Individual Assignment: Text Problem Sets

Individual Assignment: Text Problem Sets

Complete the following problem sets and show all steps in your work:

Ch 4: Problems A9 & A11 (p. 103)

A9. (Rate of return) After graduation, Adrian moved across the country to Brownville and bought a small house for $208,000. Bill moved to Columbus and bought a house for $195,000. Four years later, they both sold their houses. Adrian netted $256,000 when she sold her house and Bill netted $168,000 on his.

a. What annual rate of return did Adrian realize on her house?

b. What annual rate of return did Bill realize on his house?

Adrian = 48000/208000 = 23.07/4 = 5.77% per year

Bill = -27000/195000 = -13.85/4 =-3.47% per year

A11. (Calculating the PV and FV of an annuity) Assume an ordinary annuity of $500 at the end

of each of the next three years.

a. What is the present value discounted at 10%?

b. Value at the end of year 3 if cash flows can be invested at 10%?

a.  PV= 500 x 2.49 = 1243

b.  FV = 500 x 3.31 = 1655

Ch. 5: Problems A1, A10, A12, A14, B16, B18, & B20 (pp. 134-137)

A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a

required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond?

74 x 6.417 +1000 x .4224 = 897

A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60

next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the

required return on RHM common stock is 10%?

5.6/.04 = 140

A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividend is nongrowing. What is the required return on James River preferred stock?

3.38/45.25 = 7.46%

A14. (Stock valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock outstanding

that pays a $1.00 quarterly dividend and has a required return of 12% APR (3% per quarter).

What is the stock worth?

1/.03 = 33.33

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock

Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue

matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment

was made yesterday.

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.

What is the fair price of each bond now?

c. Suppose that the yield to maturity for all of these bonds changed instantaneously again,

this time to 9%. Now what is the fair price of each bond?

d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same,

higher, or lower for longer- versus shorter-maturity bonds?

a
at 8% / 1 / 7 / 15
Coupon rate / 0.09125 / 0.09125 / 0.09125
0.4218 / 0.7523
0.6367 / 0.3440
fair value / 1.0104 / 1.0586 / 1.0963
b
at 7%
0.4349 / 0.7980
0.6795 / 0.3955
fair value / 1.0199 / 1.1145 / 1.1935
c
At 9% / 0.4093 / 0.7105
0.5969 / 0.3005
fair value / 1.0011 / 1.0063 / 1.0110

d.  The interest rate risk varies with the duration of the bonds, it is more with longer term bond and less with shorter term bond.

B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the

$1,000 principal in 10 years. You pay only $500 for the bond.

a. You receive the coupon payments for three years and the bond defaults. After liquidating

the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5

years. What is the realized return on your investment?

Received for 3 years / 285
after 3.5 years / 150
total / 435
Investment / -500
Loss on investment / -65
total return / -13 / %
Average yearly retrun / -3.71 / %

b. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

Received for 10 years / 950
after 10 years / 1000
total / 1950
investment / -500
Profit / 1450
total return / 290%
Annual return / 29%

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its

common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will

begin paying a $1.00 per share dividend in two years and that the dividend will increase

6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm, is less optimistic.

Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend

will be $1.00, and that it will grow at 4% annually. James and Bret agree that the

required return for Medtrans is 13%.

What value would James estimate for this firm?

Expected value after two year = 1.06/.07 = 15.14 +1 as dividend = 16.14

PV of 16.14/1.13^2 = $12.64 per share the estimated value

What value would Bret assign to the Medtrans stock?

Expected value after two year = 1.04/.09 = 11.56 +1 as dividend = 16.14

PV of 12.56/1.13^4 = $7.70 per share the estimated value

Ch. 7: Problem C1 (p. 184)

C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here.

a. Calculate the expected returns on the stock market and on Chicago Gear stock.

b. What is Chicago Gear’s beta?

c. What is Chicago Gear’s required return according to the CAPM?

Realized Return
State of the Market / Probability that State Occurs / Stock Market / Chicago Gear
Stagnant / 0.20 / 10% / 15%
Slow growth / 0.35 / 10% / 15%
Average growth / 0.30 / 15% / 25%
Rapid growth / 0.15 / 25% / 35%
a / Expected Return
Probability / Stock market / Chicago gear / Stcok / C.G
0.2 / -0.1 / -0.15 / -0.02 / -0.03
0.35 / 0.1 / 0.15 / 0.035 / 0.0525
0.3 / 0.15 / 0.25 / 0.045 / 0.075
0.15 / 0.25 / 0.35 / 0.0375 / 0.0525
1 / 9.75% / 15.00%

B

b / 1 / 2 / 3 / 4 / 5 / 6
x - stock market / chicago / deviation / Deviation / Square / colm 3 x colmn 4
stock / chicago / Colmn 3
1 / -0.1 / -0.15 / -0.2 / -0.3 / 0.04 / 0.06
2 / 0.1 / 0.15 / 0 / 0 / 0 / 0
3 / 0.15 / 0.25 / 0.05 / 0.1 / 0.0025 / 0.005
4 / 0.25 / 0.35 / 0.15 / 0.2 / 0.0225 / 0.03
0.4 / 0.6 / 0 / 0 / 0.065 / 0.095
mean = / 0.10 / 0.15
Beta = .095/.065 = / 1.462

C

.06+ 1.46 x .0975-.06 = .06+.05475 = 11.475%