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# Bond and stock valuation models

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Use the following information to answer questions 3 thorough 4: Suppose a company is going to issue new bond which has an 6% coupon, 30-year maturity with par value of \$1000 paying 60 semiannual coupon payments of \$30 each. Assume that the market interest rate for this bond is 6%

a. What is the price of the bond?
b. What would be the price of the bond if the market interest rate were to rise to 10%?

8. Michael Williams Jewelers recently issued a \$1,000 face, 20-year zero-coupon bond for \$225. The initial public offering sold in January 2006. What is the yield to maturity on this bond at issuance?

11. After reading today's copy of The Wall Street Journal, you've observed that the nominal return on a one year Treasury Bill is 4.5%. Assuming an inflation rate of 3.3%, what is the real return on this investment? (Format to 4 decimal places).

12. As you read the bond pages of The Wall Street Journal, you notice a bond selling for \$340 which pays no interest and matures to a value of \$1000 eight years from today. What return would you earn if you bought this bond today and held it to maturity?

13. Kansas Electric Company is going to issue new bond which has an 6% coupon, 30-year maturity with par value of \$1000 paying 60 semiannual coupon payments of \$30 each. Assume that the market interest rate for this bond is 8%. What would be the price of the bond?

Chapter 8

1. You are contemplating buying stock. The current dividend is \$3.50 per year, and the expected dividend growth rate is a constant 4%. You require a rate of return of 9% on this investment. What would you expect to be the price of this stock today?

2. PNC Bank has just issued some new preferred stock. The issue will pay a \$17 annual dividend in perpetuity beginning four years from now. If the market requires a 14% return on this investment, how much does a share of stock cost today?

3. Southern Company is a large Atlanta utility. Its cash dividend for the current year is estimated to be \$1.30/share. Dividends are expected to grow at a 5% rate. If investors require a rate of return of 15% on the stock. What price will they be willing to pay for each share?

4. Records Inc. is a firm that archives computer records of numerous business firms to save them computer space and yet allow easy retrieval. The firm has 1 million common shares outstanding. The growth rate for Records Inc. is 6 percent and analysts expect it to remain constant for the foreseeable future. The current dividend paid was \$0.80. Investors require a 14 percent rate of return. What is the current value or price of Record's stock?

5. Pendulum Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are increasing. As a result, the company's earnings and dividends are declining at the constant rate of 10 percent per year. If the last dividend paid was \$6 and investors' required rate of return was 15 percent, what is the value of Pendulum Mining's stock?

6. Warwick Investments common stock is currently selling for \$66.25 per share. You expect the next dividend to be \$5.30 per share. If the firm has a dividend growth rate of 4%, what is its cost of equity?

#### Solution Preview

Please refer attached file for better clarity of solutions.

Use the following information to answer questions 3 thorough 4: Suppose a company is going to issue new bond which has an 6% coupon, 30-year maturity with par value of \$1000 paying 60 semiannual coupon payments of \$30 each. Assume that the market interest rate for this bond is 6%

a. What is the price of the bond?

Semi Annual Coupon payment=C=1000*6%/2=\$30
Maturity Amount=M=\$1000
Market rate=r=6%/2=3% semi annual
Number of semiannual coupon payments=n=60

Price of bond=C/r*(1-1/(1+r)^n)+M/(1+r)^n
=30/3%*(1-1/(1+3%)^60)+1000/(1+3%)^60
=\$1000

b.What would be the price of the bond if the market interest rate were to rise to 10%?

Semi Annual Coupon payment=C=1000*6%/2=\$30
Maturity Amount=M=\$1000
Market rate=r=10%/2=5% semi annual
Number of semiannual coupon payments=n=60

Price of bond=C/r*(1-1/(1+r)^n)+M/(1+r)^n
=30/5%*(1-1/(1+5%)^60)+1000/(1+5%)^60
=\$621.41

8. Michael Williams Jewelers recently issued a \$1,000 face, 20-year zero-coupon bond for \$225. The initial public offering sold in January 2006. What is the yield to maturity on this bond at issuance?

Maturity Amount=FV=\$1000
Current Price=PV=\$225
Number of periods=n=20
YTM=r=?

We know that
FV=PV*(1+r)^n
1000=225*(1+r)^20
4.4444444 =(1+r)^20
(1+r)=(4.4444444)^(1/20)= 1.077434
r=0.077434=7.74%
Yield to maturity on bond issuance=7.74%

11. After reading today's copy of The Wall Street Journal, you've ...

#### Solution Summary

There are 11 problems. Solution to each problem depicts the step by step method to find out the value of desired parameter.

\$2.19