# FIN Exercises 19-3, 19-4, 19-5 and 19-7

19-3 Maese Industries Inc. has warrants outstanding that permit the holders to purchase 1 share of stock per warrant at a price of \$28.50.
a. Calculate the exercise value of the firm’s warrants if the common sells at each of the following prices: (1) \$20, (2) \$25, (3) \$30, (4) \$100. (Hint: A warrant’s exercise value is the difference between the stock price and the purchase price specified by the warrant if the warrant were to be exercised.)
b. Assume the firm’s stock now sells for \$20 per share. The company wants to sell some 20-year, \$1,000 par value bonds with interest paid annually. Each bond will have attached 50 warrants, each exercisable into 1 share of stock at an exercise price of \$28.50. The firm’s straight bonds yield 11%. Assume that each warrant will have a market value of \$3 when the stock sells at \$20. What coupon interest rate, and dollar coupon, must the company set on the bonds with warrants if they are to clear the market? (Hint: The convertible bond should have an initial price of \$1,000.)

19-4 The Tsetsekos Company was planning to finance an expansion. The principal executives of the company all agreed that an industrial company such as theirs should finance growth by means of common stock rather than by debt. However, they felt that the current \$42 per share price of the company’s common stock did not reflect its true worth, so they decided to sell a convertible security. They considered a convertible debenture but feared the burden of fixed interest charges if the common stock did not rise enough in price to make conversion attractive. They decided on an issue of convertible preferred stock, which would pay a dividend of \$2.10 per share.
a. The conversion ratio will be 1.0; that is, each share of convertible preferred can be converted into a single share of common. Therefore, the convertible’s par value (and also the issue price) will be equal to the conversion price, which in turn will be determined as a premium (i.e., the percentage by which the conversion price exceeds the stock price) over the current market price of the common stock. What will the conversion price be if it is set at a 18% premium? At a 23% premium?
b. Should the preferred stock include a call provision? Why?

19-5 Fifteen years ago, Roop Industries sold \$400 million of convertible bonds. The bonds had a 40-year maturity, a 5.75% coupon rate, and paid interest annually. They were sold at their \$1,000 par value. The conversion price was set at \$55.00, and the common stock price was \$55 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.75% at the time Roop’s bonds were issued.
a. Calculate the premium on the bonds—that is, the percentage excess of the conversion price over the stock price at the time of issue.
b. What is Roop’s annual before-tax interest savings on the convertible issue versus a straight-debt issue?
c. At the time the bonds were issued, what was the value per bond of the conversion feature?
d. Suppose the price of Roop’s common stock fell from \$55 on the day the bonds were issued to \$45.00 now, 15 years after the issue date (also assume the stock price never exceeded \$55.00). Assume interest rates remained constant. What is the current price of the straight-bond portion of the convertible bond? What is the current value if a bondholder converts a bond? Do you think it is likely that the bonds will be converted?
e. The bonds originally sold for \$1,000. If interest rates on A-rated bonds had remained constant at 8.75% and if the stock price had fallen to \$45.00, then what do you think would have happened to the price of the convertible bonds? (Assume no change in the standard deviation of stock returns.)
f. Now suppose that the price of Roop’s common stock had fallen from \$55 on the day the bonds were issued to \$45.00 at present, 15 years after the issue. Suppose also that the interest rate on similar straight debt had fallen from 8.75% to 7.75%. Under these conditions, what is the current price of the straight-bond portion of the convertible bond? What is the current value if a bondholder converts a bond? What do you think would have happened to the price of the bonds?

19-7 Niendorf Incorporated needs to raise \$35 million to construct production facilities for a new type of USB memory device. The firm’s straight nonconvertible debentures currently yield 10%. Its stock sells for \$27 per share, has an expected constant growth rate of 5%, and has an expected dividend yield of 6%, for a total expected return on equity of 12%. Investment bankers have tentatively proposed that the firm raise the \$25 million by issuing convertible debentures. These convertibles would have a \$1,000 par value, carry a coupon rate of 8%, have a 20-year maturity, and be convertible into 35 shares of stock. Coupon payments would be made annually. The bonds would be noncallable for 5 years, after which they would be callable at a price of \$1,075; this call price would decline by \$5 per year in Year 6 and each year thereafter. For simplicity, assume that the bonds may be called or converted only at the end of a year, immediately after the coupon and dividend payments. Also assume that management would call eligible bonds if the conversion value exceeded 20% of par value (not 20% of call price).
a. At what year do you expect the bonds will be forced into conversion with a call? What is the bond’s value in conversion when it is converted at this time? What is the cash flow to the bondholder when it is converted at this time? (Hint: The cash flow includes the conversion value and the coupon payment, because the conversion occurs immediately after the coupon is paid.)
b. What is the expected rate of return (i.e., the before-tax component cost) on the proposed convertible issue?