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# Valuation

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Valuation Basics

1. A best selling author decides to cash in on her latest novel by selling the rights to the book's royalties for the next four years to an investor. Royalty payments arrive once per year, starting one year from now. In the first year, the author expects \$400,000 in royalties, followed by \$300,000, then \$100,000 then \$10,000 in the three subsequent years. If the investor purchasing the rights to royalties requires a return of 7 percent per year, what should the investor pay?

Bond Prices and Interest Rates

12. Bennifer Jewelers recently issued ten-year bonds that make annual interest payments of \$50. Suppose you purchased one of these bonds at par value when it was issued. Right away, market interest rates jumped, and the YTM on your bond rose to 6 percent. What happened to the price of your bond?

The Essential Features of Preferred and Common Stock

1. The equity section of the balance sheet for Hilton Web-Cams looks like this:
Common Stock, \$0.25 par \$400,000
Paid-in capital in excess of par \$4,500,000
Retained earnings \$1,100,000

a. How many shares has the company issued?
b. What is the book value per share?
c. Suppose that Hilton Web-Cams has made only one offering of common stock. At what price did it sell shares to the market?

Primary Markets and Issuing New Securities

3. Owners of the Internet bargain site FROOGLE.com have decided to take their company public by conducting an initial public offering of common stock. They have agreed with their investment banker to sell 3.3 million shares to investors at an offer price of \$14 per share. The underwriting spread is 7 percent.

a. What is the net price that FROOGLE.com will receive for its shares?
b. How much money will FROOGLE.com raise in the offering?
c. How much do FROOGLE.com's investment bankers make on this transaction?

Stock Valuation

6. Argaiv Towers has outstanding an issue of preferred stock with a par value of \$100. It pays an annual dividend equal to 8 percent of par value. If the required return on Argaiv preferred stock is 6 percent, and if Argaiv pays its next dividend in one year, what is the market price of the preferred stock today?

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#### Solution Preview

Please see the attached file.

Valuation Basics

1. A best selling author decides to cash in on her latest novel by selling the rights to the book's royalties for the next four years to an investor. Royalty payments arrive once per year, starting one year from now. In the first year, the author expects \$400,000 in royalties, followed by \$300,000, then \$100,000 then \$10,000 in the three subsequent years. If the investor purchasing the rights to royalties requires a return of 7 percent per year, what should the investor pay?

What the investor should pay is the present value of royalty payments. The discounting rate is given as 7%. We get
Year Royalty Payment (1) Discounting Factor (2) Present Value (1X2)
1 400,000 0.9346 373,832
2 300,000 0.8734 262,032
3 100,000 0.8163 81,630
4 10,000 0.7629 7,629
5 10,000 0.7130 7,130
6 10,000 0.6663 6,663
Total present ...

#### Solution Summary

The solution explains various questions relating to stock and bond valuation

\$2.19

## Finance: Bond Valuation, Dividend Discount Model, Return on Preferred Stock, Valuation, Risk

A 1: (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?

A 2: (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%?

A 3: (Required return for a preferred stock) James River \$3.38 preferred is selling for \$45.25. The preferred dividend is non growing. What is the required return on James River preferred stock?

A 4: (Stock valuation) Suppose Toyota has non maturing (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?

B 16: (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.
1. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
2. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now?
3. 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?
4. 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?

B 18: (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.
1. 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?
2. 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?

B 20: (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%.
1. What value would James estimate for this firm?
2. What value would Bret assign to the Medtrans stock?

Problem: (Beta and required return) The risk less return is currently 6%, and Chicago Gear has estimated the contingent returns given here.
1. Calculate the expected returns on the stock market and on Chicago Gear stock.
2. What is Chicago Gear's beta?
3. 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

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