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# Finance : Bond Returns, Stock Price and Growth Rate

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I would like assistance, solution and answers for the following.

1. Assume that a 15-year, \$1,000 face value bond pays interest of \$37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)

a. \$821.92
b. \$1,207.57
c. \$986.43
d. \$1,120.71
e. \$1,358.24

2. 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. \$7.36
b. \$8.62
c. \$9.89
d. \$10.98
e. \$11.53

3. Grateway Inc. has a weighted average cost of capital of 11.5 percent. Its target capital structure is 55 percent equity and 45 percent debt. The company has sufficient retained earnings to fund the equity portion of its capital budget. The before-tax cost of debt is 9 percent, and the company's tax rate is 30 percent. If the expected dividend next period (D1) and current stock price are \$5 and \$45, respectively, what is the company's growth rate?

a. 2.68%
b. 3.44%
c. 4.64%
d. 6.75%
e. 8.16%

#### Solution Preview

1. Assume that a 15-year, \$1,000 face value bond pays interest of \$37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)
a. \$821.92
b. \$1,207.57
c. \$986.43
d. \$1,120.71
e. \$1,358.24

FV = 1000
Payment (per quarter) = 37.50
Number of quarters = 15 * 4 = 60
Return rate = 12%/4 = 3%
Then PV of payments = PVIFA*Payment = 37.50 * 27.6748 = 1037.81
PV of FV = PVIF * FV = 1000 * 0.1697 = ...

#### Solution Summary

Bond Returns, Stock Price and Growth Rate are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

\$2.19

## Corporate Finance: Bond value, YTM, stock worth, growth rate, interest rate risk, beta

Problems:
Number 1:
(Bond valuation) A \$1,000 face value bond has a remaining maturity of 8 years and a required return of 7%. The bond's coupon rate is 8%.
What is the fair value of this bond?
Number 2
(Yield to maturity) Smith Industries has a 8.0% bond maturing in 12 years. What is the yield to maturity if the current market price of the bond is:
a. \$1,090?
B. \$1,000?
C. \$890?
Number 3
(Stock valuation) Suppose GE has nonmaturing (perpetual) preferred stock outstanding that pays a \$0.50 quarterly dividend and has a required return of 8% APR (2% per quarter). What is the stock worth?
Number 4
(Growth rate) Suppose Cisco has a payout ratio of 45% and an expected return on its future investments of 9%. What is Cisco's expected growth rate?
Number 5
(Cumulative growth rate) Jasper Inc has not paid dividends. They are considering paying a common stock dividend of \$0.75 per share next year.
Analysts indicate the required rate of return is 12% and expect the firm will grow the dividend 5%. What is the value of the firm?
Number 6
(Interest-rate risk) Reliant Energy has many bonds trading on the New York Stock Exchange.

Suppose Reliant's bonds have identical coupon rates of 8.5% but that one issue matures in 3 year, one in 9 years, and the third in 12 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?
Number 7
(Default risk) You buy a very risky bond that promises a 11% coupon and return of the \$1,000 principal in 10 years. You pay only \$750 for the bond.
a. You receive the coupon payments for four years and the bond defaults.
After liquidating the firm, the bondholders receive a distribution of \$250 per bond at the end of 4.5 years. What is the realized return on your investment?
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?

Number 8
Beta and required return
The riskless return is currently 6%, and Jupitaer Co. has estimated the contingent returns given here.
a) Calculate the expected returns on the stock market and on Jupiter Co. stock.
b) What is Jupiter's beta?
c) What is Jupitere's required return according to the CAPM?
Realized Return
State of the market Probability that state occurs stock mkt Jupiter
Stagnant 20% -10% -15%
Slow growth 35% 10% 15%
average growth 30% 15% 25%
rapid growth 15% 25% 35%

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