FIN 509 & FIN510 Class Web Page, Spring'22
Weekly SCHEDULE, LINKS, FILES and Questions
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Week |
Coverage, HW, Supplements -
Required |
Equations and
Assignments |
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Weekly Tuesday class url on blackboard
collaborate: Class Schedule:
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Week 0 |
Market
Watch Game Use the information and directions
below to join the game. 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! |
Pre-class assignment: Set up marketwatch.com account and have
fun |
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Week1,2 |
Chapter 5 Time value of money 1 Week 1 in class exercise (word file) Solution The time value of money -
German Nande (youtube)
Concept of FV, PV,
Rate, Nper Calculation of FV, PV,
Rate, Nper Concept of interest
rate, compounding rate, discount rate
Chapter 6 Time Value of Money 2 Concept of PMT, NPV Calculation of FV, PV,
Rate, Nper, PMT, NPV, NFV Concept of EAR, APR Calculation of EAR,
APR First Discussion Board Assignment (post your writing on blackboard
under discussion folder):
(due by 4/3 at 11:59 pm)
Market Watch Game
Let's start trading in the stock
market! Please join a game and report back on your experience. Directions 1.
URL for your game: 2.
Password for this private game: havefun. 3.
Click on the Join Now button to get
started. 4.
Register for a new account with your email address or sign in if
you already have an account.
1.
Why did you choose the stock? How much money did you think you
would make? Please explain. 2.
Did you make money or lose money off of your chosen stock? Which
factors contributed to that? 3.
What did you learn from this experience and how will it affect
your choices in real life when choosing stocks? Instructions · Responses should be 100 to
250 words in length and should answer all three prompts · Optional: reply to one of
your peers with meaningful, thought-provoking responses · Due by 4/3/2022
at 11:59 p.m. ET HOMEWORK of Chapters 5
and 6 (due on week 4, 4/3/2022) 1. The Thailand
Co. is considering the purchase of some new equipment. The quote consists of
a quarterly payment of $4,740 for 10 years at 6.5 percent interest. What is the
purchase price of the equipment? ($138,617.88) 2. The
condominium at the beach that you want to buy costs $249,500. You plan to
make a cash down payment of 20 percent and finance the balance over 10 years
at 6.75 percent. What will be the amount of your monthly mortgage
payment? ($2,291.89) 4. Shannon wants
to have $10,000 in an investment account three years from now. The account
will pay 0.4 percent interest per month. If Shannon saves money every month,
starting one month from now, how much will she have to save each month?
($258.81)
(Hint: Bridget’s is an annuity due, so abs(fv(8%/12, 10*12, 150, 0,
1)) --- type =1; Jordan’s is an ordinary annuity, so abs(fv(8%/12, 10*12,
150, 0) --- type =0, or omitted. There is a mistake in the help video for
this question. Sorry for the mistake.) 14. What is the
future value of weekly payments of $25 for six years at 10 percent? ($10,673.90) 15. At the end of
this month, Bryan will start saving $80 a month for retirement through his
company's retirement plan. His employer will contribute an additional $.25
for every $1.00 that Bryan saves. If he is employed by this firm for 25 more
years and earns an average of 11 percent on his retirement savings, how much
will Bryan have in his retirement account 25 years from
now? ($157,613.33) 16. Sky
Investments offers an annuity due with semi-annual payments for 10 years at 7
percent interest. The annuity costs $90,000 today. What is the amount of each
annuity payment? ($6,118.35) 17. Mr. Jones
just won a lottery prize that will pay him $5,000 a year for thirty years. He
will receive the first payment today. If Mr. Jones can earn 5.5 percent on
his money, what are his winnings worth to him
today? ($76,665.51) 18. You want to
save $75 a month for the next 15 years and hope to earn an average rate of
return of 14 percent. How much more will you have at the end of the 15 years
if you invest your money at the beginning of each month rather than the end
of each month? ($530.06) 19. What is the
effective annual rate of 10.5 percent compounded
semi-annually? (10.78%) 22. What is the
effective annual rate of 12.75 percent compounded daily? (13.60 percent) 23. Your
grandparents loaned you money at 0.5 percent interest per month. The APR on
this loan is _____ percent and the EAR is _____ percent. (6.00; 6.17) FYI only: help for homework Part 1(Qs
1-2) Part 2(Qs
4-8) Part 3(Qs 9-12) Part 4(Qs
13-16) Part 5(Qs
17-20) Part 6(Qs 21-24) (Q13: Bridget’s is an annuity
due, so abs(fv(8%/12, 10*12, 150, 0, 1)) --- type =1; Jordan’s is an ordinary
annuity, so abs(fv(8%/12, 10*12, 150, 0) --- type =0, or omitted. There is a
mistake in the help video for this question. Sorry for the mistake.) Quiz 1- Help Videos |
Calculators Time
Value of Money Calculator © 2002 - 2019 by Mark A. Lane,
Ph.D. Math Formula FV = PV *(1+r)^n PV = FV /
((1+r)^n) N
= ln(FV/PV) / ln(1+r) Rate = (FV/PV)1/n -1 Annuity: N
= ln(FV/C*r+1)/(ln(1+r)) Or N
= ln(1/(1-(PV/C)*r)))/ (ln(1+r))
EAR = (1+APR/m)^m-1 APR = (1+EAR)^(1/m)*m Excel Formulas To get FV, use FV
function. =abs(fv(rate, nper,
pmt, pv)) To get PV, use PV
function = abs(pv(rate, nper,
pmt, fv)) To get r, use rate
function =
rate(nper, pmt, pv, -fv) To get number of years,
use nper function = nper(rate, pmt, pv,
-fv) To get annuity payment, use PMT
function = abs(pmt(rate, nper, pv,
-fv)) To get Effective rate (EAR), use
Effect
function =
effect(nominal_rate, npery) To get annual percentage rate
(APR), use nominal function APR = nominal(effective rate, npery) |
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Week3 |
Chapter 7 Bond
Pricing
Yield Curve http://finra-markets.morningstar.com/BondCenter/Default.jsp Balance Sheet of WalMart https://www.nasdaq.com/market-activity/stocks/wmt/financials
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? FINRA – Bond market information http://finra-markets.morningstar.com/BondCenter/Default.jsp Go to http://finra-markets.morningstar.com/BondCenter/Default.jsp , the bond market data website of FINRA to find bond
information. For example, find bond sponsored by Wal-mart Or, just go to www.finra.org, è Investor center è market data è bond è corporate bond Corporate
Bond
1.
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
The above graph shows the cash flows of a five year 5% coupon
bond. How
Bonds Work (video) Investing Basics: Bonds(video) In class exercise: 1.
Find bonds
sponsored by WMT ·
just
go to www.finra.org, è Investor
center è market
data è bond è corporate bond ·
Search
for Walmart bonds For discussion: ·
What
are the ratings of the WMT bonds? How does the rating agency rate a bond? Altman Z Score video
·
Why
some WMT bonds are priced higher than the par value, while others are priced
at a discount? ·
Why
some WMT bonds have higher coupon rates than other bonds? How does WMT
determine the coupon rates? ·
Why
some WMT bonds have higher yields than other bonds? Does a bond’s yield
change daily? ·
Which
of the WMT bonds are the most attractive one to you? Why? http://finra-markets.morningstar.com/BondCenter/BondDetail.jsp?ticker=C610043&symbol=WMT4117477 2. 2.
Understand what is coupon, coupon rate, yield, yield to maturity, market
price, par value, maturity, annual bond, semi-annual bond, current yield. 3. 3.
Understand how to price bond Bond
price = abs(pv(yield, maturity, coupon, 1000)) ------- annual coupon Bond
price = abs(pv(yield/2, maturity*2, coupon/2, 1000)) ------- semi-annual
coupon Also change the yield and observe the
price changes. Summarize the price change pattern and draw a graph to
demonstrate your findings. Again, when yield to maturity of this semi_annual coupon
bond is 4%, how should this WMT bond sell for? 4. Understand
how to calculate bond returns Yield
to maturity = rate(maturity, coupon, -market price, 1000) ----
annual coupon Yield
to maturity = rate(maturity*2, coupon/2, -market price, 1000)*2
----- semi-annual coupon Bond
Calculator (www.jufinance.com/bond) For example, when the annual coupon bond
is selling for $1,100, what is its return to investors? For example, when the semi-annual
coupon bond is selling for $1,100, what is its return to investors? 5. Current
yield: For the above bond, calculate current yield. Note: current yield = coupon/bond price 6. Zero
coupon bond: coupon=0 and treat it as semi-annual coupon bond. Example:
A ten year zero coupon bond is selling for $400. How much is its yield to
maturity? A ten year zero coupon bond’s yield to
maturity is 10%. How much is its price? 7. Understand
what is bond rating and how to read those ratings. a. Who
are Moody, S&P and Fitch? b. What
is WMT’s rating? c. Is
the rating for WMT the highest? d. Who
earned the highest rating? Supplement:
Municipal Bond
For class
discussion: · Shall you
invest in municipal bonds? · Are
municipal bonds better than investment grade bonds? The
risks investing in a bond · Bond investing: credit Risk (video) · Bond investing: Interest rate risk (video) · Bond investing:
increased risk (video) Market data
website: 1. FINRA http://finra-markets.morningstar.com/BondCenter/Default.jsp (FINRA bond market data) 2. WSJ Market watch on Wall Street Journal has daily yield curve and bond
yield information. http://www.marketwatch.com/tools/pftools/ https://www.youtube.com/watch?v=yph8TRldW6k 3. Bond Online http://www.bondsonline.com/Todays_Market/ Homework ( due
on_4/3/2022) 1. Firm AAA’s bonds price =
$850. Coupon rate is 5% and par is $1,000. The bond has six years
to maturity. Calculate for current yield? (5.88%) 2. For a zero coupon bond, use
the following information to calculate its yield to maturity. (14.35%) Years left to maturity = 10 years.
Price = $250. 3. For a zero coupon
bond, use the following information to calculate its price. ($456.39)
Years left to maturity = 10 years. Yield = 8%. 4. Imagine that an annual
coupon bond’s coupon rate = 5%, 15 years left. Draw price-yield profile.
(hint: Change interest rate, calculate new price and draw the graph). 5. IBM
5 year 2% annual coupon bond is selling for $950. How much this
IBM bond’s YTM? 3.09% 6. IBM 10 year 4% semi-annual coupon
bond is selling for $950. How much is this IBM bond’s YTM? 4.63% 7. IBM 10 year 5% annual coupon
bond offers 8% of return. How much is the price of this
bond? 798.7 8. IBM 5 year 5% semi-annual coupon
bond offers 8% of return. How much is the price of this bond? $878.34 9. IBM 20 year zero coupon bond
offers 8% return. How much is the price of this bond? 208.29 10. Collingwood Homes has a
bond issue outstanding that pays an 8.5 percent coupon and matures in 18.5
years. The bonds have a par value of $1,000 and a market price of $964.20.
Interest is paid semiannually. What is the yield to maturity? (8.90%) 11. Grand Adventure Properties
offers a 9.5 percent coupon bond with annual payments. The yield to maturity
is 11.2 percent and the maturity date is 11 years from today. What is the
market price of this bond if the face value is $1,000? ($895.43) 12. The zero coupon bonds of D&L
Movers have a market price of $319.24, a face value of $1,000, and a yield to
maturity of 9.17 percent. How many years is it until these bonds
mature? (12.73 years) 13. A zero coupon bond with a face
value of $1,000 is issued with an initial price of $212.56. The bond matures
in 25 years. What is yield to maturity? (6.29%) 14. The
bonds issued by Stainless Tubs bear a 6 percent coupon, payable semiannually.
The bonds mature in 11 years and have a $1,000 face value. Currently, the
bonds sell for $989. What is the yield to maturity? (6.14%) Videos --- homework help (due by
10/31/2021) Part
I Q1-Q2
Q3-Q4 Q5-Q8 Q9-Q14 Quiz 2-
Help Video
(Quiz 2 Due by
3/27/2022) |
Bond Pricing Formula (FYI)
Bond Pricing Excel Formula Summary of
bond pricing excel functions To calculate bond price (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 To calculate number of years left(annual coupon bond) Number
of years =nper(yield to maturity, coupon rate*1000, -price, 1000) To calculate number of years left(semi-annual coupon bond) Number
of years =nper(yield to maturity/2, coupon rate*1000/2, -price,
1000)/2 To calculate coupon (annual coupon bond) Coupon
= pmt(yield to maturity, number of years left, -price, 1000) Coupon
rate = coupon / 1000 To calculate coupon (semi-annual coupon bond) Coupon
= pmt(yield to maturity/2, number of years left*2, -price, 1000)*2 Coupon
rate = coupon / 1000 Low interest on Walmart bonds not worthy
of investment (FYI) MONEY
& INVESTING June
28, 2018 ericBRETAN https://naples.floridaweekly.com/articles/low-interest-on-walmart-bonds-not-worthy-of-investment/ What do
you do if you need a few extra bucks and don’t have
the money? If it is a small purchase, you may put it on your credit card. If
it is something larger, you may have to go to the bank and get a loan. But
what if you are a business and need more than a few extra bucks? What if you
need $16 billion — what do you do then? Walmart
recently faced this problem after its acquisition of the Indian E-commerce
company Flipkart Group. The solution was to issue corporate bonds to the
public in return for the cash needed to fund the purchase. But just what are
corporate bonds, how are they priced and issued, and are they a good
investment? A bond
is simply an investment where the investor loans money to a borrower in
exchange for a set interest rate for a given period of time. At the bond’s maturity, the investor receives the principal back as
well. For bonds issued by corporations, typically interest is paid every six
months although some bonds pay quarterly or monthly interest payments.
Corporations issue bonds that mature anywhere from less than a year (this
debt is often called commercial paper) to 30 years or more. Large companies
like Disney or Coca-Cola have even issued 100-year maturity bonds. To
issue a bond, a company typically will meet with a bank or investment bank to
structure the investment. First, the parties will determine the size of the
bond. If the company borrows too much, it may hurt its credit rating or have
trouble making the interest payments. If it borrows too little, the borrower
may not have the funds to maximize its growth or business opportunities.
Second, the company and bank will determine the appropriate maturity for the
bonds. Factors such as the use of the funds, overall interest rate
environment, and credit worthiness of the borrower all will affect this
decision. Finally,
the bank will price the bonds. Most bonds are issued at par meaning they are issued
at the face value of the bond, often $1,000. The “price” of the bond is then the interest rate that the buyer of
the bond will receive. For example, a company can issue a 10 year bond at par
that is priced at an interest rate of 6.2 percent. The interest rate of a
corporate bond is determined by two factors. The first is the overall rate
environment, typically determined by U.S. government debt rates. The second
is the credit worthiness of the issuer, which determines the additional
interest that investors demand to hold the bonds over Treasury rates. This “spread” can be very small for well
capitalized and stable companies like Microsoft or Apple or very large for
risky biotech firms. After
the interest rate of the bonds is set, the investments are sold to the public
at the face value of the bonds. Going forward, however, the bonds will trade
on the open market and will either trade at a premium or discount to the face
value. If overall interest rates go up or the credit worthiness of the
company declines, the bond’s value will decline as
investors sell the bonds to buy more stable bonds or bonds with higher
interest rates. Conversely, if interest rates decline or the company credit
strengthens, the bonds’ value will rise as investors
buy the bond. In the
case of Walmart, several maturities of bonds were offered to investors to
fund the staggering $16 billion needed to fund its acquisition. The longest
dated bonds, 30 years to maturity, were priced at just 1.05 percent over the
30 year Treasury rate or around 4.1 percent. This very low rate speaks very
highly of the credit worthiness of Walmart. However, one of the main bond
credit ratings companies, S&P, stated that the company’s
strong AA credit rating may be placed under review because of the significant
acquisitions the company has recently made and the resulting debt issued to
pay for them. Therefore, I would be hesitant to tie up my money for 30 years
at such a low interest rate and feel that there are plenty of better
investments to earn a better risk adjusted return. ¦ — Eric
Bretan, the co- owner of Rick’s Estate & Jewelry
Buyers in Punta Gorda, was a senior derivatives marketer and investment
banker for more than 15 years at several global banks. |
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Week 4 |
Chapter 8 Stock
Valuation Part
I Dividend payout and Stock Valuation For class
discussion: · Why can we
use dividend to estimate a firm’s intrinsic value? · Are
future dividends predictable? Ford’s dividends: https://www.nasdaq.com/market-activity/stocks/f/dividend-history
Wal-Mart Dividend History · Refer
to the following table for Wal-mart
(WMT’s dividend history) http://stock.walmart.com/investors/stock-information/dividend-history/default.aspx
For class discussion: What conclusions can be drawn from
the above information? Can we figure out the stock price
of Wal-Mart based on dividend, with reasonable assumptions? Stock Splits
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:
Can you estimate the
expected dividend in 2022? And in 2023? And on and on…
Can you write down the math equation
now? WMT stock price = ? WMT
stock price = npv(return, D1, D2, …D∞) WMT
stock price = D1/(1+r) + D2/(1+r)2
+ D3/(1+r)3 + D4/(1+r)4 + … 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 that we will learn in chapter 13) From
finance.yahoo.com
What
does each item indicate? From
finviz.com https://finviz.com/quote.ashx?t=WMT
Part II: Constant Dividend
Growth-Dividend growth model Calculate
stock prices 1) Given next dividends and price Po= Po= Po= Po= ……
Refer to http://www.calculatinginvestor.com/2011/05/18/gordon-growth-model/ · Now let’s apply this Dividend
growth model in problem solving. Constant dividend
growth model calculator (www.jufinance.com/stock) Equations ·
Po=
D1/(r-g) or Po= Do*(1+g)/(r-g) ·
r
= D1/Po+g = Do*(1+g)/Po+g · g= r-D1/Po = r-
Do*(1+g)/Po ·
D1 = Po *(r-g); D0 =
Po*(r-g)/(1+g) · Capital Gain yield = g · Dividend Yield = r – g = D1
/ Po = Do*(1+g) / Po ·
D1=Do*(1+g);
D2= D1*(1+g); D3=D2*(1+g)… Exercise: 1.
Consider the valuation of a common stock that
paid $1.00 dividend at the end of the last year and is expected to pay a cash
dividend in the future. Dividends are expected to grow at 10% and the
investors required rate of return is 17%. How much is the price? How much is
the dividend yield? Capital gain yield? 2. The
current market price of stock is $90 and the stock pays dividend of $3 (D1)
with a growth rate of 5%. What is the return of this stock? How much is the
dividend yield? Capital gain yield? Part III: Non-Constant Dividend
Growth Calculate
stock prices 1) Given next dividends and price Po= Po= Po= Po= …… Non-constant
dividend growth model 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
Calculator: Non-Constant Dividend Growth Calculator In class exercise for
non-constant dividend growth model 1.
You expect AAA
Corporation to generate the following free cash flows over the next five
years:
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:
2. 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=? Answer:
Do=0 D1=0 D2=0.56 g=4%
after year 2 è
P2 = D3/(r-g), D3=D2*(1+4%) è
P2 = 0.56*(1+4%)/(12%-4%) = 7.28 r=12% Po=? Po =
NPV(12%, D1, D2+P2), D2 = 0.56, P2=7.28. SO Po = NPV(12%, 0,0.56+7.28) =
6.25 (Note: for non-constant
growth model, calculate price when dividends start to grow at the constant
rate. Then use NPV function using dividends in previous years, last dividend
plus price. Or use calculator at https://www.jufinance.com/dcf/
) 3. Required return =12%.
Do = $1.00, and the dividend will grow by 30% per year for the next 4
years. After t = 4, the dividend is
expected to grow at a constant rate of 6.34% per year forever. What is the stock price ($40)? Answer:
Do=1 D1 =
1*(1+30%) = 1.3 D2=
1.3*(1+30%) = 1.69 D3 =
1.69*(1+30%) = 2.197 D4 =
2.197*(1+30%) = 2.8561 D5 =
2.8561*(1+6.34%), g=6.34% P4 =
D5/(r-g) = 2.8561*(1+6.34%) /(12% - 6.34%) Po = NPV(12%, 1.3, 1.69, 2.197,
2.8561+2.8561*(1+6.34%)) /(12% - 6.34%)) = 40 Or use calculator at https://www.jufinance.com/dcf/ Part IV: How to pick stocks?
(FYI) How to pick
stocks – Does it work? PE ratio Stock screening tools ·
Reuters
stock screener to help select stocks http://stockscreener.us.reuters.com/Stock/US/ ·
FINVIZ.com http://finviz.com/screener.ashx use
screener on finviz.com to narrow down your choices of stocks, such as
PE<15, PEG<1, ROE>30% ·
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
Summary of stock screening rules
from class discussion PEG<1 PE<15 (? FB’s
PE>100?) Growth rate<20 ROE>10% Analyst ranking:
strong buy only Zacks average
=1 (from Ranking stocks using PEG ratio) current
price>5 How to pick stocks Capital
Asset Pricing Model (CAPM)Explained https://www.youtube.com/watch?v=JApBhv3VLTo Ranking
stocks using PEG ratio https://www.youtube.com/watch?v=bekW_hTehNU HOMEWORK (Due with final) 1. Northern
Gas recently paid a $2.80 annual dividend on its common stock. This dividend
increases at an average rate of 3.8 percent per year. The stock is currently
selling for $26.91 a share. What is the market rate of return? (14.60
percent) 3.
IBM just paid $3.00 dividend per share to
investors. The dividend growth rate is 10%. What is the expected dividend of
the next year? ($3.3) 5.
Investors of
Creamy Custard common stock earns 15% of return. It just paid a
dividend of $6.00 and dividends are expected to grow at a rate of 6%
indefinitely. What is expected price of Creamy Custard's stock? ($70.67) Homework Video of this
week Quiz 3- Help Video Part I Part II Part III Part IV
|
P/E Ratio Summary by
industry (FYI) --- Thanks to Dr Damodaran Data Used: Multiple data services Date of Analysis: Data used is as of January 2021 Download as an excel file instead: http://www.stern.nyu.edu/~adamodar/pc/datasets/pedata.xls For global datasets: http://www.stern.nyu.edu/~adamodar/New_Home_Page/data.html
Details
about how to derive the model mathematically (FYI) The Gordon growth model is a simple discounted cash flow
(DCF) model which can be used to value a stock, mutual fund, or even the
entire stock market. The model is named after Myron Gordon who first published
the model in 1959. The Gordon model assumes that a financial security
pays a periodic dividend (D) which grows at a constant rate
(g). These growing dividend payments are assumed to continue forever.
The future dividend payments are discounted at the required rate of return
(r) to find the price (P) for the stock or fund. Under these simple assumptions, the price of the
security is given by this equation:
In this equation, I’ve used the “0” subscript
on the price (P) and the “1” subscript on the dividend (D) to
indicate that the price is calculated at time zero and the dividend is the
expected dividend at the end of period one. However, the equation is
commonly written with these subscripts omitted. Obviously, the assumptions built into this
model are overly simplistic for many real-world valuation problems. Many
companies pay no dividends, and, for those that do,
we may expect changing payout ratios or growth rates as the business
matures. Despite
these limitations, I believe spending some time experimenting with the
Gordon model can help develop intuition about the relationship between
valuation and return. Deriving the Gordon Growth Model Equation
The Gordon growth model calculates the present value of
the security by summing an infinite series of discounted dividend payments
which follows the pattern shown here:
Multiplying both sides of the previous equation by
(1+g)/(1+r) gives:
We can then subtract the second equation from the first
equation to get:
Rearranging and simplifying:
Finally,
we can simplify further to get the Gordon growth model equatio When Will Disney, Ford, and AMC Pay Dividends Again? (FYI) A lot of companies
suspended their payouts in 2020. Some of them aren't coming back anytime
soon. Rick Munarriz, Aug 21,
2021 at 8:05AM https://www.fool.com/investing/2021/08/21/when-will-disney-ford-and-amc-pay-dividends-again/ Key Points Disney has returned
to profitability sooner than expected, but long-term losses at Disney+ and
the need to invest in content may keep its payout in check. Ford has been
profitable in four of the past five quarters, and only the need to ramp up
investing in electric vehicles could keep a dividend away. The number of AMC
shares have increased fivefold over the past year, and that's not even the
biggest reason its distributions aren't returning anytime soon. Income investors
saw some of their dividend streams shrivel up last year. A lot of companies
suspended their payouts in early 2020, bracing for the impact of the COVID-19
crisis. The pandemic isn't fading in the rearview mirror the way it was two
months ago, but it's fair to start wondering when some of the more prolific
companies that nixed their distributions will return to cutting shareholder
checks. Disney (NYSE:DIS),
Ford (NYSE:F), and AMC Entertainment Holdings (NYSE:AMC) are three widely
followed stocks currently yielding 0%. Will that change? More importantly,
does that have to change? All three stocks are trading sharply higher now
than they were when they paused their payouts. Let's see how soon the
dividends can return -- and how likely that is to happen in 2022. Disney The House of Mouse was shelling out $0.88 a share twice a year
until the pandemic hit. It wasn't a surprise. Its theme parks
and cruise ships as well as the multiplexes it relied on for theatrical
distribution of its popular films all closed down in mid-March of last year. Disney braced for
the worst, and reality proved to be substantially kinder. After a pair of
quarterly losses during the early stretch of the crisis Disney has come
through with three consecutive quarterly profits. Even its theme parks segment
returned to profitability in its latest report. The dividend has a good chance of returning at some point in the
next year, but Disney is probably in no rush to make it happen.
Disney is expected to continue to lose
money until 2024, and it needs content to keep growing. Some analysts
have argued that a better use of the $3.2 billion it returned to investors in
2019 would be better served on new video content. It's fair, but it would
still be a surprise if the distributions don't come back in Disney's fiscal
2022 if the economy holds up with its end of the bargain. Ford The other name on
this list that could beat Disney to the payout restarting lines is Ford. The
automaker pioneer was a bigger draw to income investors than Disney given its
much larger pre-pandemic yield. Ford has also been profitable in four of the
past five quarters, one more period in the black than Mickey Mouse. If Ford doesn't return to its quarterly distributions soon it
won't be because it lacks confidence in its near-term outlook.
Ford is just investing in its reinvention. It has made a well-received push
into electric vehicles, and it's a market darling again. The stock is
trouncing the market in 2021 with a 42% year-to-date gain. If Ford thinks it
will need to preserve more of its capital to ramp up its presence in electric
vehicles it may not return to its chunky suspended dividend that would
translate to a yield of nearly 5% at the current price. However, it would be
surprising if it doesn't come back with at least a smaller token quarterly
disbursement in the coming months. AMC Entertainment It's not going to happen. A lot has
happened at AMC since it last cut a dividend check. It's still losing money,
and even if it wasn't, its share count has exploded nearly fivefold over the
past year. In other words, it would cost AMC five times as much to pay its
former per-share dividend. There are clearly better uses for its money. It can
buy back stock. It can update its theaters. It can make more investments in
home streaming to make sure it's not left out of the migration away from the
neighborhood multiplex. It can even invest in exclusive content. None of these
options may seem feasible in the near term, with analysts expecting the red
ink to continue until 2024. However, AMC has armed itself with a record $2
billion in liquidity. It does have options to improve its turnaround chances,
but you can be sure that it won't involve sending some of that cash to its
shareholders in the form of dividend checks. Let them eat complimentary
popcorn. Disney and Ford should return to being dividend stocks in the
next year. Payout out regular distributions just isn't part of the movie
trailer at AMC. Google parent Alphabet
announces 20-for-1 stock split PUBLISHED TUE, FEB 1 20224:19 PM ESTUPDATED WED, FEB 2 20223:11
AM EST Jordan Novet https://www.cnbc.com/2022/02/01/google-parent-alphabet-announces-20-for-1-stock-split.html KEY POINTS ·
Before the Alphabet rebrand in
2015, Google effectively split its stock with the introduction of a third
class of shares. ·
Alphabet stock has doubled in
less than two years, and the new split would make it more affordable for more
people. Google parent Alphabet said
its board approved plans for a 20-for-1 stock split on Tuesday as part of the
technology company’s quarterly earnings statement. Alphabet stock rose more
than 9% in after-market trading following the news. The move comes a year and a half after Apple most recently split
its stock, giving three shares for each share that people owned. Alphabet and
Apple are among the few technology companies that have seen their market
capitalizations stretch into the trillions, as investors opted for profitable
growth. Alphabet intends to split the
Class A, Class B and Class C shares of the stock, according to the earnings
statement. The change requires shareholder
approval. Each shareholder at the close of business on July 1 will receive,
on July 15, 19 additional shares for each share of the same class of stock
they own. In 2012, Google added a third class of shares, Class C, with no
voting rights. The company already had Class A shares, which carry one vote
per share, and Class B shares, which are held closely by founders and early
investors and carry 10 votes. The company maintained this stock structure
through its 2015 rebrand to Alphabet. In a letter included the 2004 prospectus for Google’s initial public offering, Larry Page and Sergey Brin,
Google’s founders, emphasized that they would always act “with
the long-term welfare of our company and shareholders in mind.” They described the introduction of the third class as “effectively a stock split” in a
2012 letter and said it was something many shareholders had been clamoring
for. The 2-for-1 stock split came in 2014, before the switch to Alphabet. Page and Brin own a combined 12% of Alphabet’s
Class C shares, which trade under the ticker symbol “GOOG” and have no voting rights, according to FactSet. The duo
control 83% of the company’s Class B shares, which do not trade on open
markets. Shares of Alphabet stock have
become more expensive lately, at over
$2,750 each at the time of market close on Tuesday, having doubled in price
since May 2020. The lower price would mean that more investors might be able
to afford buying entire, rather than fractional, shares of the advertising
company. Were the split to happen as of Tuesday’s close, the cost of each share would go from
$2,752.88 to $137.64, and each existing holder would get 19 additional shares
for every one they own. -- CNBC’s Ari Levy contributed to this report. Stock Splits (FYI)
https://www.nasdaq.com/market-activity/stock-splits Dividend Calendar (FYI)
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Chapter 9 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:
Modified Rate of Return:
Definition & Example (video)
https://study.com/academy/lesson/modified-rate-of-return-definition-example.html NPV, IRR, Payback Period calculator I NPV, IRR, Payback Period calculator II
Excel Template - NPV, IRR, MIRR, PI, Payback,
Discounted payback NPV
Profile in Excel Demonstration (Video, FYI) In class exercise Part I: Single project 1.
How much is MIRR? IRR? Payback period?
Discounted payback period? NPV? WACC: 11.00% Year 0 1 2 3 Cash
flows -$800 $350 $350 $350 Answer: 1)
NPV: NPV = -800 + 350/(1+11%) +
350/(1+11%)2 + 350/(1+11%)3 = 55.30 Or in excel: = npv(11%, 350, 350, 350)-800 = 55.30 2)
IRR:
So NPV = 0 = -800 +
350/(1+IRR) + 350/(1+IRR)2 + 350/(1+IRR)3 , use Solver,
can get IRR = 14.93% Or in excel:
3)
PI: profitable index
SO, PI= (350/(1+11%) + 350/(1+11%)2 + 350/(1+11%)3
) / 800 = 1.069 Or PI = NPV/800 + 1 = 55.30/800 + 1 = 1.069 4)
Payback period:
A portion of the third year = (800-350-350)/350 = 100/350 =
0.2857 So it takes 2 + 0.2857 = 2.2857 years to pay off the debt of
$800. 5)
Discounted payback period:
Note: All the cash flows in the above equation should be the
present values.
A portion of the third year = (800-318.18-289.26)/262.96 =
0.72 So it takes 2 + 0.72 = 2.72 years to pay off the debt of $800.
Or use the calculator at https://www.jufinance.com/capital/ Part
II: Multi-Projects 1.
Projects S and L, whose cash flows are
shown below. These projects are
mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best
selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the
project with the higher IRR rather than the one with the higher NPV, how
much, if any, value will be forgone, i.e., what's the chosen NPV versus the
maximum possible NPV? Note that (1) “true value” is measured by NPV,
and (2) under some conditions the choice of IRR vs. NPV will have no effect
on the value gained or lost. WACC: 7.50% Year 0 1 2 3 4 CFS -$1,100 $550 $600 $100 $100 CFL -$2,700 $650 $725 $800 $1,400 Answer:
If the required rate of return is 10%. Which
project shall you choose? 1) How
much is the cross over rate? (answer: 11.8%) 2) How
is your decision if the required rate of return is 13%? (answer: NPV of
B>NPV of A) · Rule for mutually exclusive projects: (answer:
Choose B) · What about the two projects are
independent? (answer: Choose both) Solution:
Part III More on IRR – (non-conventional cash flow) Suppose an investment will
cost $90,000 initially and will generate the following cash flows: – Year 1: 132,000 – Year 2: 100,000 – Year 3: -150,000 The required return is 15%.
Should we accept or reject the project? 1) How does the
NPV profile look like? (Answer: Inverted NPV profile) 2) IRR1= 10.11% --
answer 3) IRR2= 42.66% --
answer Solution:
HOMEWORK(Due with final) Year Cash flows 1 $8,000 2 4,000 3 3,000 4 5,000 5 10,000 1) How
much is the payback period (approach one)? ----
4 years 2) If
the firm has a 10% required rate of return. How much is NPV (approach
2)?-- $2456.74 3) If
the firm has a 10% required rate of return. How much is IRR (approach
3)? ---- 14.55% 4) If
the firm has a 10% required rate of return. How much is PI (approach
4)? ---- 1.12 Question 2: Project with an initial cash outlay of $60,000 with
following free cash flows for 5 years. Year FCF Initial
outlay –60,000 1 25,000 2 24,000 3 13,000 4 12,000 5 11,000 The firm has a 15% required rate of return. Calculate payback period, NPV, IRR and PI.
Analyze your results. Question 3: Mutually Exclusive
Projects 1) Consider
the following cash flows for one-year Project A and B, with required rates of
return of 10%. You have limited capital and can invest in one but one
project. Which one? § Initial
Outlay: A = -$200; B = -$1,500 § Inflow: A
= $300; B = $1,900 2) Example:
Consider two projects, A and B, with initial outlay of $1,000, cost of
capital of 10%, and following cash flows in years 1, 2, and 3: A:
$100 $200 $2,000 B:
$650 $650 $650 Which
project should you choose if they are mutually exclusive? Independent?
Crossover rate? (mutually
exclusive: A’s NPV=758.83 > B’s NPV = 616.45, so choose A; Independent, choose
all positive NPV, so choose both; Crossover
rate = 21.01%. The calculator does not work. Use IRR in Excel) Quiz 4- chapter 9 –
(no video prepared; Could use the calculator) Homework help videos (chapter 9) |
Simple
Rules’ for Running a Business
From the 20-page cellphone contract to the five-pound employee
handbook, even the simple things seem to be getting more complicated. Companies have been complicating things for themselves, too—analyzing hundreds of factors when making decisions, or
consulting reams of data to resolve every budget dilemma. But those
requirements might be wasting time and muddling priorities. So argues Donald Sull,
a lecturer at the Sloan School of Management at the Massachusetts Institute
of Technology who has also worked for McKinsey & Co. and Clayton, Dubilier & Rice LLC. In the book Simple
Rules: How to Thrive in a Complex World, out this week from Houghton
Mifflin Harcourt HMHC -1.36%,
he and Kathleen Eisenhardt of Stanford University claim that
straightforward guidelines lead to better results than complex formulas. Mr. Sull recently spoke with At Work about
what companies can do to simplify, and why five basic rules can beat a
50-item checklist. Edited excerpts: WSJ: Where, in the business
context, might “simple rules” help more than a complicated
approach? Donald Sull: Well, a common decision that people face in organizations is
capital allocation. In many organizations, there will be thick procedure
books or algorithms–one company I worked with had an
algorithm that had almost 100 variables for every project. These are very
cumbersome approaches to making decisions and can waste time. Basically, any
decision about how to focus resources—either people
or money or attention—can benefit from simple rules. WSJ: Can you give an example of
how that simplification works in a company? Sull: There’s
a German company called Weima GmBH that makes shredders. At one point,
they were getting about 10,000 requests and could only fill about a thousand
because of technical capabilities, so they had this massive problem of
sorting out which of these proposals to pursue. They had a very detailed checklist with 40 or 50 items. People
had to gather data and if there were gray areas the proposal would go to
management. But because the data was hard to obtain and there were so many
different pieces, people didn’t always fill out the checklists completely. Then
management had to discuss a lot of these proposals personally because there
was incomplete data. So top management is spending a disproportionate amount
of time discussing this low-level stuff. Then Weima came up with guidelines that the
frontline sales force and engineers could use to quickly decide whether a
request fell in the “yes,” “no” or “maybe” category. They did it with five
rules only, stuff like “Weima had to
collect at least 70% of the price before the unit leaves the factory.” After that, only the “maybes” were sent to management. This
dramatically decreased the amount of time management spend evaluating these
projects–that time was decreased by almost a factor
of 10. Or, take Frontier Dental Laboratories in Canada. They were
working with a sales force of two covering the entire North American market.
Limiting their sales guidelines to a few factors that made someone likely to
be receptive to Frontier—stuff like “dentists
who have their own practice” and “dentists
with a website”—helped focus their efforts and
increase sales 42% in a declining market. WSJ: Weima used five factors—is
that the optimal number? And how do you choose which rules to follow? Sull: You should have four to six
rules. Any more than that, you’ll spend too much time trying to follow
everything perfectly. The entire reason simple rules help is because they
force you to prioritize the goals that matter. They’re
easy to remember, they don’t confuse or stress you,
they save time. They should be tailored to your specific goals, so you choose
the rules based on what exactly you’re trying to
achieve. And you should of course talk to others. Get information from
different sources, and ask them for the top things that worked for them. But
focus on whether what will work for you and your circumstances. WSJ: Is there a business leader
you can point to who has embraced the “simple rules” guideline? Donald Sull: Let’s look at when Alex Behring took
over America
Latina Logistica SARUMO3.BR +1.59%,
the Brazilian railway and logistics company. With a budget of $15 million,
how do you choose among $200 million of investment requests, all of which are
valid? The textbook business-school answer to this is that you run the
NPV (net present value) test on each project and rank-order them by NPV. Alex
Behring knows this. He was at the top of the class at Harvard Business School. But instead Similarly, the global-health arm of the Gates Foundation gets
many, many funding requests. But since they know that their goal is to have
the most impact worldwide, they focus on projects in developing countries
because that’s where the money will stretch farther. |
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Week 5 - Chapter 14 Cost of Capital
For class discussion: · What is WACC? · Why is it important? · WACC increases, good or bad to stock holders? · How to apply WACC to figure out firm value?
One option (if beta is given, refer to chapter 13)
Another option (if dividend is given):
WACC Formula
WACC calculator (annual
coupon bond) (www.jufinance.com/wacc)
WACC calculator (semi-annual coupon bond) (www.jufinance.com/wacc_1)
WACC Calculator help
videos FYI
Summary of Equations
Discount rate to figure out the value of projects is called WACC (weighted average cost of capital)
WACC = weight of debt * cost of debt + weight of equity *( cost of equity)
Wd= total debt / Total capital = total borrowed / total capital We= total equity/ Total capital Cost of debt = rate(nper,
coupon, -(price – flotation costs), 1000)*(1-tax rate) Cost of Equity = D1/(Po – Flotation Cost) + g D1: Next period dividend; Po: Current stock price; g: dividend growth rate Note: flotation costs = flotation percentage * price
Or if beta is given, use CAPM model (refer to chapter 13) Cost of equity = risk free
rate + beta *(market return – risk free rate) Cost of equity = risk free rate +
beta * market risk premium
In Class Exercise: A firm borrows money from bond market. The price they paid is $950 for the bond with 5% coupon rate and 10 years to mature. Flotation cost is $40. For the new stocks, the expected dividend is $2 with a growth rate of 10% and price of $40. The flotation cost is $4. The company raises capital in equal proportions i.e. 50% debt and 50% equity (such as total $1m raised and half million is from debt market and the other half million is from stock market). Tax rate 34%. What is WACC (weighted average cost of capital, cost of capital)? (Answer: 9.84%) 1) Why does the firm raise capital from the financial market? Is there of any costs of doing so? What do you think? 2) What is cost of debt? (Kd = rate(nper, coupon, -(price – flotation costs $)), 1000)*(1-tax rate)) 3) Cost of equity? (Ke = (D1/(Price – flotation costs $)) +g, or Ke = Rrf + Beta*MRP)) Why no tax adjustment like cost of debt? 4) WACC=Cost of capital = Percentage of Debt * cost of debt + percentage of stock * cost of stock = Wd*Kd + We* Ke Meaning: For a dollar raised in the capital market from debt holders and stockholders, the cost is WACC (or WACC * 1$ = several cents, and of course, the lower the better but many companies do not have good credits)
Solution: Cost
of debt = rate(10, 50, -(950-40), 1000)*(1-34%) Cost
of/equity = 2/(40-4)+10% WACC
= 0.5*cost of debt + 0.5*cost of equity
https://www.jufinance.com/wacc/ No
homework for chapter 14
Homework
help videos (chapter 9) Quiz 4- chapter 9 – (no video prepared) |
(both annual and
semi-annual) WACC calculator (annual coupon bond) WACC calculator (semi-annual coupon
bond) (www.jufinance.com/wacc_1) Wal-Mart
Inc (NYSE:WMT) WACC %: 5.05%
As of 4/4/2022 As of today (2022-4-4), Walmart's
weighted average cost of capital is 5.05%. Walmart's ROIC % is 11.37% (calculated using TTM income
statement data). Walmart 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/WMT/WACC/Walmart%2BInc
Amazon.com
Inc (NAS:AMZN) WACC %:7.32% As of 4/4/2022 As of today (2022-4-4), Amazon.com's weighted average cost of capital is 7.32%. Amazon.com's ROIC % is 9.33% (calculated using TTM income statement data). Amazon.com 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/AMZN/WACC-Percentage/Amazon.com%20Inc
Apple
Inc (NAS:AAPL) WACC %:7.41%
As of 4/4/2022 As of today (2022-4-4), Apple's
weighted average cost of capital is 7.41%. Apple's ROIC % is 35.38% (calculated
using TTM income statement data). Apple 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/AAPL/WACC/Apple%2Binc
Tesla WACC %: 19.09% As of 4/4/2022
As of today (2022-4-4), Tesla's weighted average cost of capital is 19.09%. Tesla's ROIC % is 15.26% (calculated using TTM income statement data). Tesla earns returns that do not match up to its cost of capital. It will destroy value as it grows. https://www.gurufocus.com/term/wacc/NAS:TSLA/WACC-/Tesla
Cost of Capital by
Sector (US) Date of Analysis: Data used is as of January 2022 Download as an excel file instead: https://www.stern.nyu.edu/~adamodar/pc/datasets/wacc.xls For global datasets: https://www.stern.nyu.edu/~adamodar/New_Home_Page/data.html
http://people.stern.nyu.edu/adamodar/New_Home_Page/datafile/wacc.htm |
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Chapter 13 Risk and Return Equations (FYI): 1. Expected return and
standard deviation Given a probability distribution of
returns, the expected return can be calculated using the following equation:
where
https://www.zenwealth.com/businessfinanceonline/RR/ExpectedReturn.html 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.
https://www.zenwealth.com/businessfinanceonline/RR/MeasuresOfRisk.html Exercise: Stock A has the following returns for various states of the
economy: State of the Economy Probability Stock
A's Return Recession 10% -30% Below
Average 20% -2% Average 40% 10% Above
Average 20% 18% Boom 10% 40% Stock A's expected return is?
Standard deviation? Solution: Expected return = 10%*(-30%))
+ 20%*(-2%) + 40% *10% + 20%*18% + 10%*40% = 8.2% Standard deviation = sqrt(10%*(-30%-8.2%)2 + 20%*(-2%-8.2%)2
+40%*(10%-8.2%)2 + 20%*(18%-8.2%)2 +10%*(40%-8.2%)2)
= 16.98% Or, https://www.jufinance.com/return/
W1 and W2 are the percentage of each stock in the
portfolio.
Exercise: Stocks A and B have the following returns for various states of
the economy: State of the
Economy Probability Stock
A's Return Recession 10% -30% -10% Below
Average 20% -2% 2% Average 40% 10% 1% Above
Average 20% 18% 2% Boom 10% 40% -5% Solution: (or use calculator
at https://www.jufinance.com/return/) Stock 1: Expected return = 10%*(-30%))
+ 20%*(-2%) + 40% *10% + 20%*18% + 10%*40% = 8.2% Standard deviation = sqrt(10%*(-30%-8.2%)2 + 20%*(-2%-8.2%)2
+40%*(10%-8.2%)2 + 20%*(18%-8.2%)2 +10%*(40%-8.2%)2)
= 16.98% Stock 2: Expected return = 10%*(10%)) +
20%*(2%) + 40% *1% + 20%*2% + 10%*(-5)% = 1.7% Standard deviation = sqrt(10%*(10%-1.7%)2 + 20%*(2%-1.7%)2
+40%*(1%-1.7%)2 + 20%*(2%-1.7%)2 +10%*((-5)%-1.7%)2)
= 3.41% Covariance: Covariance =
10%*(-30%-8.2%)*(10%-1.7%)+20%*(-2%-8.2%)*(2%-1.7%)+40%*(10%-8.2%)*(1%-1.7%)+20%*(18%-8.2%)*(2%-1.7%)+10%*(40%-8.2%)*((-5%)-1.7%)
= -0.54% Correlation: Correlation = -0.54%/(16.98%* 3.41%) = -0.93
]3..
Historical returns Holding period return (HPR) =
(Selling price – Purchasing price + dividend)/ Purchasing price 4. CAPM (Capital Asset
Pricing Model) model · What is Beta? Where to find Beta?
Beta
is a measurement of a stock's price fluctuations, which is often called
volatility, and is used by investors to gauge how quickly a stock's price
will rise or fall. Because beta is calculated from past returns, it's not
considered as reliable a tool to forecast rises in stock prices, and it is
more commonly used by options traders. Beta compares the changes in a
company's stock returns against the returns of the market as a whole. Online
brokerages give investors extensive data on a stock's beta value, and some
free financial news websites also show current beta measurements. · What
Is the Capital Asset Pricing Model?
The Capital Asset Pricing Model (CAPM)
describes the relationship between systematic risk and expected
return for assets, particularly stocks. CAPM is widely used throughout
finance for pricing risky securities and generating expected
returns for assets given the risk of those assets and cost of capital. 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) · SML – Security Market Line
In class
exercise Steps: 1. From finance.yahoo.com, collect stock prices of
the above firms, in the past five years Steps: · Goto finance.yahoo.com,
search for the company · Click
on “Historical prices” in the left column on the top and choose monthly stock
prices. · Change
the starting date and ending date to “Sept 30th, 2016” and “Sept 30th, 2021”,
respectively. · Download
it to Excel · Delete
all inputs, except “adj close”
– this is the closing price adjusted for dividend. · Merge
the three sets of data just downloaded Pick three stocks. Has to be the leading firm
in three different industries. · For
example: chose Apple, Dell, and Boeing. 3. Evaluate the performance of each stock: · Calculate
the monthly stock returns. · Calculate
the average return · Calculate
standard deviation as a proxy for risk · Calculate
correlation among the three stocks. · Calculate
beta. But you need to download S&P500 index values in the past five years from
finance.yahoo.com. · Calculate stock returns based on CAPM. · Draw SML ·
Stock
Price In Class exercise all included (Beta, CAPM, excel file here) · Stock Price Normal Distribution
(FYI) (
https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html) HOMEWORK (Due with final) 1. AAA
firm’s stock has a 0.25 possibility to make 30.00% return, a 0.50 chance to
make 12% return, and a 0.25 possibility to make -18% return. Calculate
expected rate of return (Answer: 9%) 2. If
investors anticipate a 7.0% risk-free rate, the market risk premium = 5.0%,
beta = 1, Find the return. (answer:12%) 3. AAA
firm has a portfolio with a value of $200,000 with the following four stocks.
Calculate the beta of this portfolio ( answer: 0.988) Stock value β A $
50,000.00 0.9500 B 50,000.00 0.8000 C 50,000.00 1.0000 D 50,000.00 1.2000 Total $200,000.00 4. A
portfolio with a value of $40,000,000 has a beta = 1. Risk free rate = 4.25%,
market risk premium = 6.00%. An additional $60,000,000 will be included in the
portfolio. After that, the expected return should be 13%. Find the average
beta of the new stocks to achieve the goal ( answer: 1.76) 5. Stock A
has the following returns for various states of the economy: State of the
Economy Probability Stock
A's Return Recession 10% -30% Below
Average 20% -2% Average 40% 10% Above
Average 20% 18% Boom 10% 40% Stock A's
expected return is? Standard deviation? (answer:
expected return = 8.2%, variance=0.02884, standard deviation=16.98%,
visit https://www.jufinance.com/return/) 6. Collectibles
Corp. has a beta of 2.5 and a standard deviation of returns of 20%. The
return on the market portfolio is 15% and the risk free rate is 4%. What is
the risk premium on the market? 7. An
investor currently holds the following portfolio: Amount Invested 8,000 shares of
Stock A $16,000 Beta = 1.3 15,000 shares of
Stock B $48,000 Beta = 1.8 25,000 shares of
Stock C $96,000 Beta = 2.2 The beta for
the portfolio is? 8. Deleted 9. Assume that
you have $165,000 invested in a stock that is returning 11.50%, $85,000
invested in a stock that is returning 22.75%, and $235,000 invested in a
stock that is returning 10.25%. What is the expected return of your portfolio? 10. If you hold
a portfolio made up of the following stocks: Investment
Value Beta Stock
A $8,000 1.5 Stock
B $10,000 1.0 Stock
C $2,000 .5 What is the
beta of the portfolio? 11. You
own a portfolio consisting of the stocks below. Stock Percentage
of
portfolio Beta 1. 20% 1 2. 30% 0.5 3. 50% 1.6 The risk free
rate is 3% and market return is 10%. a. Calculate
the portfolio beta. b. Calculate
the expected return of your portfolio. 12. An
investor currently holds the following portfolio: Amount Invested 8,000 shares of
Stock A $10,000 Beta = 1.5 15,000 shares of
Stock B $20,000 Beta = 0.8 25,000 shares of
Stock C $20,000 Beta = 1.2 Calculate the
beta for the portfolio. Homework Help videos Q1 Q5 Q2 Q3 Q4 Q6 Q7 Q9 TO THE END Quiz 5
prep video Part
I (has three questions from chapter 8) Part
II |
How much does Amazon worth?” --- FYI only: Amazon.com Inc. (AMZN) https://www.stock-analysis-on.net/NASDAQ/Company/Amazoncom-Inc/DCF/Present-Value-of-FCFF
Present
Value of Free Cash Flow to the Firm (FCFF)
In
discounted cash flow (DCF) valuation techniques the value of the stock is
estimated based upon present value of some measure of cash flow. Free cash
flow to the firm (FCFF) is generally described as cash flows after direct
costs and before any payments to capital suppliers.
Intrinsic Stock Value (Valuation Summary)
Amazon.com
Inc., free cash flow to the firm (FCFF) forecast
1 Weighted Average Cost of Capital (WACC)
Amazon.com
Inc., cost of capital
1 USD $ in millions Equity (fair value) = No. shares
of common stock outstanding × Current share price 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 WACC
= 16.17% FCFF Growth Rate (g)
FCFF growth rate
(g) implied by PRAT model
Amazon.com
Inc., PRAT model
2017
Calculations 2 Interest expense, after tax =
Interest expense × (1 – EITR) 3 EBIT(1 – EITR) = Net income
(loss) + Interest expense, after tax 4 RR = [EBIT(1 – EITR) – Interest
expense (after tax) and dividends] ÷ EBIT(1 – EITR) 5 ROIC = 100 × EBIT(1 – EITR) ÷
Total capital 6 g = RR × ROIC FCFF growth rate
(g) forecast
Amazon.com
Inc., H-model
where: Calculations g2 = g1 + (g5 – g1) × (2 – 1) ÷ (5 – 1) g3 = g1 + (g5 – g1) × (3 – 1) ÷ (5 – 1) g4 = g1 + (g5 – g1) × (4 – 1) ÷ (5 – 1) |
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Weeks 7 & 8 |
Final
Exam (will be posted on blackboard) Final prep video (on youtube) |
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Weeks 7 & 8 |
Thank you! Thank you! |
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Chapters 2, 3 - Financial Statements (not required) Based on the following information, prepare the income statement
and the cash flow statement 2017 2018 Sales 36,408 Depreciation 1,760 Tax
paid 2,070 Accounts
receivable 3,411 4,218 Inventory 18,776 21,908 Accounts
payable 7,250 8,384 Common
stock 15,000 17,500 Retained
earning 6,357 3,825 COG 28,225 Cash 2,060 1,003 Interest
paid 510 NFA 14,160 14,080 Long term
debt 9,800 11,500 Solution: (excel solution fyi)
************ 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? 1. Pay interest on debt. 2. Pay back principal on debt. 3. Pay dividends. 4. Buy back stock. 5. Buy nonoperating assets (e.g.,
marketable securities, investments in other companies, etc.)
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.
Capital expenditure = increases in NFA +
depreciation Or, capital expenditure = increases in GFA 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 1. 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%. a. $1.2 b. $1.3 c. $1.4 d. $1.5 FCF = EBIT(1 – T) + Deprec. – (Capex + NOWC) answer: EBIT $3 Tax rate 40% Depreciation $1 Capex + NOWC $1.60 So, FCF = $1.2 2. The following information should be used for the following problems: 2014 2015 Sales $ 740 $ 785 COGS 430 460 Interest 33 35 Dividends 16 17 Depreciation 250 210 Cash 70 75 Accounts receivables 563 502 Current liabilities 390 405 Inventory 662 640 Long term debt 340 410 Net fixed assets 1,680 1,413 Common stock 700 235 Tax rate 35% 35%
• What is the net income for 2015? ($52)
https://www.jufinance.com/ratio Finviz.com/screener
for ratio analysis (https://finviz.com/screener.ashx) Financial ratio analysis (VIDEO) |
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