$219,295,000 |
Current Liabilities |
||||
Accounts Payable |
$82,172,000 |
$87,349,000 |
$69,549,000 |
$69,647,000 |
Short-Term Debt / Current Portion of Long-Term Debt |
$3,724,000 |
$3,830,000 |
$6,448,000 |
$7,830,000 |
Other Current Liabilities |
$1,483,000 |
$1,466,000 |
$1,793,000 |
-- |
Total Current Liabilities |
$87,379,000 |
$92,645,000 |
$77,790,000 |
$77,477,000 |
Long-Term Debt |
$39,107,000 |
$45,041,000 |
$48,021,000 |
$50,203,000 |
Other Liabilities |
$13,009,000 |
$12,909,000 |
$16,171,000 |
-- |
Deferred Liability Charges |
$13,474,000 |
$14,370,000 |
$12,961,000 |
$11,981,000 |
Misc. Stocks |
$8,638,000 |
$6,606,000 |
$6,883,000 |
$7,138,000 |
Minority Interest |
-- |
-- |
-- |
-- |
Total Liabilities |
$161,607,000 |
$171,571,000 |
$161,826,000 |
$146,799,000 |
Stock Holders Equity |
||||
Common Stocks |
$276,000 |
$282,000 |
$284,000 |
$288,000 |
Capital Surplus |
$86,904,000 |
$88,763,000 |
$83,943,000 |
$80,785,000 |
Retained Earnings |
-- |
-- |
-- |
-- |
Treasury Stock |
$4,839,000 |
$3,646,000 |
$3,247,000 |
$2,965,000 |
Other Equity |
-$8,766,000 |
-$11,766,000 |
-$12,805,000 |
-$11,542,000 |
Total Equity |
$83,253,000 |
$80,925,000 |
$74,669,000 |
$72,496,000 |
Total Liabilities & Equity |
$244,860,000 |
$252,496,000 |
$236,495,000 |
$219,295,000 |
For discussion:
· What is this “long term debt”?
· Who is the lender of this “long term debt”?
So this long term debt is called bond in the financial
market. Where can you find the pricing information and other specifications
of the bond issued by WMT?
Investing Basics: Bonds(video)
FINRA – Bond market information
http://finra-markets.morningstar.com/BondCenter/Default.jsp
Go to http://finra-markets.morningstar.com/BondCenter/Default.jsp , the bond market data
website of FINRA to find bond information. For example, find bond sponsored
by Wal-mart
Or, just go to www.finra.org, č Investor
center č market data č bond č corporate
bond
https://finra-markets.morningstar.com/BondCenter/Results.jsp
2. Understand what is coupon, coupon rate, yield, yield to
maturity, market price, par value, maturity, annual bond, semi-annual bond,
current yield.
Refer to the following bond at http://finra-markets.morningstar.com/BondCenter/BondDetail.jsp?ticker=C104227&symbol=WMT.GP
Reading
material:
Interest rate risk — When Interest rates Go up, Prices of Fixed-rate Bonds Fall, issued by SEC at https://www.sec.gov/files/ib_interestraterisk.pdf
Question:
What shall investors do as interest
rates are expected to rise in March 2022?
All Bonds are Subject to
Interest Rate Risk—Even If the Bonds Are Insured or
Government Guaranteed
There
is a misconception that, if a bond is insured or is a u.s. government
obligation, the bond will not lose value. In fact, the U.S. government does not guarantee the market price or value of
the bond if you sell the bond before it matures. This is because the
market price or value of the bond can change over time based on several
factors, including market interest rates. https://www.sec.gov/files/ib_interestraterisk.pdf
Relationship between bond prices
and interest rates (Khan academy)
Here’s how rising interest rates may affect your bond
portfolio in retirement
PUBLISHED WED, JAN 19
20228:00 AM EST, Kate Dore, CFP®
https://www.cnbc.com/2022/01/19/heres-how-rising-interest-rates-may-affect-your-bond-portfolio-.html
KEY POINTS
·
Generally, market interest
rates and bond prices move in opposite directions, meaning as rates increase,
bond values will typically fall.
·
Retirees may reduce interest rate
risk by choosing bonds with a shorter duration, which are less sensitive to
rate hikes.
·
However, rising interest rates
may still be good for retirees with a longer timeline, experts say.
Many retirees rely on bonds for income, lower risk and portfolio
growth. However, as the Federal Reserve prepares to raise interest rates,
some worry about the effects on their nest egg.
The cost of living has swelled for months, with the Consumer
Price Index, the key measure of inflation, rising 7% year over year in
December, the fastest since 1982, according to the U.S. Department of Labor.
Last week, Federal
Reserve Chairman Jerome Powell said he expects a series of rate hikes this
year, with reduced pandemic support from the central bank, to quell rising
inflation.
This may alarm investors since
market interest rates and bond prices typically move in opposite directions,
meaning higher rates generally cause bond values to fall, known as interest
rate risk.
For example, let’s say you have a 10-year $1,000 bond paying a
3% coupon. If market interest rates rise to 4% in one year, the asset will
still pay 3%, but the bond’s value may drop to $925.
The reason for
the price dip is new bonds may be issued with the higher 4% coupon, making
the original 3% bond less attractive unless someone can buy it at a
discount.
With higher yields elsewhere, investors tend to sell their
current bonds to purchase the higher-paying ones, and heavy selling causes
prices to slide, explained certified financial planner Brad Lineberger,
president of Carlsbad, California-based Seaside Wealth Management.
Why bond
duration matters
Another
fundamental concept of bond investing is so-called duration, measuring a
bond’s sensitivity to interest rate changes. Although it’s expressed in
years, it’s different from the bond’s maturity since it factors in the
coupon, time to maturity and yield paid through the term.
As a rule of thumb, the longer a bond’s duration, the more
sensitive it will be to interest rate hikes, and the more its price will
decline, Lineberger said.
Generally, if you’re
trying to reduce interest rate risk, you’ll want to consider bonds or bond
funds with a shorter duration, said Paul Winter, a CFP and owner of Five Seasons Financial
Planning in Salt Lake City.
“Also, bonds with higher coupon rates and lower credit quality
tend to be less sensitive to higher interest rates, other factors being
equal,” he said.
A longer timeline
While rising interest
rates will cause bond values to decrease, eventually, the declines will be
more than offset as bonds mature and can be reinvested for higher yields, said CFP Anthony Watson, founder and president of Thrive
Retirement Specialists in Dearborn, Michigan.
“Rising interest
rates are good for retirees with a longer-term time frame,” he said, and that’s most people in their retirement years.
The best way to
manage interest rate risk is with a diversified portfolio, including
international bonds, with short to immediate maturities that are less
affected by rate hikes and can be reinvested sooner, Watson said.
For class discussion:
What is duration? How to calculate a bond’s duration? a
portfolio’s duration?
Bond Portfolio Duration (FYI)
There are two ways to calculate the duration of a bond
portfolio:
1)
The weighted average of the
time to receipt of aggregate cash flows. This method is based on the cash
flow yield, which is the internal rate of return on the aggregate cash flows.
Limitations: This method cannot be used for bonds with embedded
options or for floating-rate notes due to uncertain future cash flows. The
cash flow yield is not commonly calculated. The change in cash flow yield is
not necessarily the same as the change in the yields-to-maturity on the
individual bonds. Interest rate risk is not usually expressed as a change in
the cash flow yield.
2)
The weighted average of the
durations of individual bonds that compose the portfolio. The weight is the
proportion of the portfolio that a bond comprises.
3)
Portfolio Duration = w1D1 + w2D2
+ w3D3 + ... + wkDk
wi = the market value of bond i / market value of the
portfolio
Di = the duration of bond i
k = the number of bonds in the portfolio
This method is simpler to use and quite accurate when the yield
curve is flat. Its main limitation is that it assumes a parallel shift in the
yield curve.
In class exercises
Bond Pricing Excel Formula
To calculate bond price in EXCEL (annual
coupon bond):
Price=abs(pv(yield to maturity, years left to maturity,
coupon rate*1000, 1000)
To calculate yield to maturity (annual coupon bond)::
Yield to maturity = rate(years left to maturity, coupon
rate *1000, -price, 1000)
To calculate bond price (semi-annual coupon bond):
Price=abs(pv(yield to maturity/2, years left to
maturity*2, coupon rate*1000/2, 1000)
To calculate yield to maturity (semi-annual coupon
bond):
Yield to maturity = rate(years left to maturity*2,
coupon rate *1000/2, -price, 1000)*2
1.
AAA firm’ bonds will mature in eight years, and coupon is $65.
YTM is 8.2%. Bond’s market value? ($903.04, abs(pv(8.2%, 8, 65, 1000))
·
Rate 8.2%
·
Nper 8
·
Pmt 65
·
Pv ?
·
FV 1000
2. AAA firm’s bonds’ market value is $1,120, with
15 years maturity and coupon of $85. What is YTM? (7.17%,
rate(15, 85, -1120, 1000))
·
Rate ?
·
Nper 15
·
Pmt 85
·
Pv -1120
·
FV 1000
3. Sadik
Inc.'s bonds currently sell for $1,180 and have a par value of
$1,000. They pay a $105 annual coupon
and have a 15-year maturity, but they can be called in 5 years at
$1,100. What is their yield
to call (YTC)? (7.74%, rate(5, 105, -1180, 1100)) What is their yield to maturity (YTM)? (8.35%, rate(15,
105, -1180, 1000))
·
Rate ?
·
Nper 15
·
Pmt 105
·
Pv -1180
·
FV 1000
4. Malko
Enterprises’ bonds currently sell for $1,050. They have a 6-year
maturity, an annual coupon of $75, and a par value of $1,000. What
is their current yield? (7.14%,
75/1050)
5. Assume
that you are considering the purchase of a 20-year, noncallable bond with an
annual coupon rate of 9.5%. The bond has a face value of $1,000,
and it makes semiannual interest payments. If you require an 8.4%
nominal yield to maturity on this investment, what is the maximum price you
should be willing to pay for the bond? ($1,105.69, abs(pv(8.4%/2, 20*2, 9.5%*1000/2, 1000)) )
·
Rate 8.4%/2
·
Nper 20*2
·
Pmt 95/2
·
Pv ?
·
FV 1000
6. Grossnickle
Corporation issued 20-year, non-callable, 7.5% annual coupon bonds at their
par value of $1,000 one year ago. Today, the market interest rate
on these bonds is 5.5%. What is the current price of the bonds,
given that they now have 19 years to maturity? ($1,232.15, abs(pv(5.5%, 19, 75, 1000)))
·
Rate 7.5%/2
·
Nper 19
·
Pmt 75
·
Pv ?
·
FV 1000
7. McCue
Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a
25-year maturity, and a $1,000 par value, but they can be called in 5 years
at $1,050. Assume that no costs other than the call premium would
be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates
expected to remain at current levels on into the future. What is
the difference between this bond's YTM and its YTC? (Subtract the
YTC from the YTM; it is possible to get a negative answer.) (2.62%, YTM = rate(25, 90, -1250, 1000), YTC =
rate(5, 90, -1250, 1050))
·
Rate ? ------------ ?
·
Nper 25 ------------- 5
·
Pmt 90 ------------ 90
·
Pv -1250 ------------ -1250
·
FV 1000 ------------ 1000
8. Taussig
Corp.'s bonds currently sell for $1,150. They have a 6.35% annual
coupon rate and a 20-year maturity, but they can be called in 5 years at
$1,067.50. Assume that no costs other than the call premium would
be incurred to call and refund the bonds, and also assume that the yield
curve is horizontal, with rates expected to remain at current levels on into
the future. Under these conditions, what rate of return should an
investor expect to earn if he or she purchases these bonds? (4.2%, rate(5, 63.5, -1150, 1067.5))
9. A
25-year, $1,000 par value bond has an 8.5% annual payment
coupon. The bond currently sells for $925. If the yield
to maturity remains at its current rate, what will the price be 5 years from
now? ($930.11, rate(25, 85, -925, 1000),
abs(pv( rate(25, 85, -925, 1000), 20, 85, 1000))
Assignment:
Chapter 7 Case Study – Due with the first mid term
exam
· Case video part I – did in
class on 1/30/2023
· Case video part II – did in
class on 2/1/2023
Critical
thinking question= (optional for extra credits)
·
How to trade bonds when market interest rates rise?
(optional for extra credits)
· Critical thinking question: Calculate the duration and the convexity of the following bond:
Assume that you are considering the purchase of a 20-year,
noncallable bond with an annual coupon rate of 9.5%. The bond has
a face value of $1,000, and it makes semiannual interest
payments. If you require an 8.4% nominal yield to maturity on this
investment, what are the duration and the convexity of this bond?
·
---- FYI: https://www.youtube.com/watch?v=cjlq08iDlIw
Bond 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 Duration Calculator
(FYI)
https://exploringfinance.com/bond-duration-calculator/
Duration (FYI)
By ADAM HAYES Updated August 18, 2021, Reviewed by GORDON
SCOTT,
Fact checked by KIRSTEN ROHRS SCHMITT
https://www.investopedia.com/terms/d/duration.asp
What Is Duration?
Duration is a measure of the sensitivity of the price of a
bond or other debt instrument to a change in interest rates. A bond's
duration is easily confused with its term or time to maturity because certain
types of duration measurements are also calculated in years.
However, a bond's term is a linear measure of the years until
repayment of principal is due; it does not change with the interest rate
environment. Duration, on the other hand, is non-linear and accelerates as
the time to maturity lessens.
KEY TAKEAWAYS
·
Duration measures a bond's
or fixed income portfolio's price sensitivity to interest rate changes.
·
Macaulay duration estimates
how many years it will take for an investor to be repaid the bond’s price by its total cash flows.
·
Modified duration measures
the price change in a bond given a 1% change in interest rates.
·
A fixed income portfolio's
duration is computed as the weighted average of individual bond durations
held in the portfolio.
How Duration Works
Duration can measure how
long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash
flows. Duration can also measure the sensitivity of a bond's or fixed income
portfolio's price to changes in interest rates.
In general, the higher the duration,
the more a bond's price will drop as interest rates rise (and the greater the
interest rate risk). For example, if rates were to rise 1%, a bond or bond
fund with a five-year average duration would likely lose approximately 5% of
its value.
Certain factors can
affect a bond’s duration, including:
Time to maturity: The longer
the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but
have different maturities. A bond that matures faster—say,
in one year—would repay its true cost faster than a
bond that matures in 10 years. Consequently, the shorter-maturity bond would
have a lower duration and less risk.
Coupon rate: A bond’s coupon rate is a key factor
in calculation duration. If we have two bonds that are identical with the
exception of their coupon rates, the bond with the higher coupon rate will
pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the
duration, and the lower the interest rate risk.
Types of Duration
The duration of a bond in practice can refer to two different
things. The Macaulay duration is the
weighted average time until all the bond's cash flows are paid. By accounting
for the present value of future bond payments, the Macaulay duration helps an investor evaluate and compare bonds
independent of their term or time to maturity.
The second type of duration is called modified duration.
Unlike Macaulay's duration, modified
duration is not measured in years. Modified duration measures the expected
change in a bond's price to a 1% change in interest rates.
In order to understand modified duration, keep in mind that
bond prices are said to have an inverse relationship with interest rates.
Therefore, rising interest rates
indicate that bond prices are likely to fall, while declining interest rates
indicate that bond prices are likely to rise.
Macaulay Duration
Macaulay duration finds the present value of a bond's future
coupon payments and maturity value. Because Macaulay duration is a partial
function of the time to maturity, the
greater the duration, the greater the interest-rate risk or reward for bond
prices.
Macaulay duration can be calculated manually as follows:
https://exploringfinance.com/bond-duration-calculator/
Modified Duration
The modified duration of a
bond helps investors understand how much a bond's price will rise or fall if
the YTM rises or falls by 1%. This is an important number if an investor is worried that
interest rates will be changing in the short term. The modified duration of a
bond with semi-annual coupon payments can be found with the following
formula:
Usefulness of Duration
Investors need to be aware of two main risks that can affect a
bond's investment value: credit risk (default) and interest rate risk
(interest rate fluctuations). Duration
is used to quantify the potential impact these factors will have on a bond's
price because both factors will affect a bond's expected YTM.
For example, if a company begins to struggle and its credit
quality declines, investors will require a greater reward or YTM to own the
bonds. In order to raise the YTM of an existing bond, its price must fall.
The same factors apply if interest rates are rising and competitive bonds are
issued with a higher YTM.
The duration of a
zero-coupon bond equals its time to maturity since it pays no coupon.
Duration Strategies
However, a
long-duration strategy describes an investing approach where a bond investor
focuses on bonds with a high duration value. In this situation, an
investor is likely buying bonds with a long time before maturity and greater
exposure to interest rate risks. A
long-duration strategy works well when interest rates are falling, which
usually happens during recessions.
A short-duration strategy is
one where a fixed-income or bond investor is focused on buying bonds with a
small duration. This usually means the investor is focused on bonds with a small
amount of time to maturity. A strategy like this would be employed when investors think
interest rates will rise or when they are very uncertain about interest rates
and want to reduce their risk.
Why Is It Called Duration?
Duration measures a bond price's sensitivity to changes in
interest rates—so why is it called duration? A bond with a longer time to maturity
will have a price that is more sensitive to interest rates, and thus a larger
duration than a short-term bond.
What Else Does Duration Tell You?
As a bond's duration rises, its interest rate risk also rises
because the impact of a change in the interest rate environment is larger
than it would be for a bond with a smaller duration. Fixed-income traders will use duration, along with convexity, to
manage the riskiness of their portfolio and to make adjustments to it.
Bond Duration Calculator
(FYI)
https://exploringfinance.com/bond-duration-calculator/
DURATION
function in Excel
The DURATION function, one of the Financial functions,
returns the Macauley duration for an assumed par value of $100. Duration is defined
as the weighted average of the present value of cash flows, and is used as a
measure of a bond price's response to changes in yield.
Syntax
DURATION(settlement, maturity, coupon, yld, frequency,
[basis])
Important: Dates should be entered by using the DATE
function, or as results of other formulas or functions. For example, use
DATE(2018,5,23) for the 23rd day of May, 2018. Problems can occur if dates
are entered as text.
The DURATION function syntax has the following arguments:
Settlement: The security's settlement date. The security
settlement date is the date after the issue date when the security is traded
to the buyer.
Maturity: The security's maturity date. The maturity date
is the date when the security expires.
Coupon: The security's annual coupon rate.
Yld Required.
The security's annual yield.
Frequency: The number of coupon payments per year. For
annual payments, frequency = 1; for semiannual, frequency = 2; for quarterly,
frequency = 4.
Basis Optional. The type of day count basis to use.
https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038
0:02 / 1:54
Convexity in Bonds: Definition, Meaning,
and Examples (FYI only)
By JAMES CHEN Updated January 02, 2023 Reviewed by CIERRA
MURRY Fact checked by PETE RATHBURN
Change in price
= [–Modified Duration *Change in yield] +[1/2 * Convexity*(change
in yield)2]
https://www.wallstreetmojo.com/convexity-of-a-bond-formula-duration/\
What Is Convexity?
Convexity is a measure of the curvature, or the degree of the
curve, in the relationship between bond prices and bond yields.
Convexity is thus a measure
of the curvature in the relationship between bond prices and interest rates. It
reflects the rate at which the duration of a bond changes as interest rates
change. Duration is a measure of a bond's sensitivity to changes in interest
rates. It represents the expected percentage change in the price of a bond
for a 1% change in interest rates.
KEY TAKEAWAYS
·
Convexity is a
risk-management tool, used to measure and manage a portfolio's exposure to
market risk.
·
Convexity is a measure
of the curvature in the relationship between bond prices and bond yields.
·
Convexity demonstrates
how the duration of a bond changes as the interest rate changes.
·
If a bond's duration
increases as yields increase, the bond is said to have negative convexity.
·
If a bond's duration
rises and yields fall, the bond is said to have positive convexity.
Before explaining convexity, it's important to know how bond
prices and market interest rates relate to one another. As interest rates
fall, bond prices rise. Conversely, rising market interest rates lead to
falling bond prices. This opposite reaction is because as rates rise, the
bond may fall behind in the payout they offer a potential investor in
comparison to other securities.
Bond Duration
Bond duration measures the change in a bond's price when
interest rates fluctuate. If the duration of a bond is high, it means the
bond's price will move to a greater degree in the opposite direction of
interest rates.
Duration, on the other hand, measures the bond's sensitivity
to the change in interest rates. For example, if rates were to rise 1%, a
bond or bond fund with a 5-year average duration would likely lose
approximately 5% of its value.
Convexity and Risk
Convexity builds on the
concept of duration by measuring the sensitivity of the duration of a bond as
yields change. Convexity is a better measure of interest rate risk, concerning bond
duration. Where duration assumes that interest rates and bond prices have a
linear relationship, convexity allows for other factors and produces a slope.
Duration can be a good measure of how bond prices may be
affected due to small and sudden fluctuations in interest rates. However, the
relationship between bond prices and yields is typically more sloped, or convex.
Therefore, convexity is a better measure for assessing the impact on bond
prices when there are large fluctuations in interest rates.
As convexity increases, the
systemic risk to which the portfolio is exposed increases. The term systemic risk became common
during the financial crisis of 2008 as the failure of one financial
institution threatened others. However, this risk can apply to all
businesses, industries, and the economy as a whole.
The risk to a fixed-income portfolio means that as interest
rates rise, the existing fixed-rate instruments are not as attractive. As
convexity decreases, the exposure to market interest rates decreases and the
bond portfolio can be considered hedged. Typically,
the higher the coupon rate or yield, the lower the convexity—or market risk—of a bond. This lessening of risk is
because market rates would have to increase greatly to surpass the coupon on
the bond, meaning there is less interest rate risk to the investor. However, other risks, like default risk,
etc., might still exist.
Example of Convexity
Imagine a bond issuer, XYZ Corporation, with two bonds
currently on the market: Bond A and Bond B. Both bonds have a face value of
$100,000 and a coupon rate of 5%. Bond A, however, matures in 5 years, while Bond
B matures in 10 years.
Using the concept of duration, we can calculate that Bond A
has a duration of 4 years while Bond B has a duration of 5.5 years. This
means that for every 1% change in interest rates, Bond A's price will change
by 4% while Bond B's price will change by 5.5%.
Now, let's say that interest rates suddenly increase by 2%.
This means that the price of Bond A should decrease by 8% while the price of
Bond B will decrease by 11%. However, using the concept of convexity, we can
predict that the price change for Bond B will actually be less than expected
based on its duration alone. This is because Bond B has a longer maturity,
which means it has a higher convexity. The higher convexity of Bond B acts as
a buffer against changes in interest rates, resulting in a relatively smaller
price change than expected based on its duration alone.
Negative and Positive Convexity
If a bond's duration
increases as yields increase, the bond is said to have negative convexity. In
other words, the bond price will decline by a greater rate with a rise in
yields than if yields had fallen. Therefore, if a bond has negative
convexity, its duration would increase—the
price would fall. As interest rates rise, and the opposite is true.
If a bond's duration rises and
yields fall, the bond is said to have positive convexity. In other words, as
yields fall, bond prices rise by a greater rate—or duration—than
if yields rose. Positive convexity leads to greater increases in bond prices.
If a bond has positive convexity, it would typically experience larger price
increases as yields fall, compared to price decreases when yields increase.
Under normal market conditions, the higher the coupon rate or yield, the lower a bond's degree of
convexity. In other words, there's
less risk to the investor when the bond has a high coupon or yield since
market rates would have to increase significantly to surpass the bond's
yield. So, a portfolio of bonds with high yields would have low convexity and
subsequently, less risk of their existing yields becoming less attractive as
interest rates rise.
Consequently, zero-coupon bonds have the highest degree of
convexity because they do not offer any coupon payments. For investors
looking to measure the convexity of a bond portfolio, it's best to speak to a
financial advisor due to the complex nature and the number of variables
involved in the calculation.
The Bottom Line
Convexity is a measure of
the curvature of its duration, or the relationship between bond prices and
yields. It is used to describe the way in which the duration of a bond
changes in response to changes in interest rates. When
a bond's price is more sensitive to changes in interest rates, it is said to
have higher convexity. Convexity is important for bond investors because
it can impact the value of their investments. For example, when interest rates rise, the prices of
most bonds tend to fall, and the magnitude of the price decline is typically
greater for bonds with higher convexity. Conversely, when interest rates
fall, the prices of most bonds tend to rise, and the magnitude of the price
increase is typically greater for bonds with higher convexity.
There are several
factors that can impact the convexity of a bond, including the bond's coupon
rate, maturity, and credit quality. Higher
coupon bonds, for example, tend to have higher convexity than lower coupon
bonds because they are more sensitive to changes in interest rates.
Similarly, longer-term bonds tend to have higher convexity than shorter-term
bonds because they are exposed to interest rate risk for a longer period of
time.
Bond investors can use
convexity to their advantage by managing their bond portfolios to take
advantage of changes in interest rates. For example, an investor who anticipates rising interest rates might choose
to hold a portfolio of bonds with low convexity, while an investor who
anticipates falling interest rates might choose to hold a portfolio of bonds
with high convexity.
How companies like Amazon, Nike and FedEx
avoid paying federal taxes (FYI) --- Special Topic
PUBLISHED THU, APR 14 20228:05 AM EDT
The current United States tax code allows some of the biggest
company names in the country to not pay any federal corporate income tax.
In fact, at least 55 of the
largest corporations in America paid no federal corporate income taxes on
their 2020 profits, according to the Institute
on Taxation and Economic Policy. The companies include names like Whirlpool,
FedEx, Nike, HP and Salesforce.
“If a large, very profitable company isn’t paying the federal
income tax, then we have a real fairness problem on our hands,” Matthew
Gardner, a senior fellow at the Institute on Taxation and Economic Policy
(ITEP), told CNBC.
What’s more, it is entirely
legal and within the parameters of the tax code that corporations can end up paying
no federal corporate income tax, which costs the U.S. government billions of
dollars in lost revenue.
″[There’s] a bucket of
corporate tax breaks that are deliberately in the tax code … . And overall,
they cost the federal government roughly $180 billion each year. And for
comparison, the corporate tax brings in about $370 billion of revenue a year,” Chye-Ching Huang, executive director of
the NYU Tax Law Center, told CNBC, citing research from the Tax Foundation.
CNBC reached out to FedEx, Nike, Salesforce and HP for
comment. They either declined to provide a statement or did not respond
before publication.
The 55 corporations cited by
ITEP would have paid a collective total of $8.5 billion. Instead, they
received $3.5 billion in tax rebates, collectively draining $12 billion from
the U.S. government, according to the institute. The figures don’t include corporations that
paid only some but not all of these taxes.
“I think the fundamental issue here is there are two different
ways in which corporations book their profits,” Garrett Watson, senior policy
analyst at the Tax Foundation, told CNBC. “The amount of profits that
corporations may be reporting for financial purposes may be very different
from the profits that they are reporting [for tax purposes.]”
Some tax expenditures, which
come in many different forms, are used by some companies to take advantage of
rules that enable them to lower their effective tax rates.
For example, Gardner’s research into Amazon’s taxes from 2018
to 2021 showed a reported $79 billion of pretax U.S. income. Amazon paid a collective $4 billion in
federal corporate income tax in those four years, equating to an effective
annual tax rate of 5.1%, according to Gardner’s ITEP report, about a
quarter of the federal corporate tax rate of 21%.
Amazon told CNBC in a statement, “In 2021, we reported $2.3
billion in federal income tax expense, $5.2 billion in other federal taxes,
and more than $4 billion in state and local taxes of all types. We also
collected an additional $22 billion in sales taxes for U.S. states and
localities.”
One controversial form of
federal tax expenditure is the offshoring of profits. The foreign corporate income tax —
anywhere between 0% and 10.5% — can incentivize the shifting of profits to
tax havens.
For example, Whirlpool, a U.S. company known for manufacturing
home appliances both in the U.S. and Mexico, was cited in a recent case
involving both U.S. and Mexican taxes.
″[Whirlpool] did that by having the Mexican operation
owned by a Mexican company with no employees, and then having that Mexican
company owned by a Luxembourg holding company that had one employee,” Huang
told CNBC. “And then it tried to claim that due to the combination of the
U.S., Mexico and Luxembourg tax rules ... it was trying to take advantage of
the disconnect between all of those tax systems to to avoid tax and all of
those countries and of court said, no, that goes too far.”
Whirlpool defended its actions in a statement to CNBC: “The
case before the Sixth Circuit has never been about trying to avoid U.S. taxes
on the profits earned in Mexico. This tax dispute has always been about when
those profits are taxed in the U.S. In fact, years before the original Tax
Court decision in 2020, Whirlpool had already paid U.S. tax on 100% of the
profits it earned in Mexico. Simply put, the IRS thought Whirlpool should
have paid those U.S. taxes earlier.”
19 profitable Fortune 100 corporations that
reported they will owe little or no taxes for 2021
Critical
thinking question= (optional for extra credits)
·
Shall we fix this tax loophole problem and how?
(optional for extra credits)
Chapter 8 Risk and
Return
Equations
1. Expected return and standard deviation
Given
a probability distribution of returns, the expected return can be calculated
using the following equation:
where
Given
an asset's expected return, its variance can be calculated using the
following equation:
where
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:
W1 and W2 are the
percentage of each stock in the portfolio.
3.. Historical returns
Holding period return (HPR) = (Selling price – Purchasing price
+ dividend)/ Purchasing price
4. CAPM 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.
Ri = Rf + βi
*( Rm - Rf) ------ CAPM model
Ri = Expected return
of investment
Rf =
Risk-free rate
βi =
Beta of the investment
Rm =
Expected return of market
(Rm -
Rf) = Market risk premium
· What is Beta? Where to find Beta?
· SML – Security Market Line
RISK and Return General Template
In Class Exercise
1. An investor currently holds the following portfolio:
He invested 30% of the fund in Apple with Beta equal 1.1. He also invested
40% in GE with Beta equal 1.6. The rest of his fund goes to Ford, with Beta
equal 2.2. Use the above information to answer the following questions.
1) The beta for the portfolio is? (1.63)
Solution:
0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63(weighted average of beta)
2) The three month Treasury bill rate (this is
risk free rate) is 2%. S&P500 index return is 10% (this is market
return). Now calculate the portfolio’s return. 15.04%
Solution:
0.3*1.1+0.4*1.6+(1-0.3-0.4)*2.2=1.63--- This is beta and then
plug into the CAPM.
Return = 2% + 1.63*(10%-2%) = 15.04%
Refer to the following graph. The three month
Treasury bill rate (this is risk free rate) is 2%. S&P500 index return is
10% (this is market return).
2.
What is the value of A? 2%
Solution:
This is the intercept of the SML
3.
What is the value of B? 10%
Solution:
B is the market return, so 10%, since Beta =1
4.
How much is the slope of the above security market line? 8%
Solution:
Slope = rise/run = (10%-2%)/(1-0), just compare risk free rate
(Beta=0) and market return (beta=1)
5.
Your uncle bought Apple in January, year 2000 for $30. The
current price of Apple is $480 per share. Assume there are no dividend ever
paid. Calculate your uncle’s holding period return. 15 times
Solution:
Holding period return = (480-30)/30 =1500%=15
times
6.
Your current portfolio’s BETA is about 1.2. Your total
investment is worth around $200,000. You uncle just gave you $100,000 to
invest for him. With this $100,000 extra funds in hand, you plan to invest
the whole $100,000 in additional stocks to increase your whole portfolio’s
BETA to 1.5 (Your portfolio now worth $200,000 plus $100,000). What is the
average BETA of the new stocks to achieve your goal? (hint: write down the
equation of the portfolio’s Beta first) 2.10
Solution:
Total amount = 200000 + 100000 +100000=400000
New portfolio beta =
1.2*((200000+100000)/400000) + X*(100000/400000) = 1.5 č X=2.1
7.
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)
Efficient
Frontier Exercise ? (FYI only)
Chapter 8 Case study – due with the
first mid term exam
Nov 2, 2021,07:30am EDT|86,690 views
No Recession In
2022—But Watch Out In 2023
Bill Conerly
A recession will come to the United States economy, but not in
2022. Federal Reserve policy will lead to more business cycles, which many
businesses are not well prepared for. The
downturn won’t come in 2022, but could arrive as early as 2023. If the Fed
avoids recession in 2023, then look for a more severe slump in 2024 or 2025.
Recessions
usually come from demand weakness, but supply problems can also trigger a
downturn. In 2022 demand for goods and
services will be strong. Consumers have plenty of money, thanks to past
earnings, stimulus payments and extra unemployment insurance. They have paid
down their credit card balances. Even though they also increased their car
loans outstanding as they upgraded their rides, their general condition is
good. Employment will increase thanks to the spending, reinforcing the income
gains that enable expenditures.
Businesses, too, have plenty of cash on hand. Not only have
profits been good, but the Paycheck Protection Program gave nearly $800
billion to businesses. Companies want to buy computers, equipment and
machinery to substitute for the workers they cannot find, and this spending
will help manufacturers of the equipment.
Homebuilders will construct as many homes as they can, though
that will be limited by buildable lots, skilled labor and building materials.
Non-residential construction will slowly gain ground, especially in warehouse
space and suburban offices.
The government will spend, not only at the federal level but
also among state and local entities. The federal government has no worries
about deficits, while state and local governments are flush with federal
money.
The spending
side of the economy has little risk of recession in 2022, but could supply
problems trigger a recession?
Supply chain
problems can have negative impacts when factories have to shut down for lack
of parts, as happened in the automobile industry. Recently Ford Europe’s Gunnar Herrmann told CNBC, “It’s not only semiconductors. You find shortages or
constraints all over the place,” mentioning lithium,
plastics and steel in particular. The automobile industry has laid off
workers at multiple plants, mostly for a few weeks, but some long term. When
workers are laid off for lack of materials to assemble, then the economy
suffers. Most of the shortages under
discussion, however, are limiting growth rather than cutting back on current
production.
So the supply
challenge we have is not an actual reduction in materials available, just insufficient
materials to meet the stronger demand. Despite the snarls at the ports of Long Beach and Los Angeles,
more inbound containers are hitting the docks than in 2019. Mostly we are
seeing supply as a limit on growth rather than a cause of recession.
Much of the
supply limitation prevents growth, but does not push spending downward. Businesses are cutting back on variety. A shirt in a
particular size may only be available in a few colors, not 16. That is
unfortunate, and may discourage a few shoppers, but for the most part we’ll still be buying goods.
Job losses from
vaccine mandate layoffs could push the economy toward recession, given that 31% of people over age 18 are not fully vaccinated.
The various mandates cover about 100 million workers. Some of those 31
million unvaccinated workers subject to mandates will get their shots, but
others certainly won’t. In the worst of the pandemic
recession, the country lost 22 million jobs. Losing 31 million jobs because
of vaccine mandates—or even half that number—would be disastrous. And because it would be disastrous,
it will not happen. The Biden administration almost certainly will pull back
the mandate before accepting such a harsh result rise in unemployment.
Though 2022 is
unlikely to host a recession, 2023 and 2024 are extremely risky. The Federal Reserve will
start tapering its quantitative stimulus soon, and sometime in mid-2022 it
will begin raising short-term interest rates. The economy reacts with a time
lag of about one year, plus or minus. The greatest risk in the near term
is that the Fed realizes that much of
the recent inflation is long-lasting rather than transitory. They will then
hit the brakes. Because of the
time lag, the Fed may decide to stomp down harder on the brakes, triggering a
recession.
If the Fed avoids an over-reaction recession, it risks not
bringing inflation down at all. The longer the Fed waits, the more work they
will need to do later. We’ll still have massive fiscal stimulus plus the
lagged effects of past monetary stimulus. Public anger over inflation will
provoke a stronger Fed response by 2025 at the latest, but probably earlier.
Can a recession
be completely avoided in the next few years? Theoretically it’s possible. The
Fed would have to tighten at just the right time, in just the right
magnitude, then return to neutral at just the right time. It could happen, but the odds are very, very slim. The people
at the Fed are smart and knowledgeable, but the task is too difficult for
mere mortals. So businesses should enjoy their gains in 2022 while developing
contingency plans to be ready for the nearly-inevitable recession.
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.
Ri = Rf + βi
*( Rm - Rf) ------ CAPM model
Ri = Expected return
of investment
Rf =
Risk-free rate
βi =
Beta of the investment
Rm =
Expected return of market
(Rm -
Rf) = 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.
http://www.youtube.com/watch?v=RoqAcdTFVFY
http://www.youtube.com/watch?v=FrmoXog9zig
http://www.youtube.com/watch?v=V48NECmT3Ns
Understanding the Fama
and French Three Factor Model
https://www.investopedia.com/terms/f/famaandfrenchthreefactormodel.asp
Nobel
Laureate Eugene Fama and researcher Kenneth French, former professors at the
University of Chicago Booth School of Business, attempted to better measure
market
returns and, through research, found that value stocks outperform growth stocks.
Similarly, small-cap stocks tend to outperform large-cap stocks. As an
evaluation
tool, the performance of portfolios with a large number of small-cap or value
stocks would be lower than the CAPM result, as the Three-Factor Model
adjusts downward for observed small-cap and
value stock outperformance.
The Fama and French model
has three factors: the size of firms, book-to-market values, and excess
return on the market. In other words, the three factors used
are small minus big (SMB), high minus low
(HML), and the portfolio's return less the risk-free rate of return. SMB
accounts for publicly traded companies
with small market caps that
generate higher returns, while HML accounts for value stocks with high
book-to-market ratios that generate higher returns
in comparison to the market.
Fama and French’s Five
Factor Model
Researchers have expanded
the Three-Factor model in recent years to include other factors. These
include "momentum," "quality," and "low
volatility,"
among others. In 2014, Fama
and French adapted their model to include five factors. Along with the
original three factors, the new model adds the concept that
companies reporting higher
future earnings have higher returns in the stock market, a factor referred to
as profitability.
The fifth factor, referred
to as "investment", relates the concept of internal investment and
returns, suggesting that companies directing profit towards
major growth projects are
likely to experience losses in the stock market.
Small Minus Big (SMB):
Definition and Role in Fama/French Model
By
WILL KENTON Updated November 30, 2020 Reviewed by DAVID KINDNESS
https://www.investopedia.com/terms/s/small_minus_big.asp
What Does Small Minus
Big Mean?
Small
minus big (SMB) is one of the three factors in the Fama/French stock pricing
model. Along with other factors, SMB
is used to explain portfolio returns.
This
factor is also referred to as the "small
firm effect," or the "size effect," where size is based on
a company's market capitalization.
KEY TAKEAWAYS
·
Small minus big (SMB) is a factor in the
Fama/French stock pricing model that says smaller companies outperform larger
ones over the long-term.
·
High minus low (HML) is another factor in
the model that says value stocks tend to outperform growth stocks.
·
Beyond the original three factors in the
Fama/French model—the SMB, HML, and market factors—the model has been
expanded to include other factors, such as momentum, quality, and low
volatility.
Understanding Small
Minus Big (SMB)
Small minus big is the
excess return that smaller market capitalization companies return versus
larger companies. The Fama/French Three-Factor Model is an
extension of the Capital Asset Pricing Model (CAPM). CAPM is a one-factor
model, and that factor is the performance of the market as a whole. This
factor is known as
the market factor. CAPM explains a
portfolio's returns in terms of the amount of risk it contains relative to
the market. In other words, according to CAPM, the
primary
explanation for the performance of a portfolio is the performance of the
market as a whole.
The Fama/Three-Factor model
adds two factors to CAPM. The model essentially says there are two other factors in addition to
market performance
that consistently contribute
to a portfolio's performance. One is SMB, where if a portfolio has more
small-cap companies in it, it should outperform the market
over the long run.
Small Minus Big (SMB)
vs. High Minus Low (HML)
The
third factor in the Three-Factor model is High Minus Low (HML). "High" refers to companies with a
high book value-to-market value ratio. "Low'"
refers to companies with a low book
value-to-market value ratio. This factor is also referred to as the
"value factor" or the "value versus growth factor"
because companies with a high book to market
ratio are typically considered "value stocks."
Companies with a low
market-to-book value are typically "growth stocks."
And research has demonstrated that value stocks outperform growth stocks in
the long
run.
So, in the long run, a portfolio with a large proportion of value stocks
should outperform one with a large proportion of growth stocks.
Special
Considerations
The
Fama/French model can be used to evaluate a portfolio manager's returns.
Essentially, if the portfolio's performance can be attributed to the three
factors, then the portfolio manager has not added any value or demonstrated
any skill.
This
is because if the three factors can completely explain the portfolio's
performance, then none of the performance can be attributed to the manager's
ability.
A good portfolio manager
should add to a performance by picking good stocks. This outperformance is
also known as "alpha."
Application of the Fama French 5 factor model
https://blog.quantinsti.com/fama-french-five-factor-asset-pricing-model/
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:
Rit - RFt
= ai + bi(RMt — RFt) + siSMBt
+ hiHMLt + riRMWt + ciCMAt
+ eit
Where:
Rit
is the return in month t of one of the portfolios
RFt is
the riskfree rate
Rm -
Rf is the return spread between the capitalization-weighted stock market and
cash
SMB is
the return spread of small minus large stocks (i.e. the size effect)
HML
is the return spread of cheap minus expensive stocks (i.e. the value effect)
RMW
is the return spread of the most profitable firms minus the least profitable
CMA
is the return spread of firms that invest conservatively minus aggressively
(AQR, 2014)
The
purpose of the regression test is to observe whether the five-factor model
captures average returns on the variables and to see which variables are
positively
or negatively correlated to each other and
additionally identifying the size of the regression slopes and how all these
factors are related to and affect average
returns of stocks values.
The
tests done by Fama and French (2014) show that the value factor HML is
redundant for describing average returns when profitability and investment
factors
have been added into the equation and that
for applications were sole interest is abnormal returns, a four or
five-factor model can be used but if portfolio tilts are
also
of interest in addition to abnormal returns then the five-factor model is
best to use.
The
results also show that the Fama-French five-factor model explains between 71%
and 94% of the cross-section variance of expected returns for the size,
value, profitability and investment
portfolios.
It
has been proven that a five-factor model directed at capturing the size,
value, profitability, and investment patterns in average stock returns
performs better than
the three-factor model in that it lessens
the anomaly average returns left unexplained.
The
new model shows that the highest expected returns are attained by companies
that are small, profitable and value companies with no major growth prospects
(Fama
and French, 2014).
The
Fama-French five-factor model’s main setback, however, is its failure to capture
the low average returns on small stocks whose returns perform like those of
firms
that invest a lot in spite of low
profitability as well as the model’s performance being indifferent to the way
its factors are defined (Fama and French, 2015).
Efficient Frontier
(FYI only)
Excel template (www.jufinance.com/efficient_frontier_excel)
Critical
thinking challenge: Based on 8 stocks of your choice, generate an efficient
frontier (earn
5 extra points added to the first midterm exam)
Hint: (from chatgpt,
FYI)
The goal of the efficient frontier is to help
investors identify the optimal
portfolio that provides the
maximum return for a given level of risk, or the minimum risk for a given
level of return. The efficient frontier is a
graph that shows the different possible combinations of risk and return for a
given set of investments or assets. It represents the set of portfolios that
offer the highest expected return for a given level of risk, or the lowest
risk for a given level of return.
By plotting different portfolios on the
efficient frontier, investors can evaluate the risk-return trade-offs of
different investment options and choose the portfolio that best meets their
investment objectives. The efficient frontier provides a way to quantify the
trade-offs between risk and return and to help investors make informed
decisions about their investment strategies.
Step 1:
Portfolio Return:
Portfolio Return = w1 * r1 + w2 * r2 + w3 * r3 + w4 * r4 + w5 *
r5 + w6 * r6 + w7 * r7 + w8 * r8
where: w1,
w2, w3, w4, w5, w6, w7, w8 are the weights of each stock in
the portfolio, and r1, r2, r3, r4, r5, r6, r7,
r8 are the returns of each stock in the portfolio.
Portfolio Standard
Deviation:
Portfolio Standard Deviation = sqrt(w1^2 * sigma1^2 + w2^2 *
sigma2^2 + w3^2 * sigma3^2 + w4^2 * sigma4^2 + w5^2 * sigma5^2 + w6^2 *
sigma6^2 + w7^2 * sigma7^2 + w8^2 * sigma8^2 + 2 * w1 * w2 * rho12 * sigma1 *
sigma2 + 2 * w1 * w3 * rho13 * sigma1 * sigma3 + 2 * w1 * w4 * rho14 * sigma1
* sigma4 + 2 * w1 * w5 * rho15 * sigma1 * sigma5 + 2 * w1 * w6 * rho16 *
sigma1 * sigma6 + 2 * w1 * w7 * rho17 * sigma1 * sigma7 + 2 * w1 * w8 * rho18
* sigma1 * sigma8 + 2 * w2 * w3 * rho23 * sigma2 * sigma3 + 2 * w2 * w4 *
rho24 * sigma2 * sigma4 + 2 * w2 * w5 * rho25 * sigma2 * sigma5 + 2 * w2 * w6
* rho26 * sigma2 * sigma6 + 2 * w2 * w7 * rho27 * sigma2 * sigma7 + 2 * w2 *
w8 * rho28 * sigma2 * sigma8 + 2 * w3 * w4 * rho34 * sigma3 * sigma4 + 2 * w3
* w5 * rho35 * sigma3 * sigma5 + 2 * w3 * w6 * rho36 * sigma3 * sigma6 + 2 *
w3 * w7 * rho37 * sigma3 * sigma7 + 2 * w3 * w8 * rho38 * sigma3 * sigma8 + 2
* w4 * w5 * rho45 * sigma4 * sigma5 + 2 * w4 * w6 * rho46 * sigma4 * sigma6 +
2 * w4 * w7 * rho47 * sigma4 * sigma7 + 2 * w4 * w8 * rho48 * sigma4 * sigma8
+ 2 * w5 * w6 * rho56 * sigma5 * sigma6 + 2 * w5 * w7 * rho57 * sigma5 *
sigma7 + 2 * w5 * w8 * rho58 * sigma5 * sigma8 + 2 * w6 * w7 * rho67 * sigma6
* sigma7 + 2 * w6 * w8 * rho68 * sigma6 * sigma8 + 2 * w7 * w8 * rho78 *
sigma7 * sigma8)
where: sigma1, sigma2, sigma3, sigma4, sigma5,
sigma6, sigma7, sigma8 are the standard deviations of each stock in the
portfoliorho12, rho13, rho14, rho15, rho16, rho17,
rho18, rho23, rho24, rho25, rho26, rho27,
rho28, rho34, rho35, rho36, rho37, rho38,
rho45, rho46, rho47, rho48, rho56, rho57,
rho58, rho67, rho68, and rho78 are correlation
coefficients between the stock returns. They represent the pairwise
correlations between the stocks in the portfolio.
For example, rho12 represents the
correlation coefficient between the returns of stock 1 and stock 2, rho23
represents the correlation coefficient between the returns of stock 2 and
stock
Step 2: Draw CML (Capital market line)
To draw a
tangent line from the risk-free rate to the efficient frontier, follow these
steps:
· Determine the risk-free rate: The risk-free
rate is the rate of return an investor can earn with zero risk. It is
typically represented by the yield on a short-term U.S. Treasury bill.
· Find the portfolio with the highest Sharpe ratio: The Sharpe
ratio is a measure of risk-adjusted return that takes into account the
portfolio's expected return and standard deviation. The portfolio with the
highest Sharpe ratio is the portfolio that offers the best risk-adjusted
return.
· Calculate the slope of the tangent line: The slope of
the tangent line is equal to the Sharpe ratio of the portfolio with the
highest Sharpe ratio.
· Draw the tangent line: The tangent
line starts at the risk-free rate on the y-axis and has a slope equal to the
Sharpe ratio of the portfolio with the highest Sharpe ratio. The tangent line
intersects the efficient frontier at the point where the portfolio with the
highest Sharpe ratio is located.
The tangent line
represents the optimal portfolio for an investor who wants to maximize their
risk-adjusted return. Any portfolio on the tangent line is a combination of
the risk-free asset and the portfolio with the highest Sharpe ratio.
The tangent line drawn from the risk-free rate to
the efficient frontier is called the Capital Market Line (CML). The CML is a graphical representation of
the concept of the Capital Asset Pricing Model (CAPM), which is a widely
used model in finance that describes the relationship between the risk and
expected return of an asset or a portfolio.
The CML is the straight line that connects the
risk-free rate to the point of tangency with the efficient frontier, which
represents the optimal portfolio for an investor who wants to maximize their
risk-adjusted return. The slope of the CML is the market risk premium, which is the
excess return that investors require to invest in a risky asset rather than a
risk-free asset. The CML can be used to determine the required return for any
level of risk, and it provides a benchmark for evaluating the performance of
different investment portfolios.
In Class
Demonstration Results: Excel File (FYI)
Modern
Portfolio Theory: What MPT Is and How Investors Use It
By THE
INVESTOPEDIA TEAM Updated September 10, 2021 Reviewed by PETER WESTFALL Fact
checked by SUZANNE KVILHAUG
https://www.investopedia.com/terms/m/modernportfoliotheory.asp
What Is the Modern Portfolio Theory (MPT)?
The modern portfolio theory (MPT) is a practical method for
selecting investments in order to maximize their overall returns within an
acceptable level of risk. This mathematical framework is used to build a
portfolio of investments that maximize the amount of expected return for the
collective given level of risk.
American economist Harry
Markowitz pioneered this theory in his paper "Portfolio Selection,"
which was published in the Journal of Finance in 1952. He was
later awarded a Nobel Prize for his work on
modern portfolio theory.
A key component of the MPT
theory is diversification. Most investments are either high risk and high
return or low risk and low return. Markowitz argued that investors could
achieve their best results by choosing an optimal mix of the two based on an
assessment of their individual tolerance to risk.
KEY TAKEAWAYS
·
The modern portfolio
theory (MPT) is a method that can be used by risk-averse investors to
construct diversified portfolios that maximize their returns without
unacceptable levels of risk.
·
The modern portfolio
theory can be useful to investors trying to construct efficient and
diversified portfolios using ETFs.
·
Investors who are more
concerned with downside risk might prefer the post-modern portfolio theory
(PMPT) to MPT.
Understanding the Modern
Portfolio Theory (MPT)
The modern portfolio theory argues that any given investment's
risk and return characteristics should not be viewed alone but should be
evaluated by how it affects the overall portfolio's risk and return. That is,
an
investor can construct a portfolio of multiple assets that will result in
greater returns without a higher level of risk.
As an alternative, starting with a desired level of expected
return, the investor can construct a portfolio with the lowest possible risk
that is capable of producing that return.
Based on statistical measures such as variance and
correlation, a single investment's performance is less important than how it
impacts the entire portfolio.
The MPT assumes that investors are risk-averse, meaning they
prefer a less risky portfolio to a riskier one for a given level of return.
As a practical matter, risk aversion implies that most people should invest
in multiple asset classes.
Benefits of the MPT
The MPT is a useful tool for investors who are trying to build
diversified portfolios. In fact, the
growth of exchange-traded funds (ETFs) made the MPT more relevant by giving
investors easier access to a broader range of asset classes.
For example, stock investors can reduce risk by putting a
portion of their portfolios in government bond ETFs. The variance of the
portfolio will be significantly lower because government bonds have a
negative correlation with stocks. Adding a small investment in Treasuries to
a stock portfolio will not have a large impact on expected returns because of
this loss-reducing effect.
Looking for Negative
Correlation
Similarly, the MPT can be
used to reduce the volatility of a U.S. Treasury portfolio by putting 10% in
a small-cap value index fund or ETF. Although small-cap value stocks are far
riskier than Treasuries on their own, they often do well during periods of
high inflation when bonds do poorly. As a result, the portfolio's
overall volatility is lower
than it would be if it consisted entirely of government bonds. Moreover, the
expected returns are higher.
The modern portfolio theory allows investors to construct more
efficient portfolios. Every possible combination of assets can be plotted on
a graph, with the portfolio's
risk on the X-axis and
the expected return on the Y-axis. This plot reveals the most desirable
combinations for a portfolio.
For example, suppose Portfolio A has an expected return of
8.5% and a standard deviation of 8%. Assume that Portfolio B has an expected
return of 8.5% and a standard deviation of 9.5%. Portfolio A would be deemed
more efficient because it has the same expected return but lower risk.
It is possible to draw an upward sloping curve to connect all
of the most efficient portfolios. This curve is called the efficient
frontier.
Investing in a portfolio underneath the curve is not desirable
because it does not maximize returns for a given level of risk.
What Are the Benefits of the Modern
Portfolio Theory?
The modern portfolio theory
can be used to diversify a portfolio in order to get a better return overall
without a bigger risk.
Another benefit of the
modern portfolio theory (and of diversification) is that it can reduce
volatility. The best way to do that is to choose assets that have a
negative correlation, such as U.S.
treasuries and small-cap stocks.
Ultimately, the goal of the modern portfolio theory is to
create the most efficient portfolio possible.
What Is the Importance
of the Efficient Frontier in the MPT?
The efficient frontier is a
cornerstone of the modern portfolio theory. It is the line that indicates the
combination of investments that will provide the highest level
of return for the lowest
level of risk.
When a portfolio falls to the right of the efficient frontier, it possesses greater risk relative to its predicted return. When it falls beneath the slope of the efficient frontier, it offers a lower level of return relative to risk.
Firm Mid Term exam
around 2/22/2023
Study guide (Similar
to case study, in class)
Chapter 9 Stock
Return Evaluation
For class discussion:
· What is dividend growth model? Why can
we use dividend to estimate a firm’s intrinsic value?
· Are
future dividends predictable?
· Refer
to the following table for WMT’s dividend history
https://www.nasdaq.com/market-activity/stocks/wmt/dividend-history
·
EX-DIVIDEND DATE 12/08/2022
·
DIVIDEND YIELD N/A
·
ANNUAL DIVIDEND $2.24
·
P/E RATIO 33.29
Ex/EFF DATE |
TYPE |
CASH AMOUNT |
DECLARATION
DATE |
RECORD DATE |
PAYMENT DATE |
12/07/2023 |
CASH |
$0.57 |
02/21/2023 |
12/08/2023 |
01/02/2024 |
08/10/2023 |
CASH |
$0.57 |
02/17/2023 |
08/11/2023 |
09/05/2023 |
05/04/2023 |
CASH |
$0.57 |
02/21/2023 |
05/05/2023 |
05/30/2023 |
03/16/2023 |
CASH |
$0.57 |
02/21/2023 |
03/17/2023 |
04/03/2023 |
12/08/2022 |
CASH |
$0.56 |
02/17/2022 |
12/09/2022 |
01/03/2023 |
08/11/2022 |
CASH |
$0.56 |
02/17/2022 |
08/12/2022 |
09/06/2022 |
05/05/2022 |
CASH |
$0.56 |
02/17/2022 |
05/06/2022 |
05/31/2022 |
03/17/2022 |
CASH |
$0.56 |
02/17/2022 |
03/18/2022 |
04/04/2022 |
12/09/2021 |
CASH |
$0.55 |
02/18/2021 |
12/10/2021 |
01/03/2022 |
08/12/2021 |
CASH |
$0.55 |
02/18/2021 |
08/13/2021 |
09/07/2021 |
05/06/2021 |
CASH |
$0.55 |
02/18/2021 |
05/07/2021 |
06/01/2021 |
03/18/2021 |
CASH |
$0.55 |
02/18/2021 |
03/19/2021 |
04/05/2021 |
12/10/2020 |
CASH |
$0.54 |
02/18/2020 |
12/11/2020 |
01/04/2021 |
08/13/2020 |
CASH |
$0.54 |
02/18/2020 |
08/14/2020 |
09/08/2020 |
05/07/2020 |
CASH |
$0.54 |
02/18/2020 |
05/08/2020 |
06/01/2020 |
03/19/2020 |
CASH |
$0.54 |
02/18/2020 |
03/20/2020 |
04/06/2020 |
12/05/2019 |
CASH |
$0.53 |
02/19/2019 |
12/06/2019 |
01/02/2020 |
08/08/2019 |
CASH |
$0.53 |
02/19/2019 |
08/09/2019 |
09/03/2019 |
05/09/2019 |
CASH |
$0.53 |
02/19/2019 |
05/10/2019 |
06/03/2019 |
03/14/2019 |
CASH |
$0.53 |
02/19/2019 |
03/15/2019 |
04/01/2019 |
12/06/2018 |
CASH |
$0.52 |
02/21/2018 |
12/07/2018 |
01/02/2019 |
08/09/2018 |
CASH |
$0.52 |
02/21/2018 |
08/10/2018 |
09/04/2018 |
05/10/2018 |
CASH |
$0.52 |
02/20/2018 |
05/11/2018 |
06/04/2018 |
03/08/2018 |
CASH |
$0.52 |
02/20/2018 |
03/09/2018 |
04/02/2018 |
12/07/2017 |
CASH |
$0.51 |
02/21/2017 |
12/08/2017 |
01/02/2018 |
08/09/2017 |
CASH |
$0.51 |
02/21/2017 |
08/11/2017 |
09/05/2017 |
05/10/2017 |
CASH |
$0.51 |
02/21/2017 |
05/12/2017 |
06/05/2017 |
03/08/2017 |
CASH |
$0.51 |
02/21/2017 |
03/10/2017 |
04/03/2017 |
12/07/2016 |
CASH |
$0.50 |
02/18/2016 |
12/09/2016 |
01/03/2017 |
08/10/2016 |
CASH |
$0.50 |
02/18/2016 |
08/12/2016 |
09/06/2016 |
05/11/2016 |
CASH |
$0.50 |
02/18/2016 |
05/13/2016 |
06/06/2016 |
03/09/2016 |
CASH |
$0.50 |
02/18/2016 |
03/11/2016 |
04/04/2016 |
12/02/2015 |
CASH |
$0.49 |
02/19/2015 |
12/04/2015 |
01/04/2016 |
08/05/2015 |
CASH |
$0.49 |
02/19/2015 |
08/07/2015 |
09/08/2015 |
05/06/2015 |
CASH |
$0.49 |
02/19/2015 |
05/08/2015 |
06/01/2015 |
03/11/2015 |
CASH |
$0.49 |
02/19/2015 |
03/13/2015 |
04/06/2015 |
12/03/2014 |
CASH |
$0.48 |
02/20/2014 |
12/05/2014 |
01/05/2015 |
08/06/2014 |
CASH |
$0.48 |
02/20/2014 |
08/08/2014 |
09/03/2014 |
05/07/2014 |
CASH |
$0.48 |
02/20/2014 |
05/09/2014 |
06/02/2014 |
03/07/2014 |
CASH |
$0.48 |
02/20/2014 |
03/11/2014 |
04/01/2014 |
12/04/2013 |
CASH |
$0.47 |
02/21/2013 |
12/06/2013 |
01/02/2014 |
08/07/2013 |
CASH |
$0.47 |
02/21/2013 |
08/09/2013 |
09/03/2013 |
05/08/2013 |
CASH |
$0.47 |
02/21/2013 |
05/10/2013 |
06/03/2013 |
03/08/2013 |
CASH |
$0.47 |
02/21/2013 |
03/12/2013 |
04/01/2013 |
12/05/2012 |
CASH |
$0.3975 |
03/01/2012 |
12/07/2012 |
12/27/2012 |
08/08/2012 |
CASH |
$0.3975 |
03/01/2012 |
08/10/2012 |
09/04/2012 |
05/09/2012 |
CASH |
$0.3975 |
03/01/2012 |
05/11/2012 |
06/04/2012 |
03/08/2012 |
CASH |
$0.3975 |
03/01/2012 |
03/12/2012 |
04/04/2012 |
12/07/2011 |
CASH |
$0.365 |
03/03/2011 |
12/09/2011 |
01/03/2012 |
08/10/2011 |
CASH |
$0.365 |
03/03/2011 |
08/12/2011 |
09/06/2011 |
05/11/2011 |
CASH |
$0.365 |
03/03/2011 |
05/13/2011 |
06/06/2011 |
03/09/2011 |
CASH |
$0.365 |
03/03/2011 |
03/11/2011 |
04/04/2011 |
12/08/2010 |
CASH |
$0.3025 |
03/04/2010 |
12/10/2010 |
01/03/2011 |
08/11/2010 |
CASH |
$0.3025 |
03/04/2010 |
08/13/2010 |
09/07/2010 |
05/12/2010 |
CASH |
$0.3025 |
03/04/2010 |
05/14/2010 |
06/01/2010 |
03/10/2010 |
CASH |
$0.3025 |
03/04/2010 |
03/11/2010 |
|
12/09/2009 |
CASH |
$0.2725 |
03/05/2009 |
12/10/2009 |
|
08/12/2009 |
CASH |
$0.2725 |
03/05/2009 |
08/14/2009 |
09/08/2009 |
05/13/2009 |
CASH |
$0.2725 |
03/05/2009 |
05/15/2009 |
06/01/2009 |
03/11/2009 |
CASH |
$0.2725 |
03/05/2009 |
03/13/2009 |
04/06/2009 |
12/11/2008 |
CASH |
$0.2375 |
03/06/2008 |
12/15/2008 |
01/02/2009 |
08/13/2008 |
CASH |
$0.2375 |
03/06/2008 |
08/15/2008 |
09/02/2008 |
05/14/2008 |
CASH |
$0.2375 |
03/06/2008 |
05/16/2008 |
06/02/2008 |
03/12/2008 |
CASH |
$0.2375 |
03/06/2008 |
03/14/2008 |
04/07/2008 |
12/12/2007 |
CASH |
$0.22 |
03/08/2007 |
12/14/2007 |
01/02/2008 |
08/15/2007 |
CASH |
$0.22 |
03/08/2007 |
08/17/2007 |
09/04/2007 |
05/16/2007 |
CASH |
$0.22 |
03/08/2007 |
05/18/2007 |
06/04/2007 |
03/14/2007 |
CASH |
$0.22 |
03/08/2007 |
03/16/2007 |
04/02/2007 |
12/13/2006 |
CASH |
$0.1675 |
03/02/2006 |
12/15/2006 |
01/02/2007 |
08/16/2006 |
CASH |
$0.1675 |
03/02/2006 |
08/18/2006 |
09/05/2006 |
05/17/2006 |
CASH |
$0.1675 |
03/02/2006 |
05/19/2006 |
06/05/2006 |
03/15/2006 |
CASH |
$0.1675 |
03/02/2006 |
03/17/2006 |
04/03/2006 |
12/14/2005 |
CASH |
$0.15 |
|||
08/17/2005 |
CASH |
$0.15 |
03/03/2005 |
08/19/2005 |
09/06/2005 |
05/18/2005 |
CASH |
$0.15 |
03/03/2005 |
05/20/2005 |
06/06/2005 |
03/16/2005 |
CASH |
$0.15 |
03/03/2005 |
03/18/2005 |
04/04/2005 |
12/15/2004 |
CASH |
$0.13 |
03/02/2004 |
12/17/2004 |
01/03/2005 |
08/18/2004 |
CASH |
$0.13 |
03/02/2004 |
08/20/2004 |
09/07/2004 |
05/19/2004 |
CASH |
$0.13 |
03/02/2004 |
05/21/2004 |
06/07/2004 |
03/17/2004 |
CASH |
$0.13 |
03/02/2004 |
03/19/2004 |
04/05/2004 |
Can you estimate the expected dividend in 2023? And in 2024? And
on and on…
Can
you write down the math equation now?
WMT
stock price = ?
Can
you calculate now? It is hard right because we assume dividend payment goes
to infinity. How can we simplify the calculation?
We
can assume that dividend grows at certain rate, just as the table on the
right shows.
Discount
rate is r (based on Beta and CAPM learned in chapter 6)
Dividend growth model:
Refer to http://www.calculatinginvestor.com/2011/05/18/gordon-growth-model/
· Now let’s apply this
Dividend growth model in problem solving.
Dividend
Growth Model Calculator
(www.jufinance.com/stock
)
Equations
Po = D1/(r-g) = Do*(1+g)/(r-g),
Where D1= next dividend; Do = just paid
dividend; r=stock return; g= dividend growth rate; Po= current market
price
Dividend Yield = D1/Po = Do*(1+g) / Po
Capital gain yield = (P1/Po) -1 = g
Total return = dividend yield + capital gain yield = D1/Po + g
Non-constant dividend growth model
(www.jufinance.com/dcf)
Equations
Pn = Dn+1/(r-g) = Dn*(1+g)/(r-g), since
year n, dividends start to grow at a constant rate.
Where Dn+1= next dividend in year
n+1;
Do = just paid dividend in year n;
r=stock return; g= dividend growth rate;
Pn= current market price in year n;
Po = npv(r, D1, D2, …, Dn+Pn)
Or,
Po = D1/(1+r) + D2/(1+r)^2 + … +
(Dn+Pn)/(1+r)^n
Case
Study (due with the Second Midterm Exam)
Case
video in class part I (Thanks, Ethan and Ted)
Case
video in class part II (Thanks, Ethan and Ted)
In class exercise
1.
You expect AAA Corporation to
generate the following free cash flows over the next five years:
Year |
1 |
2 |
3 |
4 |
5 |
FCF
($ millions) |
75 |
84 |
96 |
111 |
120 |
Since
year 6, you estimate that AAA's free cash flows will grow at 6% per year.
WACC of AAA = 15%
· Calculate
the enterprise value for DM Corporation.
· Assume
that AAA has $500 million debt and 14 million shares outstanding, calculate
its stock price.
Answer:
Enterprise
value = npv(15%, 75, 84, 96, 111, 120+120*(1+6%)/(15%-6%)) = 1017.66
(or,
equity value = 75/(1+15%) + 84/(1+15%)^2 + 96/(1+15%)^3 + 111/(1+15%)^4 +
(120+120*(1+6%)/(15%-6%))/(1+15%)^5
Equity
value = 1017.66-500 = 517.66
Stock
price = 517.66/14=37
NPV
Excel syntax
Syntax
NPV(rate,value1,value2,
...)
Rate
is the rate of discount over the length of one period.
Value1, value2, ...
are 1 to 29 arguments representing the payments and income.
· Value1, value2,
... must be equally spaced in time and occur at the end of
each period. NPV uses the order of value1, value2,
... to interpret the order of cash flows. Be sure to enter your payment
and income values in the correct sequence.
2. AAA’s divided yield = 2.5%, equity cost =
10%, and its dividends will grow at a constant rate of g. How much is g?
A) 2.5%
B) 5.0%
C) 10.0%
D) 7.5%
Answer:
Dividend yield + capital gain
yield = total return = 10%, and g= capital yield = dividend growth rate, so g
= 10% - 2.5% = 7.5%
3. AAA pays no dividend
currently. However, you expect it pay an annual dividend of $0.56/share 2
years from now with a growth rate of 4% per year thereafter. Its equity cost
= 12%, then its stock price=?
A) $4.67
B) $5.00
C) $6.25
D) $7.00
Answer:
Stock price = Po = npv(12%, 0,
0.56 + 0.56*(1+4%)/(12%-4%)) = 6.25
Or, Po = 0.56/(1+12%)^2 +
0.56*(1+4%)/(12%-4%) /(1+12%)^2 = 6.25
4. AAA expects to have earnings
of $2.50 per share this coming year. It will retain all of the earnings for
the next year. For the following 4 years, it will retain 50% of its earnings.
It will retain 25% of its earnings after that. Each year, retained earnings
will be used in new projects with a return of 20% per year as expected. The
rest of retained earnings will paid to shareholders as dividends. Its equity cost
= 10%. Its stock price=?
A) $40.80
B) $44.70
C) $59.80
D) $63.50
Year |
EPS |
Retained Earnings |
Growth in Earnings
(.20 × R.E.) |
Dividends |
1 |
$2.50 |
$2.50 |
|
|
2 |
|
|
|
|
3 |
|
|
|
|
4 |
|
|
|
|
5 |
|
|
|
|
Hint: after year 5, the growth rate =0.2/3.99 = 5%
Answer:
Year |
EPS |
Retained Earnings |
Growth in Earnings
(.20 × R.E.) |
Dividends |
1 |
$2.50 |
$2.50 |
0.5 |
0 |
2 |
3 |
1.5 |
0.3 |
1.5 |
3 |
3.3 |
1.65 |
0.33 |
1.65 |
4 |
3.63 |
1.82 |
0.36 |
1.82 |
5 |
3.99 |
1 |
0.2 |
3 |
after year 5, the growth rate
=0.2/3.99 = 5% = growth in earnings / EPS
So price at year 4 = 3/(10%-5%)
=60
So current stock price =
1.5/(1+10%)^2 + 1.65/(1+10%)^3 + 1.82/(1+10%)^4 + 60/(1+10%)^4 = 44.70
Or price = npv(10%, 0, 1.5, 1.65,
1.82+60)
Stock screening tools
·
Reuters stock screener to help select stocks
http://stockscreener.us.reuters.com/Stock/US/
·
FINVIZ.com
http://finviz.com/screener.ashx
·
WSJ stock screen
http://online.wsj.com/public/quotes/stock_screener.html
·
Simply the Web's Best Financial Charts
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
http://www.youtube.com/watch?v=JApBhv3VLTo
Ranking stocks using PEG ratio
http://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.
The Gordon growth model calculates the
present value of the security by summing an infinite series of discounted
dividend payments which follows the pattern shown here:
Multiplying both sides of the previous
equation by (1+g)/(1+r) gives:
We can then subtract the second equation
from the first equation to get:
Rearranging and simplifying:
Finally, we can simplify further to get the Gordon growth model
equation
What Is a DRIP
Investment, How It Works, Benefits (FYI)
By
BRIAN BEERS Updated December 12, 2021 Reviewed by THOMAS J. CATALANO Fact
checked by MARCUS REEVES
https://www.investopedia.com/ask/answers/what-is-a-drip/
What Is a Drip?
The
word DRIP is an acronym for "dividend
reinvestment plan", but DRIP also happens to describe the way the
plan works. With DRIPs, the cash
dividends that an investor receives from a company are reinvested to purchase
more stock, making the investment in the company grow little by little.
KEY
TAKEAWAYS
·
A
DRIP is a dividend reinvestment plan whereby cash dividends are reinvested to
purchase more stock in the company.
·
DRIPs
use a technique called dollar-cost averaging (DCA) intended to average out
the price at which you buy stock as it moves up or down.
·
DRIPs
help investors accumulate additional shares at a lower cost since there are
no commissions or brokerage fees.
How DRIPs
Work
A
dividend is a reward to shareholders, which can come in the form of a cash
payment that is paid via a check or a direct deposit to investors. DRIPs
allow investors the choice to reinvest the cash dividend and buy shares of
the company's stock.
Many
brokerage houses offer clients the ability to reinvest dividends in the
underlying securities they hold through a DRIP program. However, investors
have the option of purchasing shares directly from the respective company,
through direct stock purchase plans (DSPPs).
Fractional
Shares
The
"dripping" of dividends is not limited to whole shares, which makes
these plans somewhat unique. The corporation keeps detailed records of share
ownership percentages.
For
example, let's say that the TSJ Sports Conglomerate paid a $10 dividend on a
stock that traded at $100 per share. Every time there was a dividend payment,
investors within the DRIP plan would receive one-tenth of a share.
Benefits
of DRIPs
DRIPs
offer a number of benefits for both the investors buying shares with their
cash dividends and the companies offering DRIP programs.
Benefits
to Investors
DRIPs
use a technique called dollar-cost averaging (DCA) intended to average out
the price at which you buy stock as it moves up or down over a long period.
You are never buying the stock right at its peak or at its low with
dollar-cost averaging.
Company-operated
DRIPS are popular with shareholders as a lower-cost option to accumulate
additional shares. There are often no commissions or brokerage fees involved.
Many companies offer shares at a discount through their DRIP ranging from 3
to 5% off the current share price.
The
price discount combined with no trading commissions allows investors to lower
their cost basis for owning a company's shares. As a result, DRIPs can help investors save money on buying additional
shares of stock versus had they bought them on the open market.
Benefits
to Companies
Companies
that offer DRIP programs receive investment dollars or capital from
shareholders. Companies can use that capital to reinvest back into the
company.
Shareholders
or investors that are part of a company's DRIP program are less likely to
sell their shares if the company has one bad earnings report or if the
overall market declines. In other words, the investors that are engaged in
the DRIP program are typically long-term investors in the company.
Special
Considerations
It's important to note that the cash
dividends that are reinvested into DRIPs are still considered taxable income
by the Internal Revenue Service (IRS) and must be reported.
Also, when investors who purchased shares via
a company's own DRIP program want to sell their shares, they must sell them
back to the company directly. In
other words, the shares are not sold on the open market via a broker.
Instead, a request to sell the shares must be made with the company, whereby
the company will, in turn, redeem the shares at the prevailing stock price. .
https://stock.walmart.com/investors/stock-information/dividend-history/default.aspx
Wal-Mart
Stores, Inc. was incorporated on Oct. 31, 1969. On Oct. 1, 1970, Walmart
offered 300,000 shares of its common stock to the public at a price of $16.50
per share. Since that time, we have had 11 two-for-one (2:1) stock splits. On
a purchase of 100 shares at $16.50 per share on our first offering, the
number of shares has grown as follows:
2:1 Stock Splits |
Shares |
Cost per Share |
Market Price on Split Date |
Record Date |
Distributed |
On the
Offering |
100 |
$16.50 |
|||
May 1971 |
200 |
$8.25 |
$47.00 |
5/19/71 |
6/11/71 |
March 1972 |
400 |
$4.125 |
$47.50 |
3/22/72 |
4/5/72 |
August 1975 |
800 |
$2.0625 |
$23.00 |
8/19/75 |
8/22/75 |
Nov. 1980 |
1,600 |
$1.03125 |
$50.00 |
11/25/80 |
12/16/80 |
June 1982 |
3,200 |
$0.515625 |
$49.875 |
6/21/82 |
7/9/82 |
June 1983 |
6,400 |
$0.257813 |
$81.625 |
6/20/83 |
7/8/83 |
Sept. 1985 |
12,800 |
$0.128906 |
$49.75 |
9/3/85 |
10/4/85 |
June 1987 |
25,600 |
$0.064453 |
$66.625 |
6/19/87 |
7/10/87 |
June 1990 |
51,200 |
$0.032227 |
$62.50 |
6/15/90 |
7/6/90 |
Feb. 1993 |
102,400 |
$0.016113 |
$63.625 |
2/2/93 |
2/25/93 |
March 1999 |
204,800 |
$0.008057 |
$89.75 |
3/19/99 |
4/19/99 |
Elon Musk’s
SpaceX to split its private stock 10-for-1
PUBLISHED FRI, FEB 18 20221:43 PM ESTUPDATED FRI, FEB 18
20222:38 PM EST
Michael Sheetz
https://www.cnbc.com/2022/02/18/elon-musks-spacex-performing-10-for-1-stock-split.html
KEY POINTS
·
Elon Musk’s
SpaceX is splitting the value of its common stock 10-for-1, CNBC has learned.
With SpaceX valued at $560 a share during its most recent
sale, the split reduces SpaceX’s common stock to $56 a share, according to a
company-wide email obtained by CNBC.
A stock split is cosmetic and does not fundamentally change
anything about the company.
Elon Musk’s SpaceX is splitting the value of its common stock
10-for-1, CNBC has learned, with the company’s valuation having soared to
more than $100 billion.
The split means that for each share of SpaceX stock owned as
of Thursday, a holder now has 10 shares after the conversion. With SpaceX
valued at $560 a share during its most recent sale, the split reduces
SpaceX’s common stock to $56 a share, according to a company-wide email
obtained by CNBC.
“The split has no impact on the overall valuation of the
company or on the overall value of your SpaceX holdings,”
the email said.
SpaceX did not immediately respond to CNBC’s request for
comment.
As the email to employees emphasizes, a stock split is
cosmetic and does not fundamentally change anything about the company.
Companies occasionally perform stock splits, such as high-growth tech
companies such as Apple or Google-parent Alphabet, and the move is typically
seen as a way to make the shares more accessible or manageable.
This is the first time SpaceX has performed a stock split,
according to multiple people familiar with the private company.
The company’s valuation has soared in the last few years as
SpaceX has raised billions to fund work on two capital-intensive projects:
the next generation rocket Starship and its global satellite internet network
Starlink.
What is SpaceX
stock?
SpaceX is not a publicly traded company. That means you cannot
buy SpaceX stock in the public market. Unless you are extremely wealthy or
have a large stake in a company that has a stake in SpaceX, it’s unlikely you
will ever be able to own anything resembling SpaceX shares, for now.
SpaceX still does of course have stakeholders. Founder Elon
Musk, who also founded famed electric vehicle manufacturer Tesla, funded the
company initially with funds from his sale of popular online payments
platform PayPal. Other equity firms, like Founders Fund and Valor Equity Partners,
also have significant stake in SpaceX.
How to buy
SpaceX stock
As mentioned, the only people buying SpaceX stock aren’t
individuals — they’re large corporations and equity firms. For instance,
Google and Fidelity together invested around a billion dollars in 2015 for a
10% stake in the company.
How much does
SpaceX’s stock cost?
SpaceX’s
shares are valued at $56 per share.
SpaceX is not a publicly traded company; therefore, publicly
traded SpaceX stock (which doesn’t exist) has no price.
The only way to know how much SpaceX shares could be worth
would be to look at the company’s last evaluation. In October of 2021, it was
reported that a private shareholder sold shares for a price of $560 per
share. That puts the worth of SpaceX at $100 billion, the second highest
valued private company in the world.
However, SpaceX went through a 10-1 stock split in February of
2022 meaning that for every one share a holder owned, they now own 10. This
also reduces the price of the share, meaning the current price of a single
share of SpaceX is now $56. A stock split doesn’t change anything about the
company except for the number of shares.
SpaceX stock
symbol
SpaceX is not a publicly traded company; therefore, publicly
traded SpaceX stock (which doesn’t exist) has no stock ticker symbol. If it
did have one, SPCX would probably be a good fit.
When will
SpaceX go public?
Elon Musk has stated that SpaceX will not go public any time
soon. Musk has stated that short-term demands of shareholders could ruin the
company’s chance of colonizing Mars, the long term goal of SpaceX. Once that
goal is achieved, Musk might rethink keeping SpaceX private.
Chapter 10 WACC
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)
WACC Calculator help videos FYI
Summary of Equations
Discount rate to figure out the value of projects is called WACC
(weighted average cost of capital)
WACC = weight of debt * cost of debt + weight
of equity *( cost of equity)
·
Wd= total debt / Total capital
= total borrowed / total capital
·
We= total equity/ Total capital
·
Cost of debt = rate(nper, coupon, -(price – flotation costs), 1000)*(1-tax rate)
·
Cost of Equity = D1/(Po – Flotation Cost) + g
·
D1: Next period dividend; Po: Current stock price; g: dividend
growth rate
·
Note: flotation costs = flotation percentage * price
·
Or if beta is given, use CAPM model
1.
Cost of equity = risk free rate + beta *(market return – risk
free rate)
2.
Cost of equity = risk free rate + beta * market risk premium
Discussion:
· Cheaper to raise capital from debt market.
Why? Why not 100% financing via borrowing?
· Why tax rate cannot reduce firms’ cost of
equity?
· Please refer to the following excel worksheet
to learn how to calculate WACC of Hertz (7.99%).
· Excel file is here. Thanks to Chris, Brian and Hanna, the
CFA competition team of 2017.
(FYI: Hertz Global Holdings Inc (NYSE:HTZ) WACC
%:3.74% As of 2/26/2022
As of today, Hertz Global
Holdings Inc's weighted average cost of capital is 3.74%. Hertz
Global Holdings Inc's ROIC % is 7.26% (calculated
using TTM income statement data). Hertz Global Holdings Inc generates higher
returns on investment than it costs the company to raise the capital needed
for that investment. It is earning excess returns. A firm that expects to
continue generating positive excess returns on new investments in the future
will see its value increase as growth increases. https://www.gurufocus.com/term/wacc/HTZ/WACC/Hertz+Global+Holdings+Inc)
In Class Exercise
1.
IBM financed 10m via debt coupon 5%, 10 year, price is $950 and
flotation is 7% of the price, tax 40%.
IBM financed 20m via equity. D1=$5. Po=50, g
is 5%. Flotation cost =0. So WACC?
Answer:
·
Wd=1/3. We=2/3.
·
Kd = rate(10, 5%*1000, -(950-950*7%), 1000)*(1-40%)------ after tax
cost of debt
·
Ke = 5/(50 – 0) + 5%
-------- cost of equity
·
WACC = Wd*Kd +We*Ke =
2. Firm AAA sold a
noncallable bond now has 20 years to maturity. 9.25% annual coupon
rate, paid semiannually, sells at a price = $1,075, par =
$1,000. Tax rate = 40%, calculate after tax cost of debt (5.08%)
Answer:
·
after tax cost of debt = rate(nper, coupon, -(price-flotation),
1000)*(1-tax rate)
·
After tax of debt = rate(20*2, 9.25%*1000/2, -(1075-0),
1000)*(1-40%)=5.08%
3.
Firm AAA’s equity condition is as follows. D1 =
$1.25; P0 = $27.50; g = 5.00%; and Flotation = 6.00% of
price. Calculate cost of equity (9.84%)
Answer:
·
Cost of equity = D1/(Po-flotation) + g= 1.25/(27.5-6%*27.5) + 5%
= 9.84%
4.
Continue from above. Firm AAA raised 10m from the capital
market. In it, 3m is from the debt market and the rest from the equity
market. Calculate WACC.
Answer:
·
WACC = Wd*Kd +We*Ke =
·
WACC = (3/10)*5.08% + (7/10)*9.84%
5.
Common
stock currently sells =
$45.00 /
share; and earn $2.75 /share this year, payout
ratio is 70%, and its constant growth rate = 6.00%.
New stock can
be sold at the current price, a flotation cost =8%. How much would the cost
of new stock beyond
the cost of retained earnings?
Answer:
Expected EPS1 $2.75
Payout ratio 70%
Current stk price $45.00
g 6.00%
F 8.00%
D1 $1.925
rs = D1/P0 + g 10.28%
re = D1/(P0 ×
(1 − F)) + g 10.65%
Difference = re – rs 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%
rRF 4.50%
RPM 5.50%
b 1.20
Weight debt 35%
Weight equity 65%
Bond yield 7.51%
A-T cost of debt 4.51%
Cost of equity, rs = rRF + b(RPM) 11.10%
WACC = wd(rd)(1
– T) + wc(rs) = 8.79%
WACC Case study (due with the 2nd mid term exam)
Case
Video in class completed (Thanks, Ethan and Maggie)
FYI: WACC calculator https://fairness-finance.com/fairness-finance/finance/calculator/wacc.dhtml
Cost of Capital
by Sector (US)
https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/wacc.html
Industry Name |
Number of Firms |
Beta |
Cost of Equity |
E/(D+E) |
Std Dev in Stock |
Cost of Debt |
Tax Rate |
After-tax Cost of Debt |
D/(D+E) |
Cost of Capital |
Advertising |
58 |
1.63 |
13.57% |
68.97% |
52.72% |
5.88% |
6.39% |
4.41% |
31.03% |
10.73% |
Aerospace/Defense |
77 |
1.41 |
12.28% |
79.33% |
37.56% |
5.50% |
8.60% |
4.13% |
20.67% |
10.59% |
Air
Transport |
21 |
1.42 |
12.29% |
34.92% |
37.73% |
5.50% |
10.47% |
4.13% |
65.08% |
6.98% |
Apparel |
39 |
1.32 |
11.75% |
65.98% |
38.51% |
5.50% |
12.04% |
4.13% |
34.02% |
9.15% |
Auto
& Truck |
31 |
1.54 |
13.03% |
66.58% |
52.61% |
5.88% |
3.00% |
4.41% |
33.42% |
10.15% |
Auto
Parts |
37 |
1.47 |
12.64% |
70.10% |
39.52% |
5.50% |
9.30% |
4.13% |
29.90% |
10.09% |
Bank
(Money Center) |
7 |
1.08 |
10.30% |
31.61% |
19.59% |
4.73% |
16.25% |
3.55% |
68.39% |
5.68% |
Banks
(Regional) |
557 |
0.5 |
6.88% |
60.75% |
16.76% |
4.73% |
18.84% |
3.55% |
39.25% |
5.57% |
Beverage
(Alcoholic) |
23 |
1.01 |
9.90% |
81.36% |
49.87% |
5.50% |
9.39% |
4.13% |
18.64% |
8.82% |
Beverage
(Soft) |
31 |
1.3 |
11.62% |
86.75% |
41.72% |
5.50% |
6.42% |
4.13% |
13.25% |
10.63% |
Broadcasting |
26 |
1.32 |
11.73% |
40.51% |
46.90% |
5.50% |
15.76% |
4.13% |
59.49% |
7.21% |
Brokerage
& Investment Banking |
30 |
1.2 |
11.04% |
33.21% |
28.00% |
5.50% |
15.32% |
4.13% |
66.79% |
6.42% |
Building
Materials |
45 |
1.28 |
11.47% |
77.56% |
29.19% |
5.50% |
16.71% |
4.13% |
22.44% |
9.82% |
Business
& Consumer Services |
164 |
1.17 |
10.84% |
78.45% |
45.78% |
5.50% |
9.43% |
4.13% |
21.55% |
9.39% |
Cable
TV |
10 |
1.26 |
11.34% |
48.25% |
25.41% |
5.50% |
21.95% |
4.13% |
51.75% |
7.60% |
Chemical
(Basic) |
38 |
1.25 |
11.29% |
67.43% |
46.58% |
5.50% |
9.83% |
4.13% |
32.57% |
8.95% |
Chemical
(Diversified) |
4 |
1.41 |
12.27% |
63.19% |
39.49% |
5.50% |
12.02% |
4.13% |
36.81% |
9.27% |
Chemical
(Specialty) |
76 |
1.28 |
11.47% |
78.49% |
42.32% |
5.50% |
10.75% |
4.13% |
21.51% |
9.89% |
Coal
& Related Energy |
19 |
1.45 |
12.51% |
82.16% |
61.96% |
5.88% |
2.28% |
4.41% |
17.84% |
11.06% |
Computer
Services |
80 |
1.17 |
10.84% |
75.44% |
47.78% |
5.50% |
6.47% |
4.13% |
24.56% |
9.19% |
Computers/Peripherals |
42 |
1.29 |
11.55% |
91.31% |
48.73% |
5.50% |
9.13% |
4.13% |
8.69% |
10.90% |
Construction
Supplies |
49 |
1.26 |
11.39% |
76.85% |
35.11% |
5.50% |
10.52% |
4.13% |
23.15% |
9.71% |
Diversified |
23 |
1.04 |
10.05% |
82.48% |
57.84% |
5.88% |
2.98% |
4.41% |
17.52% |
9.06% |
Drugs
(Biotechnology) |
598 |
1.24 |
11.26% |
86.71% |
58.41% |
5.88% |
0.94% |
4.41% |
13.29% |
10.35% |
Drugs
(Pharmaceutical) |
281 |
1.27 |
11.41% |
88.02% |
64.88% |
5.88% |
2.37% |
4.41% |
11.98% |
10.57% |
Education |
33 |
1.1 |
10.42% |
76.56% |
41.81% |
5.50% |
7.10% |
4.13% |
23.44% |
8.94% |
Electrical
Equipment |
110 |
1.59 |
13.32% |
81.62% |
58.55% |
5.88% |
4.47% |
4.41% |
18.38% |
11.68% |
Electronics
(Consumer & Office) |
16 |
1.54 |
13.02% |
85.87% |
39.56% |
5.50% |
3.98% |
4.13% |
14.13% |
11.76% |
Electronics
(General) |
138 |
1.2 |
11.02% |
84.16% |
44.94% |
5.50% |
6.29% |
4.13% |
15.84% |
9.92% |
Engineering/Construction |
43 |
1.2 |
10.99% |
75.99% |
35.17% |
5.50% |
13.30% |
4.13% |
24.01% |
9.34% |
Entertainment |
110 |
1.45 |
12.49% |
75.03% |
57.81% |
5.88% |
3.45% |
4.41% |
24.97% |
10.47% |
Environmental
& Waste Services |
62 |
1.02 |
9.91% |
79.66% |
48.09% |
5.50% |
5.42% |
4.13% |
20.34% |
8.73% |
Farming/Agriculture |
39 |
1.14 |
10.65% |
74.70% |
54.43% |
5.88% |
6.64% |
4.41% |
25.30% |
9.07% |
Financial
Svcs. (Non-bank & Insurance) |
223 |
0.89 |
9.14% |
9.05% |
27.15% |
5.50% |
14.61% |
4.13% |
90.95% |
4.58% |
Food
Processing |
92 |
0.92 |
9.33% |
77.60% |
34.23% |
5.50% |
7.74% |
4.13% |
22.40% |
8.16% |
Food
Wholesalers |
14 |
1.12 |
10.55% |
68.42% |
32.42% |
5.50% |
11.94% |
4.13% |
31.58% |
8.52% |
Furn/Home
Furnishings |
32 |
1.27 |
11.43% |
64.13% |
41.91% |
5.50% |
12.67% |
4.13% |
35.87% |
8.81% |
Green
& Renewable Energy |
19 |
1.6 |
13.39% |
45.23% |
67.60% |
7.01% |
6.73% |
5.26% |
54.77% |
8.93% |
Healthcare
Products |
254 |
1.16 |
10.78% |
88.81% |
50.94% |
5.88% |
3.70% |
4.41% |
11.19% |
10.07% |
Healthcare
Support Services |
131 |
1.16 |
10.77% |
80.90% |
47.79% |
5.50% |
6.74% |
4.13% |
19.10% |
9.50% |
Heathcare
Information and Technology |
138 |
1.47 |
12.62% |
87.56% |
53.87% |
5.88% |
4.30% |
4.41% |
12.44% |
11.60% |
Homebuilding |
32 |
1.5 |
12.80% |
75.57% |
33.33% |
5.50% |
17.81% |
4.13% |
24.43% |
10.68% |
Hospitals/Healthcare
Facilities |
34 |
1.17 |
10.85% |
53.41% |
51.19% |
5.88% |
9.56% |
4.41% |
46.59% |
7.85% |
Hotel/Gaming |
69 |
1.46 |
12.55% |
60.03% |
38.05% |
5.50% |
8.14% |
4.13% |
39.97% |
9.18% |
Household
Products |
127 |
1.16 |
10.74% |
86.56% |
56.83% |
5.88% |
6.73% |
4.41% |
13.44% |
9.89% |
Information
Services |
73 |
1.4 |
12.22% |
88.45% |
45.11% |
5.50% |
12.45% |
4.13% |
11.55% |
11.29% |
Insurance
(General) |
21 |
1.23 |
11.17% |
76.63% |
43.76% |
5.50% |
10.26% |
4.13% |
23.37% |
9.53% |
Insurance
(Life) |
27 |
0.94 |
9.46% |
51.97% |
28.89% |
5.50% |
11.41% |
4.13% |
48.03% |
6.90% |
Insurance
(Prop/Cas.) |
51 |
0.8 |
8.65% |
82.33% |
27.67% |
5.50% |
10.92% |
4.13% |
17.67% |
7.85% |
Investments
& Asset Management |
600 |
0.62 |
7.58% |
72.28% |
9.91% |
4.73% |
4.01% |
3.55% |
27.72% |
6.47% |
Machinery |
116 |
1.22 |
11.16% |
82.75% |
32.36% |
5.50% |
10.37% |
4.13% |
17.25% |
9.94% |
Metals
& Mining |
68 |
1.29 |
11.54% |
82.27% |
70.06% |
7.01% |
4.15% |
5.26% |
17.73% |
10.43% |
Office
Equipment & Services |
16 |
1.18 |
10.87% |
59.95% |
35.22% |
5.50% |
19.53% |
4.13% |
40.05% |
8.17% |
Oil/Gas
(Integrated) |
4 |
0.98 |
9.69% |
89.68% |
30.55% |
5.50% |
14.22% |
4.13% |
10.32% |
9.11% |
Oil/Gas
(Production and Exploration) |
174 |
1.26 |
11.35% |
83.28% |
56.98% |
5.88% |
4.60% |
4.41% |
16.72% |
10.19% |
Oil/Gas
Distribution |
23 |
0.99 |
9.77% |
58.34% |
33.55% |
5.50% |
6.90% |
4.13% |
41.66% |
7.42% |
Oilfield
Svcs/Equip. |
101 |
1.38 |
12.05% |
75.41% |
46.90% |
5.50% |
7.07% |
4.13% |
24.59% |
10.10% |
Packaging
& Container |
25 |
0.95 |
9.54% |
61.74% |
24.43% |
4.73% |
14.66% |
3.55% |
38.26% |
7.25% |
Paper/Forest
Products |
7 |
1.38 |
12.10% |
69.51% |
42.84% |
5.50% |
12.76% |
4.13% |
30.49% |
9.66% |
Power |
48 |
0.73 |
8.19% |
56.45% |
17.18% |
4.73% |
12.30% |
3.55% |
43.55% |
6.17% |
Precious
Metals |
74 |
1.23 |
11.21% |
85.97% |
72.54% |
7.01% |
2.87% |
5.26% |
14.03% |
10.37% |
Publishing
& Newspapers |
20 |
1.11 |
10.50% |
70.34% |
30.92% |
5.50% |
9.67% |
4.13% |
29.66% |
8.61% |
R.E.I.T. |
223 |
1.06 |
10.20% |
56.39% |
21.54% |
4.73% |
3.38% |
3.55% |
43.61% |
7.30% |
Real
Estate (Development) |
18 |
1.52 |
12.89% |
47.05% |
51.25% |
5.88% |
6.66% |
4.41% |
52.95% |
8.40% |
Real
Estate (General/Diversified) |
12 |
0.79 |
8.57% |
71.52% |
28.66% |
5.50% |
9.37% |
4.13% |
28.48% |
7.31% |
Real
Estate (Operations & Services) |
60 |
1.35 |
11.87% |
47.79% |
44.43% |
5.50% |
5.47% |
4.13% |
52.21% |
7.83% |
Recreation |
57 |
1.42 |
12.30% |
65.76% |
42.13% |
5.50% |
9.49% |
4.13% |
34.24% |
9.50% |
Reinsurance |
1 |
0.83 |
8.81% |
68.92% |
19.37% |
4.73% |
6.48% |
3.55% |
31.08% |
7.17% |
Restaurant/Dining |
70 |
1.41 |
12.26% |
76.47% |
41.15% |
5.50% |
8.54% |
4.13% |
23.53% |
10.34% |
Retail
(Automotive) |
30 |
1.52 |
12.91% |
63.50% |
35.71% |
5.50% |
15.84% |
4.13% |
36.50% |
9.70% |
Retail
(Building Supply) |
15 |
1.79 |
14.51% |
82.50% |
37.55% |
5.50% |
13.39% |
4.13% |
17.50% |
12.69% |
Retail
(Distributors) |
69 |
1.28 |
11.45% |
71.65% |
37.08% |
5.50% |
13.59% |
4.13% |
28.35% |
9.38% |
Retail
(General) |
15 |
1.36 |
11.98% |
83.35% |
31.53% |
5.50% |
21.26% |
4.13% |
16.65% |
10.67% |
Retail
(Grocery and Food) |
13 |
0.67 |
7.85% |
60.31% |
28.26% |
5.50% |
16.45% |
4.13% |
39.69% |
6.37% |
Retail
(Online) |
63 |
1.49 |
12.71% |
83.91% |
59.41% |
5.88% |
4.09% |
4.41% |
16.09% |
11.38% |
Retail
(Special Lines) |
78 |
1.48 |
12.64% |
71.86% |
38.59% |
5.50% |
15.02% |
4.13% |
28.14% |
10.25% |
Rubber&
Tires |
3 |
0.84 |
8.86% |
23.24% |
39.79% |
5.50% |
0.00% |
4.13% |
76.76% |
5.22% |
Semiconductor |
68 |
1.61 |
13.43% |
89.88% |
38.40% |
5.50% |
8.18% |
4.13% |
10.12% |
12.49% |
Semiconductor
Equip |
30 |
1.76 |
14.32% |
89.46% |
41.57% |
5.50% |
10.94% |
4.13% |
10.54% |
13.24% |
Shipbuilding
& Marine |
8 |
0.94 |
9.49% |
71.93% |
41.16% |
5.50% |
6.23% |
4.13% |
28.07% |
7.98% |
Shoe |
13 |
1.33 |
11.77% |
91.73% |
39.37% |
5.50% |
10.70% |
4.13% |
8.27% |
11.13% |
Software
(Entertainment) |
91 |
1.36 |
11.98% |
95.42% |
58.71% |
5.88% |
3.82% |
4.41% |
4.58% |
11.63% |
Software
(Internet) |
33 |
1.55 |
13.09% |
84.99% |
55.24% |
5.88% |
2.37% |
4.41% |
15.01% |
11.79% |
Software
(System & Application) |
390 |
1.47 |
12.61% |
91.44% |
52.11% |
5.88% |
3.40% |
4.41% |
8.56% |
11.91% |
Steel |
28 |
1.34 |
11.85% |
77.76% |
38.30% |
5.50% |
14.95% |
4.13% |
22.24% |
10.14% |
Telecom
(Wireless) |
16 |
1.03 |
10.00% |
60.55% |
51.92% |
5.88% |
3.83% |
4.41% |
39.45% |
7.80% |
Telecom.
Equipment |
79 |
1.23 |
11.20% |
89.54% |
41.35% |
5.50% |
4.06% |
4.13% |
10.46% |
10.46% |
Telecom.
Services |
49 |
0.88 |
9.12% |
45.93% |
55.37% |
5.88% |
6.54% |
4.41% |
54.07% |
6.57% |
Tobacco |
15 |
2 |
15.76% |
80.61% |
44.06% |
5.50% |
9.83% |
4.13% |
19.39% |
13.51% |
Transportation |
18 |
1.06 |
10.17% |
77.21% |
28.05% |
5.50% |
16.39% |
4.13% |
22.79% |
8.79% |
Transportation
(Railroads) |
4 |
1.11 |
10.46% |
78.46% |
16.34% |
4.73% |
16.57% |
3.55% |
21.54% |
8.97% |
Trucking |
35 |
1.55 |
13.06% |
69.49% |
41.17% |
5.50% |
14.79% |
4.13% |
30.51% |
10.33% |
Utility
(General) |
15 |
0.64 |
7.65% |
57.41% |
14.97% |
4.73% |
13.20% |
3.55% |
42.59% |
5.90% |
Utility
(Water) |
16 |
1.15 |
10.73% |
69.74% |
27.96% |
5.50% |
8.45% |
4.13% |
30.26% |
8.73% |
Total
Market |
7165 |
1.16 |
10.75% |
65.14% |
41.37% |
5.50% |
7.52% |
4.13% |
34.86% |
8.44% |
Total
Market (without financials) |
5649 |
1.29 |
11.56% |
79.11% |
47.98% |
5.50% |
6.38% |
4.13% |
20.89% |
10.01% |
Recommended websites for WACC
Tesla
·
https://www.gurufocus.com/term/wacc/TSLA/WACC-Percentage/Tesla
·
https://valueinvesting.io/TSLA/valuation/wacc // cost of equity = long term bond rate +
premium
Wal-Mart
·
https://valueinvesting.io/WMT/valuation/wacc
Apple
·
https://www.gurufocus.com/term/wacc/AAPL/WACC-Percentage/Apple
·
https://valueinvesting.io/AAPL/valuation/wacc
Amazon
·
https://valueinvesting.io/AMZN/valuation/wacc
·
https://www.gurufocus.com/term/wacc/AMZN/WACC-Percentage/Amazon.com
Chapter 11: Capital Budgeting
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.
· 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. 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 )
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. |
4)
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.
·
Sorry for the mistake in class
for accidentally closing the recording in class
·
Thanks to Ted and Maggie for
taking the lead in class for this case study.
Case
study video in class 3/23/2023 – Part II (Thanks, Ted and Christian)
Let’s have some fun with ChatGPT – generate NPV
Calculator by ChatGPT Here are step-by-step instructions: 1. Ask
ChatGPT to generate a NPV calculator using JavaScript in HTML format. You
can ask something like: "Hey ChatGPT, could you please generate a NPV
calculator using JavaScript in HTML format to calculate the NPV, given cash
flows and the discount rate?" 2. ChatGPT
should respond with the code for the calculator. Copy the code to your
clipboard. 3. Open
Notepad or any other text editor and paste the code into a new document. 4. Save
the file as an HTML file. You can name it anything you like, but make sure
the file extension is ".html". For example, you can name it
"npv_calculator.html". 5. Open
the saved HTML file in your web browser (e.g. Chrome, Firefox, etc.) by double-clicking
on the file or right-clicking and selecting "Open with". The NPV
calculator should load and be ready to use. 6. Test
the calculator by entering different values for the cash flows and the
disount rate. Make sure the calculated NPV is correct and matches your
expectations. 7.
If you find any
issues with the calculator, you can ask ChatGPT to generate it again with
the desired changes. Or use the code from my experiment with
ChatGPT earlier this week to get both NPV and NFV <!DOCTYPE
html> <html> <head> <title>Net Present and Future
Value Calculator</title> <script> function calculateNPV() { var initialInvestment =
parseFloat(document.getElementById("initial-investment").value); var discountRate = parseFloat(document.getElementById("discount-rate").value); var cashFlows =
document.getElementById("cash-flows").value.trim(); // check for empty input if (cashFlows === "")
{
document.getElementById("npv-result").innerHTML =
"";
document.getElementById("nfv-result").innerHTML =
"";
document.getElementById("error-message").innerHTML =
"Please enter at least one cash flow."; return; } // split input into an array of cash
flows cashFlows =
cashFlows.split(","); // parse each cash flow and
check for invalid input for (var i = 0; i <
cashFlows.length; i++) { var cashFlow = parseFloat(cashFlows[i]); if (isNaN(cashFlow)) {
document.getElementById("npv-result").innerHTML =
"";
document.getElementById("nfv-result").innerHTML =
"";
document.getElementById("error-message").innerHTML =
"Invalid cash flow entered at position " + (i+1) + "."; return; } cashFlows[i] = cashFlow; } // calculate net present value var npv = -initialInvestment; for (var i = 0; i <
cashFlows.length; i++) { npv += cashFlows[i] /
Math.pow(1 + discountRate, i+1); } // calculate net future value var nfv = npv * Math.pow(1 + discountRate,
cashFlows.length); // display results
document.getElementById("npv-result").innerHTML =
"Net Present Value: $" + npv.toFixed(2);
document.getElementById("nfv-result").innerHTML =
"Net Future Value: $" + nfv.toFixed(2);
document.getElementById("error-message").innerHTML =
""; } </script> </head> <body> <h1>Net Present and Future Value
Calculator</h1> <label
for="initial-investment">Initial Investment:</label> <input type="number"
id="initial-investment" value="10000"
step="any"><br><br> <label
for="discount-rate">Discount Rate:</label> <input type="number"
id="discount-rate" value="0.1"
step="any"><br><br> <label
for="cash-flows">Cash Flows:</label> <textarea id="cash-flows"
rows="5"
cols="50"></textarea><br><br> <button
onclick="calculateNPV()">Calculate NPV and NFV</button> <p
id="npv-result"></p> <p
id="nfv-result"></p> <p class="error"
id="error-message"></p> </body> </html> |
||
Another
example for MIRR:
<!DOCTYPE
html>
<html>
<head>
<meta
charset="utf-8">
<title>Modified Internal
Rate of Return (MIRR) Calculator</title>
</head>
<body>
<h1>Modified Internal
Rate of Return (MIRR) Calculator</h1>
<label
for="initial-investment">Initial Investment:</label>
<input
type="number" id="initial-investment"
step="any">
<br><br>
<label
for="cash-flows">Cash Flows (comma separated):</label>
<input type="text"
id="cash-flows">
<br><br>
<label
for="finance-rate">Finance Rate (%):</label>
<input
type="number" id="finance-rate">
<br><br>
<label
for="reinvest-rate">Reinvestment Rate (%):</label>
<input
type="number" id="reinvest-rate">
<br><br>
<button
onclick="calculateMIRR()">Calculate MIRR</button>
<br><br>
<label for="result">MIRR:</label>
<input type="text"
id="result" readonly>
<script>
function
calculateMIRR() {
const
initialInvestment =
parseFloat(document.getElementById("initial-investment").value);
const
cashFlows = document.getElementById("cash-flows").value.split(",").map(Number);
const
financeRate =
parseFloat(document.getElementById("finance-rate").value) / 100;
const
reinvestRate =
parseFloat(document.getElementById("reinvest-rate").value) / 100;
//
Calculate terminal value of cash flows
const
terminalValue = cashFlows.reduce((pv, cf, i) => {
return
pv + cf / Math.pow(1 + reinvestRate, i + 1);
},
0);
//
Calculate MIRR
const
numerator = terminalValue + initialInvestment;
const
denominator = Math.pow(1 + financeRate, cashFlows.length);
const
mirr = Math.pow(numerator / denominator, 1 / cashFlows.length) - 1;
document.getElementById("result").value
= mirr.toFixed(4);
}
</script>
</body>
</html>
Second Midterm Exam
·
3/27/2023
·
in class
·
similar to case studies
·
chapters 9, 10, 11
One common
method for evaluating a firm is the Discounted Cash Flow (DCF) analysis. This method involves estimating the future cash flows of the firm and
discounting them back to their present value using a discount rate.
Video – General
Introduction DCF
Here are the
detailed steps and equations involved in the DCF analysis:
·
Estimate
future cash flows: The first step is to estimate the future cash flows that
the firm is expected to generate. This typically involves forecasting
revenue, expenses, and capital expenditures for a number of years into the
future. Let's denote these cash flows as CF1, CF2, ..., CFn.
·
Determine
the discount rate: The discount rate is the rate of return that an investor
requires to invest in the firm. This rate should reflect the risk associated
with the investment, with higher-risk investments requiring a higher rate of
return. Let's denote the discount rate as r.
·
Calculate
the present value of future cash flows: Once the future cash flows and
discount rate have been determined, we can calculate the present value of
each cash flow using the following formula:
PV
= CF / (1 + r)^n
where
PV is the present value of the cash flow, CF is the cash flow for a given
year, r is the discount rate, and n is the number of years into the future
that the cash flow occurs.
·
Calculate
the terminal value: After estimating cash flows for a number of years, we
need to estimate the value of the firm beyond the forecast period. Let's
denote the terminal value as TV.
·
Calculate
the total present value: Once we have calculated the present value of each
cash flow and the terminal value, we can sum them up to get the total present
value (PV) of the firm:
PV
= PV1 + PV2 + ... + PVn + PV of TV
·
Subtract
the firm's debt: Finally, we need to subtract the firm's outstanding debt
from the total present value to arrive at the firm's equity value:
·
Equity
value = PV - Debt
·
Overall,
the DCF analysis provides an estimate of the intrinsic value of the firm
based on its expected future cash flows and the WACC. However, it should be
noted that the accuracy of the analysis is highly dependent on the accuracy
of the cash flow and discount rate estimates. --- ChatGPT
DCF - An
Example – ChatGPT (FYI)
XYZ
Corp. DCF Analysis Report
Introduction:
This
report is a DCF analysis of XYZ Corp., a publicly traded company with a current
market capitalization of $10 billion. The purpose of this report is to
estimate the intrinsic value of the company using a discounted cash flow
(DCF) model. Assuming that the
company’s funding is entirely based on equity.
Step 1: Forecast Future Cash Flows
To
forecast future cash flows, we have assumed that the company's cash flows
will grow at a rate of 5% per year for the next five years. The forecasted
cash flows are as follows:
Year 0:
$1.00 billion
Year 1:
$1.05 billion
Year 2:
$1.10 billion
Year 3:
$1.16 billion
Year 4:
$1.22 billion
Year 5:
$1.28 billion
Step 2: Estimate the Terminal Value
To
estimate the terminal value, we have assumed that the cash flows beyond Year
5 will grow at a rate of 2% per year, which is lower than the growth rate
assumed for the forecasted cash flows. The terminal value is calculated as
follows:
Terminal
Value = Year 6 Cash Flow / (Discount Rate - Growth Rate)
Year 6
Cash Flow = $1.28 billion *(1+ 2%) = $1.30 billion
Discount
Rate = 10%
Growth
Rate = 2%
Therefore,
Terminal Value = $1.30 billion / ( cost of equity - 2%)
Step 3: Determine the Discount Rate
To
determine the discount rate, we have used the Capital Asset Pricing Model
(CAPM) to estimate the company's cost of equity. The CAPM formula is:
Cost of
Equity = Risk-Free Rate + Beta * (Market Risk Premium)
where:
Risk-Free
Rate = 2%
Beta =
1.2 (estimated based on industry comparables)
Market
Risk Premium = 7% (historical average)
Therefore,
Cost of Equity = 2% + 1.2 * 7% = 10.4%
Terminal
Value = $1.30 billion / (cost of equity - 2%)
= $1.30 billion / (10.4% - 2%) = $15.50 billion
Step 4:
Calculate the Present Value of Future Cash Flows
To
calculate the present value of each cash flow, we have used the following
formula:
Present
Value = Cash Flow / (1 + Discount Rate) ^ Year
Using
this formula, we can calculate the present value of each cash flow as
follows:
Year 1:
$1.05 billion / (1 + 10.4%)^1 = $951 million
Year 2:
$1.10 billion / (1 + 10.4%)^2 = $905 million
Year 3:
$1.16 billion / (1 + 10.4%)^3 = $860 million
Year 4:
$1.22 billion / (1 + 10.4%)^4 = $818 million
Year 5:
$1.28 billion / (1 + 10.4%)^5 = $778 million
Terminal
Value: $15.50 billion / (1 + 10.4%)^5 = $9.45 billion
Step 5: Sum the present value of cash flows and
terminal value
We can
now sum up the present value of each cash flow and the terminal value to get
the total intrinsic value of XYZ Corp.
Total
Intrinsic Value = Present Value of Cash Flows + Terminal Value
= $951
million + $905 million + $860 million + $818 million + $778 million + $9.45
billion
=
$13.76 billion
Step 6: Compare the intrinsic value with the
market capitalization
Finally,
we need to compare the intrinsic value of XYZ Corp. with its market
capitalization to determine whether the stock is undervalued, overvalued, or
fairly valued. In this case, the intrinsic value of XYZ Corp. is $13.76
billion, while its market capitalization is $10 billion. This suggests that
the stock is undervalued and may be a good investment opportunity.
Note that
this example is simplified and does not take into account other factors such
as changes in working capital or debt payments. Also, it's important to keep
in mind that DCF analysis is only one of several methods used to value a
company and should be used in conjunction with other valuation techniques.
Overall,
based on the DCF analysis, XYZ Corp. appears to be undervalued relative to
its intrinsic value. However, investors should conduct further research and
analysis before making any investment decisions.
Step 7: Sensitivity Analysis (Monte Carlo
Analysis is a method used for conducting sensitivity analysis)
Sensitivity
analysis is an important tool in determining the robustness of our valuation.
It helps us understand how changes in assumptions can affect the estimated
intrinsic value. In our DCF analysis of XYZ Corp., we assumed a 5% growth
rate for the next five years and a 2% growth rate beyond that. Let's see how
our intrinsic value would change if we vary these assumptions.
Assumption 1: Growth Rate
If we
assume a lower growth rate of 4% for the next five years, the intrinsic value
of XYZ Corp. decreases to $13.20 billion. On the other hand, if we assume a
higher growth rate of 6%, the intrinsic value increases to $14.34 billion.
This tells us that our estimate is sensitive to changes in the growth rate
assumption.
Assumption 2: Terminal Growth Rate
If we
assume a lower terminal growth rate of 1%, the intrinsic value of XYZ Corp. decreases
to $12.67 billion. Conversely, if we assume a higher terminal growth rate of
3%, the intrinsic value increases to $15.14 billion. Again, this tells us
that our estimate is sensitive to changes in the terminal growth rate
assumption.
Overall,
our DCF analysis suggests that XYZ Corp. is undervalued, with an intrinsic
value of $13.76 billion compared to its market capitalization of $10 billion.
However, we must keep in mind that this is just one method of valuation and
there are many other factors that can affect the stock price. As always,
investors should conduct their own due diligence and consult with financial
professionals before making any investment decisions.
Evaluation of
Amazon based on DCF - ChatGPT
DCF (Discounted Cash Flow) analysis is a commonly used method
for evaluating the intrinsic value of a company. It is based on the idea that
the value of a company is determined by the present value of its expected
future cash flows.
Here are the steps to evaluate Amazon using DCF:
Step 1: Estimate Amazon's
Free Cash Flow (FCF)
FCF is the cash generated by a company after accounting for
all capital expenditures needed to maintain or grow the business. To calculate
Amazon's FCF, we can start with its operating cash flow and subtract its
capital expenditures.
Operating cash flow for the last 12 months (as of September
2021) was $92.5 billion, and capital expenditures were $24.5 billion.
Therefore, Amazon's FCF is:
FCF = Operating cash flow - Capital expenditures
FCF = $92.5 billion - $24.5 billion
FCF = $68 billion
Step 2: Estimate Amazon's
growth rate
Next, we need to estimate the rate at which Amazon's FCF is likely
to grow in the future. One way to do this is to look at the historical growth
rates and make an educated guess about future growth.
Amazon's FCF has grown at an average rate of 25% over the past
five years. Assuming a conservative growth rate of 15% for the next five
years, and then a terminal growth rate of 3% after that, we can estimate
Amazon's future FCF as follows:
Year 1 FCF = $68 billion x (1 + 15%) = $78.2 billion
Year 2 FCF = $78.2 billion x (1 + 15%) = $89.9 billion
Year 3 FCF = $89.9 billion x (1 + 15%) = $103.4 billion
Year 4 FCF = $103.4 billion x (1 + 15%) = $119 billion
Year 5 FCF = $119 billion x (1 + 15%) = $137 billion
Terminal FCF = $137 billion x (1 + 3%) / (11% - 3%) = $1760.94
billion (11% is the WACC)
Step 3: Determine Amazon's
Discount Rate
The discount rate is the rate of return required by investors
to compensate for the risk of investing in a company. A higher discount rate
indicates a higher level of risk. To determine Amazon's discount rate, we can
use the CAPM (Capital Asset Pricing Model), which takes into account the
risk-free rate, market risk premium, and Amazon's beta.
Assuming a risk-free rate of 2%, a market risk premium of 6%,
and Amazon's beta of 1.5, we can calculate Amazon's discount rate as follows:
Discount rate = Risk-free rate + Beta x Market risk premium
Discount rate = 2% + 1.5 x 6%
Discount rate = 11%
Step 4: Calculate Amazon's
Intrinsic Value
Finally, we can calculate Amazon's intrinsic value using the
discounted cash flow formula, which is the sum of the present value of all
future cash flows.
Intrinsic value = (Year 1 FCF / (1 + Discount rate)^1) + (Year
2 FCF / (1 + Discount rate)^2) + ... + (Terminal FCF / (1 + Discount rate)^5)
Intrinsic value = ($78.2 billion / (1 + 11%)^1) + ($89.9 billion
/ (1 + 11%)^2) + ($103.4 billion / (1 + 11%)^3) + ($119 billion / (1 +
11%)^4) + ($137 billion / (1 +11%)^5) + ($1.76 trillion / (1 + 11%)^5)
Intrinsic value = $1,423 billion
We made the assumption that AMAZON's cost of equity is roughly
equivalent to its WACC for the purpose of simplifying the calculation.
However, according to gurufocus.com, as of the end of March 2023, AMAZON's
WACC is 9.65%.
Step 5: Compare Intrinsic
Value with Market Value
The last step is to compare the intrinsic value we calculated
with the current market value of Amazon. As of March 2023, Amazon's market
capitalization is around $2.4 trillion.
Comparing the intrinsic value of $1,423 billion with the
market capitalization of $2.4 trillion, we can see that the market value is
higher than the intrinsic value, which suggests that the stock may be
overvalued. However, it's important to keep in mind that the DCF analysis is
based on various assumptions and estimates, and the actual value of a company
may differ from the calculated intrinsic value.
Therefore, it's important to use multiple valuation methods
and take into account other factors such as industry trends, competitive
landscape, and management quality to make an informed investment decision.
To calculate the estimated per-share stock price based on the
DCF analysis, we can divide the intrinsic value by the total number of shares
outstanding. As of December 2021, Amazon had around 500 million shares
outstanding.
Estimated Per-Share Stock Price = Intrinsic Value / Shares
Outstanding
Estimated Per-Share Stock Price = $1,423 billion / 500 million
Estimated Per-Share Stock Price = $2,847
Therefore, based on this DCF analysis, the estimated per-share
stock price for Amazon is $2,847. However, it's important to note that this
is just an estimate based on certain assumptions and estimates, and the
actual stock price may differ based on various factors such as market
sentiment, company performance, and global economic conditions.
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.
Amazon.com
Inc., free cash flow to the firm (FCFF) forecast
Year |
Value |
FCFFt or
Terminal value (TVt) |
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 |
1
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%
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% |
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%
Amazon.com
Inc., H-model
Year |
Value |
gt |
1 |
g1 |
0.00% |
2 |
g2 |
0.00% |
3 |
g3 |
0.00% |
4 |
g4 |
0.00% |
5 and thereafter |
g5 |
0.00% |
where:
g1 is implied by PRAT model
g5 is implied by single-stage model
g2, g3 and g4 are calculated using
linear interpoltion between g1 and g5
Calculations
g2 = g1 + (g5 – g1) × (2 – 1) ÷ (5 – 1)
= 0.00% + (0.00%
– 0.00%) × (2 – 1) ÷ (5 – 1) = 0.00%
g3 = g1 + (g5 – g1) × (3 – 1) ÷ (5 – 1)
= 0.00% + (0.00%
– 0.00%) × (3 – 1) ÷ (5 – 1) = 0.00%
g4 = g1 + (g5 – g1) × (4 –
1) ÷ (5 – 1)
= 0.00% + (0.00%
– 0.00%) × (4 – 1) ÷ (5 – 1) = 0.00%
Chapter 3 Financial Statement
http://www.jufinance.com/10k/bs
http://www.jufinance.com/10k/is
http://www.jufinance.com/10k/cf
Note:
All companies, foreign and domestic, are required to file registration
statements, periodic reports, and other forms electronically through
EDGAR.
************
What is Free Cash Flow **************
What is free cash flow (video)
What
is free cash flow (FCF)? Why is it important?
• FCF is
the amount of cash available from operations for distribution to all
investors (including stockholders and debtholders)
after making the necessary investments to support operations.
• A
company’s value depends on the amount of FCF it can
generate.
What are the five uses
of FCF?
o
Pay interest on debt.
o
Pay back principal on debt.
o
Pay dividends.
o
Buy back stock.
o
Buy nonoperating assets
(e.g., marketable securities, investments in other companies, etc.)
Capital expenditure =
increases in NFA + depreciation
Or, capital expenditure
= increases in GFA
What
are operating current assets?
• Operating
current assets are the CA needed to support operations.
• Op CA
include: cash, inventory, receivables.
• Op CA
exclude: short-term investments, because these are not a part of operations.
What
are operating current liabilities?
• Operating
current liabilities are the CL resulting as a normal part of operations.
• Op CL
include: accounts payable and accruals.
• Op
CL exclude: notes payable, because this is a
source of financing, not a part of operations.
Note:
All companies, foreign and domestic, are required to file registration
statements, periodic reports, and other forms electronically through
EDGAR. https://www.sec.gov/edgar/searchedgar/companysearch.html
In class exercise
Firm AAA has EBIT (operating income) of $3
million, depreciation of $1 million. Firm AAA’s
expenditures on fixed assets = $1 million. Its net operating working capital
= $0.6 million. Calculate for free cash flow. Imagine that the tax
rate =40%.
FCF = EBIT(1
– T) + Deprec. – (Capex + NOWC)
answer:
EBIT $3
Tax
rate 40%
Depreciation $1
Capex + NOWC $1.60
So, FCF = 3*(1-40%) + 1 –(1+0.6) =
1.2
Case study of chapter 3
·
FCF
·
MVA: How to calculate market
value added | MVA calculation | FIN-Ed (video)
·
EVA: Economic Value Added: EVA
Explained (video)
·
Balance Sheet
·
Income Statement
· Excel File here (due with the final exam,) ‘
Industry name |
Number of firms |
Dividends |
Net Income |
Dividends + Buybacks - Stock Issuances |
FCFE (before debt cash flows) |
FCFE (after debt cash flows) |
Advertising |
58 |
$1,053.13 |
$1,557.12 |
$2,099.32 |
$701.92 |
$1,441.35 |
Aerospace/Defense |
77 |
$10,261.13 |
$14,514.28 |
$26,339.72 |
$11,777.55 |
$7,574.30 |
Air Transport |
21 |
$0.00 |
($3,270.31) |
($143.96) |
($7,598.89) |
($21,052.22) |
Apparel |
39 |
$1,985.68 |
$3,655.80 |
$7,841.46 |
($2,499.16) |
($1,233.15) |
Auto & Truck |
31 |
$2,124.50 |
$20,137.80 |
($7,894.97) |
$2,434.31 |
($3,779.69) |
Auto Parts |
37 |
$694.40 |
$1,869.70 |
$1,567.87 |
($1,796.70) |
($246.25) |
Bank (Money Center) |
7 |
$29,107.12 |
$102,625.92 |
$40,338.00 |
$141,352.92 |
$280,520.92 |
Banks (Regional) |
557 |
$19,659.99 |
$67,543.37 |
$32,945.14 |
$58,434.71 |
$192,772.18 |
Beverage (Alcoholic) |
23 |
$1,270.60 |
$1,608.29 |
$2,592.31 |
($195.71) |
($105.87) |
Beverage (Soft) |
31 |
$12,915.35 |
$22,852.32 |
$15,024.79 |
$21,780.18 |
$25,887.17 |
Broadcasting |
26 |
$1,266.31 |
$8,817.25 |
$3,464.83 |
($5,822.60) |
($7,578.38) |
Brokerage & Investment Banking |
30 |
$11,022.99 |
$38,423.51 |
$23,872.69 |
$100,348.33 |
$171,525.17 |
Building Materials |
45 |
$1,861.54 |
$14,370.39 |
$11,720.67 |
$9,419.22 |
$13,041.20 |
Business & Consumer Services |
164 |
$3,112.87 |
$11,028.56 |
$8,943.99 |
$11,231.01 |
$16,410.59 |
Cable TV |
10 |
$5,128.40 |
$17,653.30 |
$36,833.00 |
$18,830.08 |
$28,294.38 |
Chemical (Basic) |
38 |
$4,333.80 |
$15,819.51 |
$9,182.00 |
$9,847.05 |
$6,877.91 |
Chemical (Diversified) |
4 |
$330.00 |
$2,259.24 |
$1,683.10 |
$1,824.07 |
$1,901.91 |
Chemical (Specialty) |
76 |
$7,557.41 |
$18,677.57 |
$19,090.45 |
$5,618.06 |
$25,052.17 |
Coal & Related Energy |
19 |
$513.96 |
$2,515.23 |
($345.25) |
$2,307.19 |
$1,255.10 |
Computer Services |
80 |
$7,172.66 |
$7,664.51 |
$12,895.07 |
$7,927.03 |
$13,115.96 |
Computers/Peripherals |
42 |
$18,124.95 |
$106,948.54 |
$123,564.50 |
$107,732.42 |
$105,646.15 |
Construction Supplies |
49 |
$4,538.96 |
$14,115.59 |
$12,082.06 |
$4,323.04 |
$10,297.31 |
Diversified |
23 |
$6,865.35 |
$4,556.31 |
$23,473.13 |
($8,333.02) |
($28,355.90) |
Drugs (Biotechnology) |
598 |
$17,685.00 |
$1,336.62 |
$13,735.23 |
$6,456.49 |
$513.27 |
Drugs (Pharmaceutical) |
281 |
$37,183.45 |
$72,397.57 |
$50,169.94 |
$75,076.60 |
$72,293.14 |
Education |
33 |
$90.00 |
$516.08 |
$2,104.63 |
$407.23 |
($685.19) |
Electrical Equipment |
110 |
$2,409.19 |
$6,991.17 |
$3,687.43 |
($116.23) |
$10,494.28 |
Electronics (Consumer & Office) |
16 |
$0.00 |
$39.39 |
$230.06 |
($353.91) |
($344.21) |
Electronics (General) |
138 |
$916.43 |
$8,638.31 |
$4,921.24 |
$486.37 |
$7,877.66 |
Engineering/Construction |
43 |
$432.10 |
$2,558.96 |
$2,727.69 |
($1,888.01) |
$3,697.80 |
Entertainment |
110 |
$959.84 |
$1,903.67 |
$2,560.07 |
$5,417.98 |
($1,283.68) |
Environmental & Waste Services |
62 |
$2,146.70 |
$4,640.61 |
$3,975.31 |
$3,314.61 |
$8,304.54 |
Farming/Agriculture |
39 |
$3,015.71 |
$14,341.24 |
$8,068.02 |
($4,214.13) |
$4,957.79 |
Financial Svcs. (Non-bank & Insurance) |
223 |
$13,017.30 |
$95,373.69 |
$60,726.69 |
$86,528.70 |
($162,222.92) |
Food Processing |
92 |
$10,574.62 |
$19,663.08 |
$15,571.88 |
$11,098.26 |
$9,624.51 |
Food Wholesalers |
14 |
$1,021.60 |
$2,343.41 |
$1,699.52 |
($1,201.28) |
($540.28) |
Furn/Home Furnishings |
32 |
$796.43 |
$1,170.87 |
$3,857.91 |
($1,718.25) |
$507.55 |
Green & Renewable Energy |
19 |
$657.02 |
$1,155.76 |
$196.87 |
($392.33) |
$2,042.75 |
Healthcare Products |
254 |
$6,570.31 |
$14,242.60 |
$14,559.38 |
$8,342.26 |
$21,726.15 |
Healthcare Support Services |
131 |
$13,557.74 |
$41,031.69 |
$44,679.36 |
$39,997.55 |
$35,170.62 |
Heathcare Information and Technology |
138 |
$1,581.92 |
($529.78) |
$8,491.10 |
($3,101.06) |
$4,235.22 |
Homebuilding |
32 |
$1,361.39 |
$24,986.04 |
$7,894.75 |
$9,262.75 |
$10,501.21 |
Hospitals/Healthcare Facilities |
34 |
$949.00 |
$6,999.96 |
$9,476.79 |
$2,703.89 |
$9,327.11 |
Hotel/Gaming |
69 |
$793.83 |
$1,606.13 |
$15,579.42 |
$4,108.84 |
$1,538.00 |
Household Products |
127 |
$14,431.34 |
$22,657.09 |
$19,606.34 |
$17,895.42 |
$24,106.84 |
Information Services |
73 |
$10,475.09 |
$37,313.93 |
$46,377.01 |
$41,679.42 |
$56,500.60 |
Insurance (General) |
21 |
$3,403.41 |
$20,197.72 |
$13,417.34 |
$11,622.09 |
$16,243.71 |
Insurance (Life) |
27 |
$5,853.45 |
$15,306.23 |
$18,439.95 |
$15,021.27 |
$10,250.87 |
Insurance (Prop/Cas.) |
51 |
$7,922.51 |
$10,805.47 |
$16,179.26 |
$7,392.63 |
$8,226.39 |
Investments & Asset Management |
600 |
$15,100.19 |
$35,375.45 |
($17,337.91) |
$32,624.12 |
$62,520.16 |
Machinery |
116 |
$5,613.08 |
$15,291.50 |
$13,889.15 |
$8,070.20 |
$26,845.63 |
Metals & Mining |
68 |
$4,009.40 |
$6,414.92 |
$6,402.72 |
$3,994.43 |
$5,889.08 |
Office Equipment & Services |
16 |
$392.50 |
$473.13 |
$576.86 |
($167.91) |
$929.15 |
Oil/Gas (Integrated) |
4 |
$26,119.36 |
$99,099.30 |
$40,345.10 |
$111,781.80 |
$75,992.90 |
Oil/Gas (Production and Exploration) |
174 |
$20,127.07 |
$86,953.77 |
$41,719.95 |
$59,398.57 |
$46,696.46 |
Oil/Gas Distribution |
23 |
$8,450.90 |
$2,683.10 |
$9,512.83 |
($192.46) |
$1,748.88 |
Oilfield Svcs/Equip. |
101 |
$7,323.11 |
$41,659.69 |
$25,266.85 |
$34,325.07 |
$24,456.82 |
Packaging & Container |
25 |
$2,718.41 |
$9,491.27 |
$8,916.47 |
$2,669.65 |
$2,600.74 |
Paper/Forest Products |
7 |
$99.00 |
$1,255.70 |
$1,313.61 |
$921.51 |
$905.06 |
Power |
48 |
$21,251.45 |
$35,093.37 |
$13,635.40 |
($35,714.94) |
$17,634.52 |
Precious Metals |
74 |
$1,943.35 |
$1,211.84 |
$1,658.21 |
$243.93 |
$1,104.43 |
Publishing & Newspapers |
20 |
$407.90 |
$778.84 |
$989.17 |
$715.58 |
$1,365.97 |
R.E.I.T. |
223 |
$51,601.83 |
$47,868.79 |
$1,818.52 |
$88,400.76 |
$150,282.44 |
Real Estate (Development) |
18 |
$0.00 |
$538.86 |
$469.87 |
$787.35 |
$879.40 |
Real Estate (General/Diversified) |
12 |
$48.10 |
$144.88 |
$89.51 |
$60.37 |
$160.86 |
Real Estate (Operations & Services) |
60 |
$229.56 |
($830.15) |
$4,494.01 |
$2,587.49 |
$2,975.10 |
Recreation |
57 |
$1,069.82 |
$784.68 |
$1,160.86 |
($4,087.93) |
($1,988.65) |
Reinsurance |
1 |
$201.00 |
$575.00 |
$306.00 |
$533.30 |
$1,264.30 |
Restaurant/Dining |
70 |
$8,430.28 |
$13,628.14 |
$20,501.45 |
$10,248.10 |
$15,970.87 |
Retail (Automotive) |
30 |
$738.77 |
$11,025.24 |
$12,507.54 |
$7,563.78 |
$22,789.96 |
Retail (Building Supply) |
15 |
$10,186.13 |
$24,750.59 |
$37,174.05 |
$12,747.23 |
$25,674.25 |
Retail (Distributors) |
69 |
$3,130.07 |
$14,460.39 |
$8,006.13 |
($3,931.77) |
$3,217.19 |
Retail (General) |
15 |
$10,568.63 |
$26,032.60 |
$33,456.72 |
($5,214.18) |
$12,954.65 |
Retail (Grocery and Food) |
13 |
$1,013.25 |
$5,113.51 |
$2,585.48 |
$2,892.69 |
$1,299.14 |
Retail (Online) |
63 |
$513.40 |
$3,688.55 |
$12,759.24 |
($51,160.77) |
($39,972.87) |
Retail (Special Lines) |
78 |
$5,685.91 |
$17,547.91 |
$22,107.18 |
$3,438.49 |
$8,185.60 |
Rubber& Tires |
3 |
$0.00 |
$864.12 |
($1.46) |
($352.39) |
$295.70 |
Semiconductor |
68 |
$23,911.23 |
$72,801.99 |
$62,269.76 |
$36,738.16 |
$41,487.00 |
Semiconductor Equip |
30 |
$2,591.80 |
$18,191.87 |
$16,041.22 |
$8,840.69 |
$20,856.58 |
Shipbuilding & Marine |
8 |
$256.30 |
$2,071.70 |
$629.34 |
$2,064.45 |
$1,634.49 |
Shoe |
13 |
$2,072.05 |
$7,698.70 |
$1,090.41 |
$6,060.83 |
$8,598.47 |
Software (Entertainment) |
91 |
$60.03 |
$91,628.19 |
$103,663.72 |
$56,468.04 |
$67,774.87 |
Software (Internet) |
33 |
$0.34 |
($5,178.90) |
$3,398.96 |
($7,707.22) |
($6,077.91) |
Software (System & Application) |
390 |
$24,238.73 |
$71,266.94 |
$64,479.06 |
$48,833.83 |
$71,160.04 |
Steel |
28 |
$1,342.77 |
$25,593.54 |
$9,591.24 |
$18,329.90 |
$16,980.17 |
Telecom (Wireless) |
16 |
$145.71 |
$2,321.21 |
$1,011.06 |
($3,333.42) |
($1,972.90) |
Telecom. Equipment |
79 |
$7,183.58 |
$14,067.43 |
$19,482.92 |
$9,251.85 |
$11,450.13 |
Telecom. Services |
49 |
$21,546.93 |
$41,509.34 |
$13,044.09 |
$38,803.38 |
($4,787.07) |
Tobacco |
15 |
$14,569.30 |
$13,594.15 |
$17,637.73 |
$12,523.43 |
$11,467.92 |
Transportation |
18 |
$6,209.10 |
$18,562.94 |
$13,749.07 |
$10,682.41 |
$10,330.74 |
Transportation (Railroads) |
4 |
$5,115.98 |
$14,258.80 |
$19,545.00 |
$11,470.98 |
$18,925.38 |
Trucking |
35 |
$729.19 |
$2,048.54 |
$9,226.79 |
($11,721.86) |
($3,931.09) |
Utility (General) |
15 |
$9,711.00 |
$16,381.30 |
$8,442.10 |
($12,850.02) |
($2,207.72) |
Utility (Water) |
16 |
$937.33 |
$2,065.11 |
$677.24 |
($1,100.09) |
$656.97 |
Total Market |
7165 |
$636,300.29 |
$1,834,489.12 |
$1,464,406.32 |
$1,330,007.52 |
$1,727,349.81 |
Total Market (without financials) |
5649 |
$531,213.34 |
$1,448,837.76 |
$1,275,825.16 |
$876,682.75 |
$1,147,513.33 |
Note: Dividends and Free Cash Flows to Equity, i.e.,
cash flows left over after taxes, reinvestment needs and debt payments
(FCFE), by industry
https://pages.stern.nyu.edu/~adamodar/
FYI: Market Value Added (MVA)
By
JAMES CHEN Updated May 26, 2021, Reviewed by DAVID KINDNESS, Fact checked by
HANS DANIEL JASPERSON
What Is
Market Value Added?
Market value added (MVA) is a calculation
that shows the difference between the market value of a company and the
capital contributed by all investors, both bondholders and shareholders. In other words, it is the market value of debt and equity minus all
capital claims held against the company. It is calculated as:
MVA = V
- K
where MVA
is the market value added of the firm, V is the market value of the firm,
including the value of the firm's equity and debt (its enterprise value), and
K is the total amount of capital invested in the firm.
MVA is
closely related to the concept of economic value added (EVA), representing
the net present value (NPV) of a series of EVA values.
Understanding
Market Value Added (MVA)
When investors want to look under the hood to
see how a company performs for its shareholders, they first look at MVA. A company’s MVA is an indication of its capacity to increase
shareholder value over time. A high
MVA is evidence of effective management and strong operational capabilities.
A low MVA can mean the value of management’s actions and investments is less
than the value of the capital contributed by shareholders. A negative MVA
means the management's actions and investments have diminished and reversed
the value of capital contributed by shareholders.
FYI: Economic Value Added (EVA)
By
JAMES CHEN Updated March 22, 2022, Reviewed by JANET BERRY-JOHNSON, Fact
checked by KIRSTEN ROHRS SCHMITT
https://www.investopedia.com/terms/e/eva.asp
What Is
Economic Value Added (EVA)?
Economic value added (EVA) is a measure of a
company's financial performance based on the residual wealth calculated by
deducting its cost of capital from its operating profit, adjusted for taxes
on a cash basis. EVA can also be referred to as economic
profit, as it attempts to capture the true economic profit of a company. This
measure was devised by management consulting firm Stern Value Management,
originally incorporated as Stern Stewart & Co.
Understanding Economic Value Added
(EVA)
EVA is
the incremental difference in the rate of return (RoR) over a company's cost
of capital. Essentially, it is used to measure the value a company generates
from funds invested in it. If a
company's EVA is negative, it means the company is not generating value from
the funds invested into the business. Conversely, a positive EVA shows a
company is producing value from the funds invested in it.
The formula for calculating EVA is:
EVA = NOPAT - (Invested Capital * WACC)
Where:
NOPAT = Net operating profit after taxes
Invested capital = Debt + capital leases +
shareholders' equity
WACC = Weighted average cost of capital2
Chapter 12: Cash
Flow Estimation (2nd step
of DCF)
Chapter
12 case study (due with final. Monte
Carol is not required. FYI only)
Monte
Carlo Demonstration Based on Case in Class (FYI, Video)
Critical thinking
challenge (due with final, optional for extra credits):
· Recalculate 100 times of the NPV based on the Monte Carlo
simulation method by randomly changing the tax rate and the WACC
· Report
statistical results: Mean, Standard Deviation, Min, Max of the NPV.
· Report the
Histogram of the NPV, or the probability distribution of the NPV, such as the
following:
Monte Carlo
Simulation Demonstration (FYI)
Structure
or template: |
|
|||||||||||
|
|
|
|
|
|
|||||||
0 |
1 |
2 |
3 |
4 |
||||||||
Investment Outlay |
||||||||||||
Equipment
cost |
$(----------) |
|||||||||||
Installation |
(--------) |
|||||||||||
Increase
in inventory |
(-------) |
|||||||||||
Increase
in A/P |
------- |
|||||||||||
Initial
net investment |
$(-------) |
|||||||||||
Operating Cash Flows |
||||||||||||
Units
sales |
------- |
------- |
------- |
------- |
||||||||
Price
per unit |
*
$ --- |
$ --- |
$ --- |
$ --- |
||||||||
Total
revenues |
------- |
------- |
------- |
------- |
||||||||
Operating
costs (w/o deprn) |
------- |
------- |
------- |
------- |
||||||||
Depreciation |
------- |
------- |
------- |
------- |
||||||||
Total
costs |
------- |
------- |
------- |
------- |
||||||||
Operating
income |
------- |
------- |
------- |
------- |
||||||||
Taxes
on operating income |
------- |
------- |
------- |
------- |
||||||||
A-T
operating income |
------- |
------- |
------- |
------- |
||||||||
Depreciation |
------- |
------- |
------- |
------- |
||||||||
Operating
cash flow |
------- |
------- |
------- |
------- |
Terminal Year Cash
Flows
Recovery of net
working capital -------
|
Salvage
value |
------- |
||||||||||
|
Tax
on salvage value |
(-------) |
||||||||||
|
Total
termination cash flow |
------- |
||||||||||
|
Project Cash Flows |
|
|
|
|
|
||||||
Net
cash flows |
$(-------) |
$ ------- |
$ ------- |
$ ------- |
||||||||
In class exercise (self-study)
1. What is the project's Year 1 cash
flow?
Sales revenues $22,250
Depreciation $8,000
Other operating costs $12,000
Tax rate 35.0%
Answer:
Sales revenues $22,250
− Operating costs (excl. deprec.) 12,000
− Depreciation 8,000
Operating income (EBIT) $ 2,250
−
Taxes Rate = 35% 788
After-tax EBIT $ 1,463
+
Depreciation 8,000
Cash
flow, Year 1 $ 9,463
2. The required equipment has a
3-year tax life, and it will be depreciated by the straight-line method over
3 years. What is the project's Year 1
cash flow?
Equipment cost (depreciable basis) $65,000
Straight-line depreciation rate 33.333%
Sales revenues, each year $60,000
Operating costs (excl. deprec.) $25,000
Tax rate 35.0%
Answer:
Equipment life, years 3
Equipment cost $65,000
Depreciation: rate = 33.333% $21,667
Sales revenues $60,000
− Basis x rate =
depreciation 21,667
− Operating costs (excl. deprec.)
25,000
Operating income (EBIT) $13,333
− Taxes Rate
= 35.0% 4,667
After-tax EBIT $ 8,667
+
Depreciation 21,667
Cash
flow, Year 1 $30,333
3. The equipment that would be used
has a 3-year tax life, and the allowed depreciation rates for such property
are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are
expected to be constant over the project's 10-year expected life. What is the Year 1 cash flow?
Equipment cost (depreciable basis) $65,000
Sales revenues, each year $60,000
Operating costs (excl. deprec.) $25,000
Tax rate 35.0%
Answer:
Equipment cost $65,000
Depreciation rate 33.0%
Sales revenues $60,000
− Operating costs (excl. deprec.) 25,000
− Depreciation 21,450
Operating income (EBIT) $13,550
−
Taxes Rate = 35% 4,743
After-tax EBIT $ 8,808
+
Depreciation 21,450
Cash
flow, Year 1 $30,258
4. The equipment that would be used
has a 3-year tax life, would be depreciated by the straight-line method over
its 3-year life, and would have a zero salvage value. No new working capital would be
required. Revenues and other operating
costs are expected to be constant over the project's 3-year life. What is the project's NPV?
Risk-adjusted WACC 10.0%
Net investment cost (depreciable
basis) $65,000
Straight-line deprec. rate 33.3333%
Sales revenues, each year $65,500
Operating costs (excl. deprec.),
each year $25,000
Tax rate 35.0%
Answer:
WACC 10.0% Years 0 1 2 3
Investment cost -$65,000
Sales revenues $65,500 $65,500 $65,500
− Operating costs (excl. deprec.) 25,000 25,000 25,000
− Depreciation rate = 33.333% 21,667 21,667 21,667
Operating income (EBIT) $18,833 $18,833 $18,833
−
Taxes Rate = 35% 6,592 6,592 6,592
After-tax EBIT $12,242 $12,242 $12,242
+
Depreciation 21,667
21,667 21,667
Cash flow -$65,000 $33,908 $33,908 $33,908
NPV $19,325
5. The equipment originally cost
$22,500, of which 75% has been depreciated.
The firm can sell the used equipment today for $6,000, and its tax
rate is 40%. What is the equipment’s
after-tax salvage value for use in a capital budgeting analysis? Note that if the equipment's final market
value is less than its book value, the firm will receive a tax credit as a
result of the sale.
Answer:
% depreciated on equip. 75%
Tax rate 40%
Equipment cost $22,500
− Accumulated deprec. 16,875
Current book value of equipment $ 5,625
Market value of equipment 6,000
Gain (or loss): Market value − Book value $
375
Taxes paid on gain (−) or
credited (+) on loss -150
AT
salvage value = market value +/− taxes $
5,850
FYI: Analyzing
Business Performance through Monte Carlo Sensitivity Analysis – ChatGPT
Let's
consider an example of a coffee shop that sells coffee and baked goods. The
coffee shop has historical data for the past year, which shows that the
average daily revenue is $1000 with a standard deviation of $100, and the
average daily cost is $600 with a standard deviation of $50.
To use Monte
Carlo simulation to simulate the profits, we can follow the following steps:
Determine the distribution of the revenue and
costs data:
Based
on the historical data, we can assume that revenue and costs follow a normal distribution. We can estimate the
distribution parameters (mean and standard deviation) for each variable as
follows:
Revenue:
Mean = $1000, Standard Deviation = $100
Costs:
Mean = $600, Standard Deviation = $50
Generate
random values for revenue and costs based on their respective distributions:
We can
use a Monte Carlo simulation software like Excel or Python to generate random
values. Let's say we want to simulate 1000 days of operation for the coffee
shop. We can use the following formulas in Excel to generate random values
for revenue and costs:
Revenue:
=NORM.INV(RAND(), 1000, 100)
Costs:
=NORM.INV(RAND(), 600, 50)
We can
copy these formulas down for 1000 rows to generate 1000 random values for
revenue and costs.
Calculate the profit for each set of random
values:
We can
use the following formula in Excel to calculate the profit for each set of
random values:
Profit: =
Revenue - Costs
We can
copy this formula down for 1000 rows to calculate the profit for each set of
random values.
Repeat steps 2
and 3 thousands of times:
We can
repeat steps 2 and 3 thousands of times to get a large sample size of
profits.
In Excel, we
can use the data table feature to simulate profits for thousands of
iterations.
We can set up
the data table as follows:
Column A:
Iteration number (1 to 1000)
Column
B: Random revenue (generated using the formula above)
Column
C: Random costs (generated using the formula above)
Column
D: Profit (calculated using the formula above)
We can then
select columns B, C, and D and go to Data > What-If Analysis > Data
Table. In the "Column Input Cell" box, we can enter a reference to
a cell that contains a random number (e.g., =RAND()). Excel will then
simulate profits for thousands of iterations.
Analyze the
simulated profit distribution:
We can
use the simulation results to analyze the profit distribution. In Excel, we
can calculate the mean, standard deviation, and other statistical measures
for the profit column. We can also create a histogram or probability density
plot to visualize the distribution.
Use the
simulation results to make business decisions:
We can
use the simulation results to estimate the probability of different profit
outcomes.
For example,
we can use the following formulas in Excel to estimate the probability of making
a profit of at least $500 or at least $600:
Probability of
profit >= $500: =1-COUNTIF(D2:D1001,"<500")/1000
Probability of
profit >= $600: =1-COUNTIF(D2:D1001,"<600")/1000
Based
on the simulation results, we can estimate that the probability of making a
profit of at least $500 is around 76%, and the probability of making a profit
of at least $600 is around 50%. We can use these probabilities to make
decisions such as setting pricing strategies, reducing costs, or investing in
new products or services.
Overall, Monte Carlo simulation is a powerful
tool for analyzing uncertainty and risk in business operations. By simulating
different scenarios, we can estimate the probability of different outcomes
and make informed decisions based on the simulation results. However, it's important to note that the accuracy of the simulation
depends on the quality of the input data and assumptions made about the
distribution of revenue and costs. Therefore, it's important to carefully
analyze the input data and assumptions to ensure that the simulation results
are reliable. However, the accuracy of
the simulation depends on the quality of the input data and assumptions made
about the distribution of revenue and costs. It's crucial to carefully
analyze the input data and assumptions to ensure that the simulation results
are reliable. Monte Carlo simulation is not a crystal ball and cannot predict
future outcomes with certainty, but it can help businesses analyze
uncertainty and risk.
Chapter 19 Derivatives
Chapter 19 Case Study
Part I - due with final
Chapter 19 Case
Study part II – due with final
Case
video in class Part I (4.10.2023)
Case
video in class part II (4.12.2023)
Case
video in class ----- Part I Part II
1st, understand what is call and put
option
2nd,
understand the pay off of call and put option
3rd,
can draw payoff profile of call and put option
Call
and Put Option Calculator
Call and Put Option Diagram Illustration Excel
(Thanks to
Dr. Greence at UAH)
4th, can calculate call option
pricing using binomial model
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
https://www.mystockoptions.com/black-scholes.cfm
or
Black Scholes Option
Calculator (at jufinance.com)
www.jufinance.com/https://www.jufinance.com/option_chatgpt/
Black-Scholes Model Illustration
Excel
(Thanks to
Dr. Greence at UAH)
Binomial Tree (FYI)
A binomial tree is a representation of the intrinsic values an option may take at
different time periods. The value of the
option at any node depends on the probability that the price of the
underlying asset will either decrease or increase at any given node.
Black-Scholes model (reference only)
https://www.youtube.com/watch?v=D9-_Jar2UpQ
https://www.youtube.com/watch?v=q_z1Zx_BALo
Binomial Option Pricing Model Explained ----
using In Class Case Study as an example (FYI only)
The
binomial option pricing model is a mathematical formula that allows us to
calculate the fair value of an option by modeling the possible future prices
of the underlying asset, and calculating the probability of each price
occurring.
The model works by
creating a binomial tree that represents the possible future prices of the
asset, and then working backward through the tree to calculate the expected
value of the option at each node.
Here
are the steps to use the binomial option pricing model:
Step 1: Determine the
Inputs
The
first step is to gather the inputs needed for the model. These include:
·
The current price of the underlying asset
·
The range of possible future prices of the
asset
·
The exercise price of the option
·
The risk-free rate of interest
·
The time until expiration of the option
Let’s
try to work on the same question as we did in class. A stock that is currently trading at $40, and two possible future
prices at the end of one year are: $30 and $50. The exercise price of the
option is $35, the risk-free rate is 8%, and the time until expiration is one
year --- our case study example
Step 2: Calculate the Up
and Down Factors
The
next step is to calculate the up and down factors, which represent the
expected percentage increase and decrease in the stock price over one period.
These factors are calculated as:
·
Up factor (u) = Future price if stock goes
up / Current stock price
·
Down factor (d) = Future price if stock
goes down / Current stock price
In
our example, the up factor is $50 /
$40 = 1.25, and the down factor is $30 / $40 = 0.75.
Step 3: Create the
Binomial Tree
This
step involves creating the binomial tree as below.
Binomial Tree
$40
/
\
$50
$30
Step 4: Calculate the
Risk-Neutral Probability
The
next step is to calculate the probability of each future price occurring,
using the risk-neutral probability. The
risk-neutral probability is the probability of the stock going up or down,
assuming that the market is risk-neutral and the expected return of the stock
is equal to the risk-free rate.
The
risk-neutral probability is calculated as:
Risk-neutral probability
(p) = (1+r-d)/(u-d)
where
r is the risk-free rate and t is the time until expiration.
In
our example, the risk-neutral probability is approximately:
Pu =
(1+0.08-0.75)/(1.25-0.75)= 0.66
Or
use the more accurate model:
Risk-neutral
probability Pu = (e^((r * t)/n) - d) / (u - d)
where
r is the risk-free rate and t is the time until expiration, and n is the
height of the binomial tree. In our example, n=1.
In
our example, the risk-neutral probability is:
Pu
= (e^(0.08 * 1) - 0.75) / (1.25 - 0.75) = 0.6666
Step 5: Calculate the Option
Value at Each Node of the Tree
To
get the value of the option at each node of the tree, we should work backward
from the end of the tree to the current price of the stock.
Simply
speaking, at the end of the tree, the option value = difference between the
stock price and the exercise price, or zero if the stock price is below the
exercise price.
For
example, we need to calculate the value of the option if the stock price goes
up to $50, and if it goes down to $30. The results are as follows.
Vu
= Max($50 - $35, 0) = $15
Vd
= $0
Working
backward up the tree, we can calculate the option value at each node as the
discounted expected value of the option at the next period:
Option
value = v = (Pu * Vu + Pd * Vd) / (1 + r)^t;
Option
Value at $40 = (0.66 x $15 + (1 - 0.66) x $0) / (1 + 0.08)^1 = $9.17
Therefore,
the value of the option is approximately $9.17 if the stock price is $40.
Black-Scholes Option Pricing Model Explained ----
using In Class Case Study as an example (FYI only)
C = SN(d1) –
X*exp(-r*t)*N(d2)
where:
·
S
= the current stock price
·
X
= the option strike price
·
r
= the risk-free interest rate
·
t
= time until expiration, expressed as a fraction of a year
V = |
P[
N (d1) ] − Xe-rRF t [ N (d2) ] |
||||
d1 = |
{
ln (P/X) + [rRF + s2 /2) ] t } / s (t1/2) |
||||
d2
= |
d1
− s (t 1 / 2) |
||||
d1 = [ln(S/X) + (r + σ^2/2)t] / [σsqrt(t)]
d2 = d1 - σ*sqrt(t)
σ
= the annualized standard deviation of stock returns
Using
the values used in the case study in class:
·
S
= X = 21
·
r
= 0.05
·
σ
= 0.3
·
t
= 0.36
First,
we calculate d1 and d2:
d1 = ln(21/21)+(0.05+0.3^2/2)*0.36)/(0.3*sqrt(0.36))
=0.19
d2 =
0.19 - 0.3*sqrt(0.36) = 0.01
Next,
we calculate the call option price using the Black-Scholes formula:
C = SN(d1) –
X*exp(-r*t)*N(d2)
C =
21*normdist(0.19, 0, 1, true) - 21*exp(-0.05*0.36)*normdist(0.01, 0, 1, true)
= 1.687 (rounded to three decimal places)
Therefore,
the expected result for the call option price using
the Black-Scholes formula with the given inputs is
approximately 1.687.
By the
way, based on Put - Call Parity, the put option price (P) is the following:
P = C - S +
Xe^(-rt)
= 1.687
- 21 + 21*exp(-0.05*0.36) = 1.3124
FYI – normdist
function in Excel
The
normdist function is used in Excel to calculate the probability density
function of a normally distributed random variable. This function takes four
arguments: x, mean, standard_dev, and cumulative.
Here is
a brief explanation of each argument:
·
x:
This is the value for which you want to calculate
the probability density function. It must be a numeric value.
·
mean: This is the mean of
the distribution. It must be a numeric value.
·
standard_dev: This is
the standard deviation of the distribution. It must be a numeric value.
·
cumulative: This is an
optional argument that specifies whether you want to calculate the cumulative
distribution function or the probability density function. If this argument
is omitted or set to TRUE, the function will calculate the cumulative
distribution function. If it is set to FALSE, the function will calculate the
probability density function.
To use the normdist function in Excel, follow these steps:
.
·
In a cell, type
=NORMDIST(x, mean, standard_dev, cumulative) and replace the values of x,
mean, standard_dev, and cumulative with the values you want to use.
·
Press Enter. Excel will
calculate the probability density function or the cumulative distribution
function of the normally distributed random variable, depending on the value
of the cumulative argument.
For example,
1)
if you want to calculate
the probability density function of a normally distributed random variable
with a mean of 10 and a standard deviation of 2 at the value of 12, use the following:
=NORMDIST(12, 10, 2, FALSE) = probability density at that point.
2) =NORMDIST(12, 10, 2, true) calculates the
cumulative distribution function (CDF) of a normally distributed random
variable with a mean of 10 and a standard deviation of 2, evaluated at the
value of 12.
·
The true value of the
fourth argument - calculate the CDF.
Chapter 15 Distributions to Shareholders
· This
chapter will not be covered in the final exam
Theory one: Indifference
theory
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 ke
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
Dividends
are less risky. Therefore, high dividend payout ratios will lower ke
(reducing the cost of capital), and increase stock price
Theory three: Tax effect
theory – Low dividend can increase firm value
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 ke (reducing the cost of capital), raise
g, and increase stock price.
Which theory is most
correct? – again, results are mixed.
1)
Some research suggests that high payout
companies have high required return on stock, supporting the tax effect
hypothesis.
2)
But other research using an international
sample shows that in countries with poor investor protection (where agency
costs are most severe), high payout companies are valued more highly than low
payout companies.
Stock
Repurchase: Buying
own stock back from stockholders.
Reasons
for repurchases:
·
As an alternative to distributing cash as
dividends.
·
To dispose of one-time cash from an asset
sale.
·
To make a large capital structure change.
·
May be viewed as a negative signal (firm
has poor investment opportunities).
·
IRS could impose penalties if repurchases
were primarily to avoid taxes on dividends.
·
Selling stockholders may not be well
informed, hence be treated unfairly.
·
Firm may have to bid up price to complete
purchase, thus paying too much for its own stock.
Stock Split: Firm
increases the number of shares outstanding, say 2:1. Sends shareholders more shares.
Reasons
for stock split:
·
There’s a widespread belief that the
optimal price range for stocks is $20 to $80.
·
Stock splits can be used to keep the price
in the optimal range.
·
Stock splits generally occur when
management is confident, so are interpreted as positive signals.
Chapter 21 Mergers and Divestitures
·
This chapter will not be covered in the final
exam
· watch TV series Succession and gain insights of the
dynamics of such corporate fights
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) |
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 |
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 DEFA 14A 8k form with SEC 6/16/2017
Whole foods is providing materials for the upcoming shareholder
voting.
Whole foods DEFA 14A 8k with SEC 7/21/2017
Has law suit documents
Whole foods DEFA 14A 8k with SEC 7/21/2017
Notifying shareholders for upcoming special shareholder meeting
********* Amazon SEC filing *********
Amazon Form 8k with SEC on 6/15/2017
Financing of the Merger
The Company expects to
finance the Merger with debt financing ……
Amazon Whole Foods Merger Agreement on
6/15/2017
For the term project, if you work on this M&A case, you
should be able to find most of the information in this agreement.
Amazon 8k form Completion of acquisition or
disposition of assets 8/28/2018
********** Miscellaneous **********
7 potential bidders, a call to Amazon, and an ultimatum:
How the Whole Foods deal went down (from business
insider.com)
********** SDC Amazon Whole Foods Deal Record
(For this class only)*****
Tear Sheet (SDC) (on blackboard)
For discussion:
· Why
does Amazon want to buy Whole Foods?
· Did
Whole Foods want to be acquired? What can Whole Foods do to defend itself?
(poison pill, white knight, classified board, golden parachute, etc.)
· What
can Amazon do to persuade Whole Foods shareholders to sell their stocks?
· Why
does Elon Musk want to acquire Twitter?
· Did
Twitter want to be acquired? What can Twitter do to defend itself? (poison
pill, white knight, classified board, golden parachute, etc.)
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
·
When a firm is being taken over and the senior managers of
that firm are let go, a very lucrative severance package is offered to those
senior managers. It is referred to as a:
golden
parachute
Final Exam (during final week, in class,
non-cumulative, similar to case study)
Finance Exit Exam (with final, in class,
close book close notes, 40 multiple choice questions)
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