4200 Example Problems Set 3

Problem Set 3 - FINA 4200 Spring 2013
Due Wednesday February 26th before class
I.

Multiple Choices

Chapter 2
1.
According to the Capital Asset Pricing Model, investors are primarily concerned with portfolio risk, not the isolated risks of individual stocks. Thus, the relevant risk is an individual stock's contribution to the overall riskiness of the portfolio.
a. True
b. False
2.
Diversifiable risk, which is measured by beta, can be lowered by adding more stocks to a portfolio. a. True
b. False
3.

If an investor buys enough stocks, he or she can, through diversification, eliminate all of the non-market risk inherent in owning stocks, but as a general rule it will not be possible to eliminate all market risk.
a. True
b. False

4.

The Y-axis intercept of the SML indicates the return on the individual asset when the realized return on an average stock (beta = 1.0) is zero.
a. True
b. False

5.

Which of the following statements is most correct?
a. Risk refers to the chance that some unfavorable event will occur, and a probability distribution is completely described by a listing of the likelihood of unfavorable events.
b. Portfolio diversification reduces the variability of returns on an individual stock.
c. When company-specific risk has been diversified, the inherent risk that remains is market risk which is constant for all securities in the market.
d. A stock with a beta of -1.0 has zero market risk.
e. The SML relates required returns to firms' market risk. The slope and intercept of this line cannot be controlled by the financial manager.
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6.

Stock A has a beta of 1.5 and Stock B has a beta of 0.5. Which of the following statements must be true about these securities? (Assume the market is in equilibrium.)
a.
b.
c.
d.
e.

7.

When held in isolation, Stock A has greater risk than Stock B.
Stock B would be a more desirable addition to a portfolio than Stock A.
Stock A would be a more desirable addition to a portfolio than Stock B.
The expected return on Stock A will be greater than that on Stock B.
The expected return on Stock B will be greater than that on Stock A.

Which of the following statements is most correct?
a.
b.
c.
d.

The slope of the security market line is beta.
A stock with a negative beta must have a negative required rate of return.
If a stock’s beta doubles its required rate of return must double.
If a stock has a beta equal to 1.0, its required rate of return will be unaffected by changes in the market risk premium.
e. None of the above statements is correct.
8.

Which of the following statements is most correct?
a. Portfolio diversification reduces the variability of the returns on the individual stocks held in the portfolio.
b. If an investor buys enough stocks, he or she can, through diversification, eliminate virtually all of the nonmarket (or company-specific) risk inherent in owning stocks.
Indeed, if the portfolio contained all publicly traded stocks, it would be riskless.
c. The required return on a firm's common stock is determined by its systematic (or market) risk. If the systematic risk is known, and if that risk is expected to remain constant, then no other information is required to specify the firm's required return.
d. A security's beta measures its nondiversifiable (systematic, or market) risk relative to that of an average stock.
e. A stock's beta is less relevant as a measure of risk to an investor with a well-diversified portfolio than to an investor who holds only that one stock.

9.

Which of the following statements is most correct?
a. Market participants are able to eliminate virtually all market risk if they hold a large diversified portfolio of stocks.
b. Market participants are able to eliminate virtually all company- specific risk if they hold a large diversified portfolio of stocks.
c. It is possible to have a situation where the market risk of a single stock is less than that of a well diversified portfolio.
d. Answers a and c are correct.
e. Answers b and c are correct.

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10.

Inflation, recession, and high interest rates are economic events which are characterized as
a.
b.
c.
d.
e.

11.

Assume that the risk-free rate is 5 percent, and that the market risk premium is 7 percent. If a stock has a required rate of return of 13.75 percent, what is its beta?
a.
b.
c.
d.
e.

12.

1.25
1.35
1.37
1.60
1.96

You are holding a stock which has a beta of 2.0 and is currently in equilibrium. The required return on the stock is 15 percent, and the return on the market portfolio is 10 percent. What would be the percentage change in the return on the stock, if the return on the market portfolio increased by 30 percent while the risk-free rate remained unchanged?
a.
b.
c.
d.
e.

13.

Company-specific risk that can be diversified away.
Market risk.
Systematic risk that can be diversified away.
Diversifiable risk.
Unsystematic risk that can be diversified away.

+20%
+30%
+40%
+50%
+60%

A call provision gives bondholders the right to demand, or "call for," repayment of a bond.
Typically, calls are exercised if bond price declines, because when bond price declines the bondholder can replace the old bonds with new bonds through refunding operation.
a. True
b. False

14.

You are considering two bonds. Both are rated double A (AA), both mature in 20 years, both have a 10 percent coupon, and both are offered to you at their $1,000 par value.
However, Bond X has a sinking fund while Bond Y does not. This is probably not an equilibrium situation, as Bond X, which has the sinking fund, would generally be expected to have a higher yield than Bond Y.
a. True
b. False

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15.

You have just noticed in the financial pages of the local newspaper that you can buy a $1,000 par value bond for $800. If the coupon rate is 10 percent, with annual interest payments, and there are 10 years to maturity, you should make the purchase if your required return on investments of this type is 12 percent.
a. True
b. False

16.

A bond with a $100 annual interest payment with five years to maturity (not expected to default) would sell for a premium if interest rates were below 9 percent and would sell for a discount if interest rates were greater than 11 percent.
a. True
b. False

17.

Which of the following statements is most correct?
a. All else equal, if a bond’s yield to maturity increases, its price will fall.
b. All else equal, if a bond’s yield to maturity increases, its current yield will fall.
c. If a bond’s yield to maturity exceeds the coupon rate, the bond will sell at a premium over par.
d. All of the answers above are correct.
e. None of the answers above is correct.

18.

Which of the following statements is most correct?
a. Everything else equal, long-term bonds will have larger maturity risk premium than short-term bonds.
b. If the Federal Reserve unexpectedly announces that it expects inflation to increase, then we would probably observe an immediate increase in bond prices.
c. The total yield on a bond is derived from interest payments and changes in the price of the bond.
d. Statements a and c are correct.
e. All of the statements above are correct.

19.

Assume that you wish to purchase a bond with a 30-year maturity, an annual coupon rate of
10 percent, a face value of $1,000, and semiannual interest payments. If you require a 9 percent yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
a.
b.
c.
d.
e.

$905.35
$1,102.74
$1,103.19
$1,106.76
$1,149.63

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20.

Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
a.
b.
c.
d.
e.

21.

You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000. Unfortunately,
Euler is on the brink of bankruptcy. The creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6 percent, and they will then be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is now 28 percent. What is the present value of each bond?
a.
b.
c.
d.
e.

22.

$538.21
$426.73
$384.84
$266.88
$249.98

Marie Snell recently inherited some bonds (face value $100,000) from her father, and soon thereafter she became engaged to Sam Spade, a University of Florida marketing graduate.
Sam wants Marie to cash in the bonds so the two of them can use the money to "live like royalty" for two years in Monte Carlo. The 2 percent annual coupon bonds mature in exactly twenty years. Interest on these bonds is paid annually on December 31 of each year, and new annual coupon bonds with similar risk and maturity are currently yielding 12 percent. If Marie sells her bonds now and puts the proceeds into an account which pays 10 percent compounded annually, what would be the largest equal annual amounts she could withdraw for two years, beginning today (i.e., two payments, the first payment today and the second payment one year from today)?
a.
b.
c.
d.
e.

23.

$619
$674
$761
$828
$902

$13,255
$29,708
$12,654
$25,305
$14,580

JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds
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that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash?
a.
b.
c.
d.
e.
24.

2,400
2,596
3,000
5,000
4,275

In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures to a market value basis. KJM Corporation's balance sheet as of today, is as follows:
Long-term debt (bonds, at par) $10,000,000
Preferred stock
2,000,000
Common stock ($10 par)
10,000,000
Retained earnings
4,000,000
Total debt and equity
$26,000,000
The bonds have a 4 percent coupon rate, payable semiannually, and a par value of $1,000.
They mature exactly 10 years from today. The yield to maturity is 12 percent, so the bonds now sell below par. What is the current market value of the firm's debt?
a.
b.
c.
d.
e.

25.

A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 15 percent, and if investors require a 19 percent rate of return, what is the price of the stock?
a.
b.
c.
d.
e.

26.

$5,412,000
$5,480,000
$2,531,000
$7,706,000
$7,056,000

$57.50
$62.25
$71.86
$64.00
$44.92

Albright Motors is expected to pay a year-end dividend of $3.00 a share (D1 = $3.00). The stock currently sells for $30 a share. The required (and expected) rate of return on the stock is 16 percent. If the dividend is expected to grow at a constant rate, g, what is g?
a. 13.00%
b. 10.05%
c. 6.00%
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d.
e.
27.

A share of common stock has just paid a dividend of $3.00. If the expected long-run growth rate for this stock is 5 percent, and if investors require an 11 percent rate of return, what is the price of the stock?
a.
b.
c.
d.

28.

5.33%
7.00%

$50.00
$50.50
$52.50
$53.00

The last dividend paid by Klein Company was $1.00. Klein's growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein's required rate of return on equity (rs) is 12 percent. What is the current price of Klein's common stock?
a.
b.
c.
d.
e.

$21.00
$33.33
$42.25
$50.16
$58.75

29.
The last dividend paid by a company was $2.20. Klein's growth rate is expected to be 10 percent for one year, after which dividends are expected to grow at a rate of 6 percent forever. The company’s stockholders require a rate of return on equity (rs) of 11 percent. What is the current price of the stock?
a.
b.
c.
d.
e.
30.

The Jones Company has decided to undertake a large project. Consequently, there is a need for additional funds. The financial manager plans to issue preferred stock with a perpetual annual dividend of $5 per share and a par value of $30. If the required return on this stock is currently 20 percent, what should be the stock's market value?
a.
b.
c.
d.
e.

31.

$44.00
$46.64
$48.40
$48.64
$50.40

$150
$100
$ 50
$ 25
$ 10

Grant Corporation's stock is selling for $40 in the market. The company's beta is 0.8, the market risk premium is 6 percent, and the risk-free rate is 9 percent. The previous dividend

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was $2 (i.e., D0 = $2) and dividends are expected to grow at a constant rate. What is the growth rate for this stock?
a. 5.52%
b. 5.00%
c. 13.80%
d. 8.80%
e. 8.38%
32.

A stock is not expected to pay a dividend over the next four years. Five years from now, the company anticipates that it will establish a dividend of $1.00 per share (i.e., D5 = $1.00).
Once the dividend is established, the market expects that the dividend will grow at a constant rate of 5 percent per year forever. The risk-free rate is 5 percent, the company's beta is 1.2, and the market risk premium is 5 percent. The required rate of return on the company’s stock is expected to remain constant. What is the current stock price?
a.
b.
c.
d.
e.

33.

$ 7.36
$ 8.62
$ 9.89
$10.98
$11.53

R. E. Lee recently took his company public through an initial public offering. He is expanding the business quickly to take advantage of an otherwise unexploited market.
Growth for his company is expected to be 40 percent for the first three years and then he expects it to slow down to a constant 15 percent. The most recent dividend (D0) was $0.75.
Based on the most recent returns, the beta for his company is approximately 1.5. The riskfree rate is 8 percent and the market risk premium is 6 percent. What is the current price of
Lee's stock?
a.
b.
c.
d.
e.

$77.14
$75.17
$67.51
$73.88
$93.20

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34.

ABC Company has been growing at a 10 percent rate, and it just paid a dividend of D0 =
$3.00. Due to a new product, ABC expects to achieve a dramatic increase in its short-run growth rate, to 20 percent annually for the next 2 years. After this time, growth is expected to return to the long-run constant rate of 10 percent. The company's beta is 2.0, the required return on an average stock is 11 percent, and the risk-free rate is 7 percent. What should the dividend yield (D1/P0) be today?
a. 3.93%
b. 4.60%
c. 10.00%
d. 7.54%
e. 2.33%

35.

The before-tax cost of debt, which is lower than the after-tax cost, is used as the component cost of debt for purposes of developing the firm's WACC.
a. True
b. False

36.

In capital budgeting and cost of capital analyses, the firm should always consider retained earnings as the first source of capital, since this is a free source of funding to the firm.
a. True
b. False

37.

Since 70 percent of preferred dividends received by a corporation is excluded from taxable income, the component cost of equity for a company which pays half of its earnings out as common dividends and half as preferred dividends should, theoretically, be
Cost of equity = rs(0.30)(0.50) + rps(1 - T)(0.70)(0.50).
a. True
b. False

38.

The cost of debt, rd, is always less than rs, so rd(1 - T) will certainly be less than rs. Therefore, as long as the firm is not completely debt financed, the weighted average cost of capital will always be greater than rd(1 - T).
a. True
b. False

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39.

Which of the following is not considered a capital component for the purpose of calculating the weighted average cost of capital as it applies to capital budgeting?
a.
b.
c.
d.
e.

40.

Long-term debt.
Common stock.
Accounts payable.
Preferred stock.
All of the above are considered capital components for WACC and capital budgeting purposes. Which of the following statements is most correct?

a. The CAPM approach to estimating a firm's cost of common stock never gives a better estimate than the DCF approach.
b. The CAPM approach is typically used to estimate a firm's cost of preferred stock.
c. The risk premium used in the bond-yield-plus-risk-premium method is the same as the one used in the CAPM method.
d. The DCF method and the CAPM method produce exactly the same estimate for rs.
e. The statements above are all false.
41.

The Global Advertising Company has a marginal tax rate of 40 percent. The last dividend paid by Global was $0.90. Global's common stock is selling for $8.59 per share, and its expected growth rate in earnings and dividends is 5 percent. What is Global's cost of common stock?
a.
b.
c.
d.
e.

12.22%
17.22%
10.33%
9.66%
16.00%

10

42. An analyst has collected the following information regarding Christopher Co.:

43.

The company’s capital structure is 70 percent equity, 30 percent debt.
The yield to maturity on the company’s bonds is 9 percent.
The company’s year-end dividend is forecasted to be $0.80 a share.
The company expects that its dividend will grow at a constant rate of 9 percent a year.
The company’s stock price is $25.
The company’s tax rate is 40 percent.
The company anticipates that it will need to raise new common stock this year. Its investment bankers anticipate that the total flotation cost will equal 10 percent of the amount issued. Assume the company accounts for flotation costs by adjusting the cost of capital. Given this information, calculate the company’s WACC.

a.
b.
c.
d.
e.

10.41%
12.56%
10.78%
13.55%
9.29%

Martin Corporation's common stock is currently selling for $50 per share. The current dividend is $2.00 per share. If dividends are expected to grow at 6 percent per year, then what is the firm's cost of common stock?
a.
b.
c.
d.
e.

44.

•
•
•
•
•
•
•

10.0%
10.2%
10.6%
10.8%
11.0%

A company’s balance sheets show a total of $30 million long-term debt with a coupon rate of 9 percent. The yield to maturity on this debt is 11.11 percent, and the debt has a total current market value of $25 million. The balance sheets also show that that the company has 10 million shares of stock; the total of common stock and retained earnings is $30 million. The current stock price is $7.5 per share. The current return required by stockholders, rS, is 12 percent. The company has a target capital structure of 40 percent debt and 60 percent equity. The tax rate is 40%. What weighted average cost of capital should you use to evaluate potential projects?
a. 8.55%
b. 9.33%
c. 9.36%
d. 9.87%
e. 10.67%

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45.

Johnson Industries finances its projects with 40 percent debt, 10 percent preferred stock, and 50 percent common stock.
•
•
•
•
•
•

The company can issue bonds at a yield to maturity of 8.4 percent.
The cost of preferred stock is 9 percent.
The company's common stock currently sells for $30 a share.
The company's dividend is currently $2.00 a share (D0 = $2.00), and is expected to grow at a constant rate of 6 percent per year.
Assume that the flotation cost on debt and preferred stock is zero, and no new stock will be issued.
The company’s tax rate is 30 percent.

What is the company’s weighted average cost of capital (WACC)?
a. 8.33%
b. 9.32%
c. 9.79%
d. 9.99%
e. 13.15%

II. Essay Questions
BD Chapter 2 Problems (p71), Q2, Q3, Q7, Q11
BD Chapter 4 Problems (p157): Q1, Q7, Q11, Q22 (excluding part d.)
BD Chapter 5 Problems (p196): Q4, Q13
BD Chapter 10 Problems (p395): Q4, Q10, Q12, Q16

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