Introduction
Assignment 1
Time Value Adjustment
Question 3.2:
The following series of cash flows exists:
Time Period Amount
t = 1 $300
t = 2 $200
t = 3 $100
t = 4 $100
Show at least four different ways you could set up the cash flow stream to solve for the present value of this stream of cash inflows.
Problem 3.6: Future Value (Note: Ignore any tax considerations)
Your firm has a retirement plan that matches all contributions on a one-to-two basis. That is, if you contribute $2,000 per year, the company will add $1,000 to make it $3,000. The firm guarantees an 8% return on the funds. Alternatively you can “do it yourself”; you think you can earn 11% on your money this way. The first contribution will be made 1 year from today. At that time, and every year thereafter, you will put $2,000 into the retirement account. If you want to retire in 25 years, which way are you better off?
Problem 3.8: Present Value
Olympia Electric has a line of large motors that no longer fits its corporate image. It is attempting to determine the minimum selling price for the small motors line. Olympia presently receives $250,000 per year after taxes in cash flows from the line. If the opportunity cost of capital is 16%, how much should Olympia ask if it thinks the life expectancy of the line is as follows?
a. 10 years
b. 20 years
c. infinity
Problem 3.13: Internal Rate of Return
You are the winner in the Down South Lottery. As a result you have the choice between three alternative payment plans:
Plan I: A lifetime annuity of $60,425 annually, with the first payment one
year from now.
Plan II: A 70,000 annual annuity for 20 years, with the first payment 1
year from now.
Plan III: $800,000 today
Your life expectancy is 45 more years. Ignoring any tax effects,
determine the following:
a. At what interest rate would you be indifferent between Plans I and III?
b. At what interest rate would you be indifferent between Plans II and III?
c. At what interest rate (to the nearest whole number) would you be indifferent between Plans I and II?
d. What if (c) is now changed so you know the interest rate for both Plans I and II is 12% for the first 20 years? What rate would you have earn on the remaining 25 years of the $60,425 annuity to be indifferent between Plans I and II?
Problem 3.16: Cost of Alternative Loans
Hacienda Winery needs $500,000 for expansion of its warehouse. The company plans to finance $100,000 with internally generated funds but wants to secure a loan for the remainder. The contracting firm’s finance subsidiary has offered to provide the loan based on six annual payments of $97,300 each. Alternatively, Hacienda’s bankers will lend the firm $400,000, to be repaid in six equal annual installments (covering both principal and interest) at a 15 percent interest rate. Finally, an insurance firm would also loan the money; it requires a lump sum payment of $750,000 at the end of 6 years.
a. Based on the respective annual percentage costs of the three loans, which one should Hacienda select?
b. What other considerations might be important in addition to cost?
Problem 3.18: Future Value and Compounding
How much would you have in the future in each of the following cases?
a. $2,500, invested today, if continuous compounding is employed, the nominal rate is 9 percent, and the period is 2 1/2 years.
b. $4.80, invested today, if the nominal rate is 12.6 percent continuously compounded, and the period is 15 years.
c. $100 invested today, if the nominal rate is 14 percent compounded annually, and the period is 10 years.
d.Same as in (c), except interest is compounded continuously.
Assignment 2
Valuation of Bonds and Stocks
Question 4.3:
(Note: In answering 4.3, ignore any reinvestment problem associated with the future interest to be received.)
The rate of return you will receive on a bond if you buy it today and hold it until maturity is its yield to maturity, YTM.
a. What happens to the YTM as market interest rates change?
b. Will you receive any more, or any less, if interest rates change as long as you hold the bond to maturity? Why?
c. Will you receive any more, or any less, as interest rates change if you are forced to sell before maturity? Why?
Question 4.5:
Does a high price/earnings ratio mean a firm is a “growth firm?” Explain.
Problem 4.2: Bond Price Change and Time to Maturity
Find the current market price of a 20-year, 9% coupon rate bond with par
value of $1,000, if interest is paid annually and if current market rates are
(a) 11% or (b) 7%. What are the current market prices if everything is the
same except the bond has only (1) 10 years to maturity, or (2) 2 years to
maturity? What can we say about the relative influence of changing market
interest rates on the market prices of short-term versus long-term bonds?
Can you speculate on why this is so?
Problem 4.3: Yield to Maturity
Sandberg Engineering has some 15-year, $1,000 par bonds outstanding which have a coupon rate of 9% and pay interest annually. What is the yield to maturity on the bonds if their current market price is
a. $1,180?
b. $800?
c. Would you be willing to pay $800 if your minimum required rate of return was 11%? Why or why not?
Problem 4.7: Implied Growth Rate
Reilly Supermarkets’ common stock is selling at $54, the cash dividend expected next year (at time t = 1) is $3.78 per share, and the required rate is of return is 15 percent. What is the implied compound growth rate (to infinity) in cash dividends?
Problem 10: Constant Versus Nonconstant Growth
Brett is contemplating the purchase of a small, one-island service station. After-tax cash flows are presently $20,000 per year, and his required rate of return is 14%
a. What is the maximum price Brett should pay for the service station if he expects cash flows to grow at 4% per year to infinity?
b. If Brett decides he needs a 15% return, and there will be no growth in after-tax cash flows for 3 years, followed by a 10% per year for years 4 and 5, followed by 3% growth to infinity, what is the maximum amount he should pay?
Problem 4.14: Forgoing Cash Dividends
Downing Enterprises is a no-growth firm that pays cash dividends of $8 per year. Its current required rate of return is 12%.
a. What is Downing’s current market price?
b. Management is considering an investment that will convert the firm into a constant-growth firm, but it requires stockholders to forgo cash dividends for the next 6 years. When cash dividends are resumed in year 7, they will be $8 plus the expected constant growth of 11% [i.e., ($8)(1.11)] from year 6 to infinity. If its new required return is 16%, will the stockholders be better off?
c. What happens if everything is the same as in (b), except that the growth rate is only 10%.
Assignment 3
Risk and Return
Question 5.1:
(Note: In answering 5.1 (b), you must consider whether it is absolute risk, or relative risk, CV, that is important.)
Security A has a mean of 25 and a standard deviation of 15; security B has a mean of 40 and a standard deviation of 10.
a. Which security is riskier? Why?
b. What if the standard deviation on security B was 15? 20?
Problem 5.2: Portfolio Risk
(Note: In (a), convert the individual security returns for A and B to a single series of returns via 0.50(60) + 0.50(50) = 55, which has a 0.30 probability of occurrence. Do the same for A and B for the other two probabilities, and then for A and C. Once you have the probability distributions in (a), then in (b) you can treat the returns like that of a single security.)
Securities A, B, and C have rates of return and probabilities of occurrence as follows:
Security Return (%)
Probability A B C
0.30 60 50 10
0.40 40 30 50
0.30 20 10 90
a. Calculate the probability distribution of expected rates of return for a
portfolio composed 50% of security A and 50% of security B. Now do
the same for a portfolio composed of 50% security A and 50% security
C.
b. Calculate the expected value (or mean) and the standard deviation for
portfolios AB and AC from (a).
c. Which portfolio has the highest expected return? The lowest risk?
Which portfolio is preferable?
d. Assume that the standard deviation calculated for portfolio AC is 21%,
but that everything else remains the same. Which portfolio would now
be preferable? Why?
Problem 5.3: Correlation and Standard Deviation
Consider two stocks, A and B, with their expected returns and standard deviations, as follows:
_ A B
expected return, k 15% 10%
standard deviation, 10 8
a. What is the expected return if the portfolio contains equal amounts (0.50) of each security?
b. What is the standard deviation for the equally weighted portfolio in (a) if the correlation between the security return is (1) Corr ab = +1.00 (2) Corr ab = +0.50, and (3) Corr ab = -0.50?
c. How does the decrease in the portfolio standard deviation (as the correlation between the security returns drops) relate to the diversifiable and nondiversifiable risk?
Problem 5.9: Portfolio Required Return
Excallibur Fund has a total investment in five stocks as follows:
Investment
Stock(market value)Beta
1$3.0 million0.50
2 2.5 million1.00
3 1.5 million2.00
4 2.0 million1.25
5 1.0 million1.50
The risk-free rate, kRF, is 7 percent, and the returns on the market portfolio are given by the following probability distribution:
ProbabilitykM
0.10 8%
0.2010
0.3013
0.3015
0.1017
What is Excalibur Fund’s required rate of return?
Problem 5.11: Required Return and Common Stock Valuation
Danford Products has dividends today, D0, of $2 per share, an expected growth rate of 9 percent per year to infinity, a beta of 1.40, kM = 13%, and kRF = 8%.
a. What is the required rate of return?
b. What is the current market price of Danford’s common stock?
c. Danford is contemplating the divestiture of an unprofitable but stable revenue-producing division. The effect will be to increase the growth rate in cash dividends to 11 percent, and also increase beta to 1.60. What will be the new market value?
d. Instead of (c), Danford could merge with another firm that is a steady cash producer but is less risky. The effect would be to lower beta to 1.20 and reduce the growth rate in dividends to 8 percent. What would be the market value in that case?
e. Instead of either (c) or (d), a new, aggressive management could be brought in. Beta would go to 2.00, and the growth rate in dividends would be 13 percent. Now what would be the stock price?
f. Is Danford better off staying where it is, or moving to one of the plans outlined in (c), (d), or (e)? Which plan should the firm choose? Why is this the best plan?
Problem 5.13: Risk, Correlation, and Stock Price
(Note: j = ( j)(CorrjM)/M)
O’Meara Instruments is in the process of evaluating the effect of different factors on its market value. O’Meara expects to pay dividends of $3 a year from now (D1 = $3), and the growth rate in its dividends is 4 percent per year until infinity. O’Meara estimates the following:
kRF = 6%, kM = 11%, j = 16%, M =10% and CorrjM = 0.50.
a. What is the required rate of return for O’Meara and the current market value of its stock?
b. What is O’Meara’s required rate of return and stock market value if everything stays the same, except that its correlation with the market increases to 0.75?
c. If all the conditions are as in (a) except that j increases to 64 percent and M increases to 20 percent, what is the required rate of return and market price for O’Meara?
d. If all the conditions are as in (a) except that j decreases to 8 percent, what is the required rate of return and market price for O’Meara?
Problem 5.14: Disequilibrium and Stock Price
The stock of Ross Furniture is currently selling for $25. You have evaluated the future prospects of both the firm and the market and made the following estimates. Ross is expected to pay a dividend of $2.00 at t = 1, and this dividend is expected to grow indefinitely at 6 percent a year. The standard deviation for Ross and the market are 10 percent and 6.25 percent, respectively. The correlation between the returns for Ross and for the market is +0.80. If the return on the market is 14 percent and the risk-free rate is 8 percent, is Ross a good buy?
Assignment 4
The Opportunity Cost of Capital
Capital Structure
Question 6.1:
“Internally generated funds are costless. Accordingly, the cost of new common stock is the only relevant cost of common equity for cost of capital purposes.” Evaluate this statement.
Problem 6.1: After-Tax Cost of Debt
Calculate the after-tax cost of debt under the following conditions if the maturity value of the debt is $1,000, interest is paid annually, and the corporate tax rate is 35 percent.
a. Coupon interest rate is 8 percent, proceeds are $900, and the life is 20 years.
b. Bond pays $100 per year in interest, proceeds are $960, and life is 10 years.
c. Coupon interest rate is 14 percent, proceeds are $1,120, and bond has 30-year life.
d. Proceeds are $1,000, coupon interest rate is 12 percent, and the life is 5 years.
Problem 6.2: Cost of Preferred Stock
What is the after-tax cost of preferred stock under the following circumstances?
a. Par is $80, dividend is $8 per year, and the proceeds are $76.
b. Proceeds are $46, and dividends are $7.
c. Par is $60, dividend is 9 percent (of par), and proceeds are $55.
d. Par is $40, dividend is 11 percent (of par), and proceeds are $40.
Problem 6.5: Cost of Common: All Three Approaches
Luxury Suites has hired you as a consultant to estimate its cost of common equity. After talking with its CFO and an econometric forecasting firm, you have come up with the following facts and estimates:
EstimatesYearDividends per Share
P0 = $85-5$1.21
Luxury Suites = 1.50-4 1.21
Treasury security rate = 10%-3 1.30
Market yield on comparable-2 1.40
quality long-term debt = 13%-1 1.71
Expected return on the market 0 1.86
portfolio = 16%
Expected risk premium of stocks
over bonds = 4%
Current earnings per share, EPS = $5.75
Luxury Suites plans to use 30 percent debt and 70 percent equity for its incremental financing. Also, the firm’s marginal tax rate is 33 percent.
a. What do you estimate the past growth rate in cash dividends per share has been? Employ this as your estimate of g (round to the nearest whole number).
b. What is the estimated cost of common equity employing the following approaches: (1) dividend valuation, (2) CAPM, and (3) bond yield plus expected risk premium?
c. Explain why one of the estimates from (b) is substantially lower than the other two.
d. Take an average of all three answers from (b) for your estimate of Luxury’s cost of common equity.
d. What is your estimate of Luxury’s opportunity cost of capital? How confident of it are you?
Capital Structure
Question 12.1:
Assume the MM no-tax model holds, A firm exists that has 20 percent of its capital structure in the form of debt, which has a cost of 6 percent. Now the firm moves to 60 percent debt in its capital structure, again with a cost of 6 percent. What two effects occur as the firm moves from 20 percent debt to 60 percent debt? How do these effects counterbalance each other?
Question 12.3:
Explain Miller’s personal tax model. Under what circumstances does it lead to the same conclusion as MM without corporate taxes? With corporate taxes?
Problem 12.5: Levered and Unlevered Firms
Graphics Resources is an unlevered firm with an EBIT of $4 million. Its tax rate is 40 percent, and the opportunity cost of equity capital is 15 percent. Assume that the MM tax case holds and that Graphics is fairly valued.
a. What is the market value of Graphics?
b. Suppose that Graphics now issues $10 million of 8 percent bonds. What is the new market value of Graphics?
c. Assume there are two firms, Y and Z, that are identical in all respects to the unlevered Graphics and the levered Graphics, respectively. Explain what will happen if the current market value of Y is $14 million, while that of Z is $23 million.
Problem 12.6: Personal and Corporate Taxes
Debt-Free Co. is an unlevered firm that has an equilibrium market value of $7 million. The firm is contemplating issuing $4 million of 10 percent coupon bonds. The firm has a corporate tax rate of 30 percent and has estimated that the tax rates for its investors are 20 percent on stock income and 25 percent on bond income. Assume that Miler’s personal tax case holds.
a. If only corporate taxes exist, what is the new total value of the firm and gain from leverage?
b. With both corporate and personal taxes, what is the gain from leverage and total value of the firm?
c. Why is the gain from leverage (or, alternatively, the total value of the firm) less in (b) than in (a)?
Cover homework & Review for test
Test
Assignment 5
Capital Budgeting Techniques
Problem 7.1: Payback Versus NPV
Cash flow streams for two mutually exclusive projects are given below.
After-Tax Cash Inflows
Year Project A Project B
1 $300 $600
2 $400 $200
3 $ 50 $100
4 $ 50 $700
Project A requires an initial investment of $600, and project B requires
an initial investment of $1,000.
a. Use the payback period to determine which project should be selected.
b. If the opportunity cost is 8%, determine the net present value for both
projects.
c. Which project should be chosen? What are the drawbacks of the payback
period method?
Problem 7.6: NPV and IRR
Project A and B both require a $20,000 initial investment and have projected cash inflows as follows:
After-Tax Cash Inflows
Year Project A Project B
1 $10,000 $7,000
2 $ 8,000 $7,000
3 $ 6,000 $7,000
4 $ 4,000 $7,000
a. Calculate each project’s net present value if the opportunity cost is 12 percent.
b. Calculate the internal rate of return for each project.
c. Should either project be rejected if they are independent?
d. Which project should be selected if they are mutually exclusive?
Problem 7.8: Conflicting Rankings
Michael’s Costumes is analyzing two mutually exclusive projects. Both require an initial investment of $65,000 and provide cash inflows as follows:
After-Tax Inflows
Year Project C Project D
1 $40,000 0
2 30,000 0
3 20,000 $104,200
a. If the opportunity cost is 10 percent, which product would Michael’s choose if NPV is employed?
b. Calculate the internal rate of return for both projects. Which project should be selected according to IRR? Why does the difference in ranking occur?
Problem 7.10: Unequal Lives
Consider a firm in need of a stamping machine. It can buy a one-speed machine that requires an initial investment of $350 and produces after-tax cash inflows of $300 for each of 2 years, or it can purchase a three-speed machine that costs $1,200 and produces cash inflows of $500 for each of 4 years. Neither machine has any resale value, and the opportunity cost is 16 percent. Which machine should be purchased?