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Chapter 4: Q10-1BP (page 321)

The Lone Star Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is

a.6 percent.

b.9 percent.

c.13 percent.

Short Answer

Expert verified

a.$1,459

b.$1,090.90

c.$789.50

Step by step solution

01

Definition of Bonds

Bonds are defined as securities issued by a business that requires regular interest payment to its holder. These are debt securities and offer regular income to its holder.

02

Present value of bond under first case – 6% yield to maturity

Presentvalueofbond=CouponAmount脳1-11+YieldrateNumverofyearsYieldrate+Amount脳11+YieldrateNumverofyears=$100脳1-11+0.06200.06+$1000脳11+0.0620=$1,147+$312=$1,459

03

Present value of bond under the second case – 9% yield to maturity

Presentvalueofbond=CouponAmount脳1-11+YieldrateNumverofyearsYieldrate+Amount脳11+YieldrateNumverofyears=$100脳1-11+0.09200.09+$1000脳11+0.0920=$912.9+$178=$1,090.90

04

Present value of bond under the third case – 13% yield to maturity

Presentvalueofbond=CouponAmount脳1-11+YieldrateNumverofyearsYieldrate+Amount脳11+YieldrateNumverofyears=$100脳1-11+0.13200.13+$1000脳11+0.1320=$7,02.5+$87=$789.50

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Question:Stagnant Iron and Steel currently pays a $12.25 annual cash dividend (D0). The company plans to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. If the required rate of return by common stockholders (Ke) is 18 percent, what is the price of the common stock?

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a. What is the value of the stock based on the dividend valuation model (Formula 10-8)?

b. Indicate that the value you computed in part a is correct by showing the value of D1, D2, and D3 and by discounting each back to the present at 14 percent. D1 is \)1.30, and it increases by 10 percent (g) each year. Also discount the anticipated stock price at the end of year three back to the present and add it to the present value of the three dividend payments.

The value of the stock at the end of year three is: P3 5 D4 _____ Ke 2 g D4 5 D3 (1 1 g)

If you have done all these steps correctly, you should get an answer approximately equal to the answer in part a.

c. As an alternative measure, you also examine the value of the firm based on the price-earnings (P/E) ratio times earnings per share. Since the company is privately traded (not in the public stock market), you will get your anticipated P/E ratio by taking the average value of five publiclytraded chemical companies. The P/E ratios were as follows during the time period under analysis:

P/E Ratio

Dow Chemical .................. 15

DuPont ............................. 18

Georgia Gulf ..................... 7

3M .................................... 19

Olin Corp .......................... 21

Assume Dunning Chemical has earnings per share of \(2.10. What is the stock value based on the P/E ratio approach? Multiply the average P/E ratio you computed times earnings per share. How does this value compare to the dividend valuation model values that you computed in parts a and b?

d. If in computing the industry average P/E, you decide to weight Olin Corp. by 40 percent and the other four firms by 15 percent, what would be the new weighted average industry P/E? (Note: You decided to weight Olin Corp. more heavily because it is similar to Dunning Chemical.) What will the new stock price be? Earnings per share will stay at \)2.10.

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Question:Surgical Supplies Corporation paid a dividend of $1.12 per share over the last 12 months. The dividend is expected to grow at a rate of 2.5 percent over the next three years (supernormal growth). It will then grow at a normal, constant rate of 7 percent for the foreseeable future. The required rate of return is 12 percent (this will also serve as the discount rate).

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