FIN 509 & FIN510 Class Web Page, Fall '20
Weekly SCHEDULE, LINKS, FILES and Questions
Coverage, HW, Supplements
Equations and Assignments
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Chapter 5 Time value of money 1
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
(due by Sunday at 11:59 pm)
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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?
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HOMEWORK of Chapters 5 and 6 (due on 10/27, updated)
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)
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
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?
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)
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
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
Quiz 1- Help Videos (new)
© 2002 - 2019 by Mark A. Lane, Ph.D.
FV = PV *(1+r)^n
PV = FV / ((1+r)^n)
N = ln(FV/PV) / ln(1+r)
Rate = (FV/PV)1/n -1
N = ln(FV/C*r+1)/(ln(1+r))
N = ln(1/(1-(PV/C)*r)))/ (ln(1+r))
EAR = (1+APR/m)^m-1
APR = (1+EAR)^(1/m)*m
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)
Chapter 7 Bond Pricing
Simplified Balance Sheet of WalMart
· 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?
How Bonds Work (video)
FINRA – Bond market information
WAL-MART STORES INC
For class discussion:
Fed has hiked interest rates. So, shall you invest in short term bond or long term bond?
1. Find bond sponsored by WMT
just go to www.finra.org, è Investor center è market data è bond è corporate bond
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.
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?
Supplement: The risks investing in a bond
Homework (Due on 10/27)
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?
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
Quiz 2- Help Video
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
Chapter 8 Stock Valuation
To learn about non-constant
growth of dividend (Here dividend growth model will not work), please refer
to the following calculator (FYI, not required)
Po = Do*(1+g1) / r + Do*(1+g1) *(1+g2) / (r2)+ ... Do*(1+g1) *(1+g2)*...(1+gn-1)/ (rn-1) + Do*(1+g1) *(1+g2)*...(1+gn-1)*(1+gn)/(r-gn)
g1: next year's growth rate; gn: nth year's growth rate; Po: current stock price
If non-constant dividend growth rates in the next several years are not given, refer to the following equations.
g1 = D1/Do-1; g2 = D2/D1-1; g3=D3/D2-1,... Until dividend growth rate stays fixed.
The Gordon growth model is a simple discounted cash flow (DCF) model which can be used to value a stock, mutual fund, or even the entire stock market. The model is named after Myron Gordon who first published the model in 1959.
The Gordon model assumes that a financial security pays a periodic dividend (D) which grows at a constant rate (g). These growing dividend payments are assumed to continue forever. The future dividend payments are discounted at the required rate of return (r) to find the price (P) for the stock or fund.
Under these simple assumptions, the price of the security is given by this equation:
In this equation, I’ve used the “0” subscript on the price (P) and the “1” subscript on the dividend (D) to indicate that the price is calculated at time zero and the dividend is the expected dividend at the end of period one. However, the equation is commonly written with these subscripts omitted.
Obviously, the assumptions built into this model are overly simplistic for many real-world valuation problems. Many companies pay no dividends, and, for those that do, we may expect changing payout ratios or growth rates as the business matures.
Despite these limitations, I believe spending some time experimenting with the Gordon model can help develop intuition about the relationship between valuation and return.
Deriving the Gordon Growth Model Equation
The Gordon growth model calculates the present value of the security by summing an infinite series of discounted dividend payments which follows the pattern shown here:
Multiplying both sides of the previous equation by (1+g)/(1+r) gives:
We can then subtract the second equation from the first equation to get:
Rearranging and simplifying:
Finally, we can simplify further to get the Gordon growth model equation
dividend growth model:
· Now let’s apply this Dividend growth model in problem solving.
· Stockholders’ rights
· Risk and return – where to find how risky the stock is
2. Calculate stock prices
1) Given next dividends and price expected to be sold for
Po= + +
Po= + ++
2) Given all dividends – Dividend growth model
· Po= D1/(r-g) or Po= Do*(1+g)/(r-g)
· r = D1/Po+g = Do*(1+g)/Po+g; So r = total return = dividend yield + capital gain yield
· g= r-D1/Po = r- Do*(1+g)/Po
· Capital Gain yield = g = (P1-Po)/Po; P1: Stock price one year later (P1=D2/(r-g))
· Dividend Yield = r – g = D1 / Po = Do*(1+g) / Po
· D1=Do*(1+g); D2= D1*(1+g); D3=D2*(1+g)…
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 with a growth rate of 5%. What is the return of this stock? How much is the dividend yield? Capital gain yield?
3. How to pick stocks – Does it work?
PE ratio; PEG ratio (peg ratio vs. PE ratio – video)
HOMEWORK (Due with final on 11/17/2020)
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)
2. Douglass Gardens pays an annual dividend that is expected to increase by 4.1 percent per year. The stock commands a market rate of return of 12.6 percent and sells for $24.90 a share. What is the expected amount of the next dividend? ($2.12)
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)
4. The current market price of stock is $50 and the stock is expected to pay dividend of $2 with a growth rate of 6%. How much is the expected return to stockholders? (10%)
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
Chapter 9 Capital Budgeting
chapter 9 in class excel notes FYI (newly added)
1. NPV Excel syntax
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
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)
Chapter 9 Study Guide
Part I: Single project
Consider the following scenario.
You are reviewing a new project and have estimated the following cash flows:
Year 0: CF = -165,000
Year 1: CF = 63,120; NI = 13,620
Year 2: CF = 70,800; NI = 3,300
Year 3: CF = 91,080; NI = 29,100
Your required return for assets of this risk level is 12%.
1) Using payback period method to make capital budgeting decision.
2) Using discounted payback period method to make capital budgeting decision.
3) Using net present value method (NPV) (answer: $12,627.41)
4) Using profitable index method (PI) (answer: 1.077)
5) Using the Internal Rate of Return method (answer: 16.13%)
6) Using modified IRR method (MIRR, using 12% for both investment rate and financing rate. Answer: 14.79%)
Part II: Multi-Projects
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)
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)
2) IRR1= 10.11% -- answer
3) IRR2= 42.66% -- answer
An investment project has the following cash flows:
CF0 = -1,000,000; C01 – C08 = 200,000 each
If the required rate of return is 12%, what decision should be made using NPV?
How would the IRR decision rule be used for this project, and what decision would be reached?
How are the above two decisions related?
HOMEWORK(Due on 11/17/2020)
Year Cash flows
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.
Initial outlay –60,000
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?
Chapter 14 Cost of Capital
in class excel notes FYI (newly added)
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?
What is DCF?
One option (if beta is given, refer to chapter 13)
Another option (if dividend is given):
WACC calculator (annual coupon bond)
WACC calculator (semi-annual coupon bond)
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)
No homework for chapter 14
Homework help videos (chapter 9)
Quiz 4- chapter 9 – (no video prepared)
As of today (2020-11-02), Walmart's weighted average cost of capital is 3.36%. Walmart's ROIC % is 8.73% (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 %:8.44% As of Today
As of today (2020-11-02), Amazon.com's weighted average cost of capital is 8.44%. Amazon.com's ROIC % is 10.01% (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 %:8.23% As of Today
As of today (2020-11-02), Apple's weighted average cost of capital is 8.23%. Apple's ROIC % is 24.02% (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 (NAS:TSLA) %:12.09% As of Today As of Today
As of today (2020-11-02), Tesla's weighted average cost of capital is 12.09%. Tesla's ROIC % is 4.60% (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 2019