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Chapter 19

Questions and Problems

Discussion Questions

19-1.

What are the basic advantages to the corporation of issuing convertible securities? 

 

 

19-2.

Why are investors willing to pay a premium over the theoretical value (pure bond value or conversion value)? 

 

 

19-3.

Why is it said that convertible securities have a floor price? 

 

 

19-4.

The price of Gordon Corporation 5 ? 2018 convertible bonds is $1,390. For the Marshall Corporation, the 6 ? 2017 convertible bonds are selling at $730. 

 

 

19-5.

How can a company force conversion of a convertible bond? 

 

 

19-6.

What is meant by a step-up in the conversion price? 

 

 

19-7.

Explain the difference between basic earnings per share and diluted earnings per share. 

 

 

19-8.

Explain how convertible bonds and warrants are similar and different. 

 

 

19-9.

Explain why warrants are issued. (Why are they used in corporate finance?) 

 

 

19-10.

What are the reasons that warrants often sell above their intrinsic value? 

 

 

19-11.

What is the differences between a call option and a put option? 

 

 

19-12.

Suggest two areas where the use of futures contracts are most common. What percent of the value of the underlying security is typical in a futures contract? 

 

 

19-13.

You buy a stock option with an exercise price of $50. The cost of the option is $3. If the stock ends up at $55, indicate whether you have a profit or loss with a call option? With a put option? 

Problems

19-1.

National Motors, Inc., has warrants outstanding that allow the holder to purchase 1.5 shares of stock per warrant at $28 per share (exercise price). Thus, each individual share can be purchased at $28 under the warrant. 

The common stock is currently selling for $35. The warrant is selling for $14. 

a.   What is the intrinsic (minimum) value of this warrant?

b.   What is the speculative premium on this warrant?

c.   What should happen to the speculative premium as the expiration date approaches? 

(Assume all bonds in the following problems have a par value of $1,000.) 

 

 

19-2.

DNA Labs, Inc., has a $1,000 convertible bond outstanding that can be converted into 40 shares of common stock. The common stock is currently selling for $26.75 a share and the convertible bond is selling for $1,118.50. 

a.   What is the conversion value of the bond?

b.   What is the conversion premium?

c.   What is the conversion price? 

 

 

19-3.

The bonds of Stein Co. have a conversion premium of $35. Their conversion price is $20. The common stock price is $18.50. What is the price of the convertible bonds? 

 

 

19-4.

Sherwood Forest Products has a convertible bond quoted on the NYSE bond market at 95. (Bond quotes represent percentage of par value. Thus, 70 represents $700, 80 represents $800, and so on.) It matures in 10 years and carries a coupon rate of 6 ? percent. The conversion ratio is 25, and the common stock is currently selling for $35 per share on the NYSE. 

a.   Compute the conversion premium.

b.   At what price does the common stock need to sell for the conversion value to be equal to the current bond price? 

 

 

19-5.

Pittsburgh Steel Company has a convertible bond outstanding, trading in the marketplace at $930. The par value is $1,000, the coupon rate is 8 percent, and the bond matures in 25 years. The conversion price is $50 and the company's common stock is selling for $44 per share. Interest is paid semiannually.

a.   What is the conversion value?

b.   If similar bonds, which are not convertible, are currently yielding 10 percent, what is the pure bond value of this convertible bond? (Use semiannual analysis as described in Chapter 10.) 

 

 

19-6.

In problem 5, if the interest rate on similar bonds, which are not convertible, goes up from 10 percent to 12 percent, what will be the new pure bond value of the Pittsburgh Steel Company bonds? Assume the Pittsburgh Steel Company bonds have the same coupon rate of 8 percent as described in problem 5 and that 25 years remain to maturity. Use semiannual analysis. 

 

 

19-7.

The Olsen Mining Company has been very successful in the last five years. Its $1,000 par value convertible bonds have a conversion ratio of 32. The bonds have a quoted interest rate of 5 percent a year. The firm's common stock is currently selling for $39.50 per share. The current bond price has a conversion premium of $10 over the conversion value. 

a.   What is the current price of the bond?

b.   What is the current yield on the bond (annual interest divided by the bond's market price)?

c.   If the common stock price goes down to $21.50 and the conversion premium goes up to $100, what will be the new current yield on the bond? 

 

 

19-8.

Standard Olive Company of California has a convertible bond outstanding with a coupon rate of 9 percent and a maturity date of 15 years. It is rated Aa, and competitive, nonconvertible bonds of the same risk class carry a 10 percent return. The conversion ratio is 25. Currently the common stock is selling for $30 per share on the New York Stock Exchange. 

a.   What is the conversion price?

b.   What is the conversion value?

c.   Compute the pure bond value. (Use semiannual analysis.)

d.   Draw a graph that includes the pure bond value and the conversion value but not the convertible bond price. For the stock price on the horizontal axis, use 10, 20, 30, 40, 50, and 60.

e.   Which will influence the bond price more—the pure bond value or the conversion value? 

 

19-9.

Swift Shoe Co. has convertible bonds outstanding that are callable at $1,080. The bonds are convertible into 22 shares of common stock. The stock is currently selling for $59.25 per share. 

a.   If the firm announces it is going to call the bonds at $1,080, what action are bondholders likely to take, and why?

b.   Assume that instead of the call feature, the firm has the right to drop the conversion ratio from 22 down to 20 after 5 years and down to 18 after 10 years. If the bonds have been outstanding for 4 years and 11 months, what will the price of the bonds be if the stock price is $60? Assume the bonds carry no conversion premium.

c.   Further assume that you anticipate in two months that the common stock price will be up to $63.50. Considering the conversion feature, should you convert now or continue to hold the bond for at least two more months? 

 

 

19-10.

Vernon Glass Company has $20 million in 10 percent convertible bonds outstanding. The conversion ratio is 50, the stock price is $19, and the bond matures in 10 years. The bonds are currently selling at a conversion premium of $70 over their conversion value.

 

If the price of the common stock rises to $25 on this date next year, what would your rate of return be if you bought a convertible bond today and sold it in one year? Assume on this date next year, the conversion premium has shrunk from $70 to $15.

 

 

19-11.

Assume you can buy a warrant for $5 that gives you the option to buy one share of common stock at $15 per share. The stock is currently selling at $18 per share.

a.   What is the intrinsic value of the warrant?

b.   What is the speculative premium on the warrant?

c.   If the stock rises to $27 per share and the warrant sells at its theoretical value without a premium, what will be the percentage increase in the stock price and the warrant price if you bought the stock and the warrant at the prices stated above? Explain this relationship. 

 

 

19-12.

The Gifford Investment Company bought 100 Cable Corporation warrants one year ago and would like to exercise them today. The warrants were purchase at $30 each, and they expire when trading ends today. (Assume there is no speculative premium left.) Cable Corp. common stock is selling today for $60 per share. The exercise price is $36, and each warrant entitles the holder to purchase two shares of stock, each at the exercise price. 

a.   If the warrants are exercised today, what would Gifford's total profit or loss be?

b.   What is Gifford's percentage rate of return? 

 

 

19-13.

Assume in problem 12 that Cable Corporation common stock was selling for $50 per share when Gifford Investment Company bought the warrants. 

a.   What was the intrinsic value of a warrant at that time?

b.   What was the speculative premium per warrant when the warrants were purchased? The purchase price, as indicated above, was $30.

c.   What would Gifford's total dollar profit or loss have been had they invested the $3,000 directly in Cable Corporation's common stock one year ago at $50 per share? Recall the current value is $60 per share.

d.   What would the percentage rate of return be on this common stock investment? Compare this to the rate of return on the warrant computed in problem 12b. 

 

 

19-14.

Mr. John Hailey has $1,000 to invest in the market. He is considering the purchase of 50 shares of Comet Airlines at $20 per share. His broker suggests that he may wish to consider purchasing warrants instead. The warrants are selling for $5, and each warrant allows him to purchase one share of Comet Airlines common stock at $18 per share. 

a.   How many warrants can Mr. Hailey purchase for the same $1,000?

b.   If the price of the stock goes to $30, what would be his total dollar and percentage return on the stock?

c.   At the time the stock goes to $30, the speculative premium on the warrant goes to 0 (though the market value of the warrant goes up). 

      What would be Mr. Hailey's total dollar and percentage return on the warrant?

d.   Assuming that the speculative premium remains $3.50 over the intrinsic value, how far would the price of the stock have to fall before the warrant has no value? 

 

19-15.

Online Network, Inc. has had a net income of $600,000 in the current fiscal year. There are 100,000 shares of common stock outstanding along with convertible bonds, which have a total face value of $1.4 million. The $1.4 million is represented by 1,400 different $1,000 bonds. Each $1,000 bond pays 5 percent interest. The conversion ratio is 20. The firm is in a 30 percent tax bracket. 

a.   Calculate basic earnings per share.

b.   Calculate diluted earnings per share. 

 

 

19-16.

Myers Drugs, Inc. has 2 million shares of stock outstanding. Earnings after taxes are $6 million. Myers also have warrants outstanding, which allow the holder to buy 100,000 shares of stock at $15 per share. The stock is currently selling for $50 per share. 

a.   Compute basic earnings per share.

b.   Compute diluted earnings per share considering the possible impact of the warrants. Use the formula: 

 

 

19-17.

Tulsa Drilling Company has $1 million in 11 percent convertible bonds outstanding. Each bond has a $1,000 par value. The conversion ratio is 40, the stock price is $32, and the bonds mature in 10 years. The bonds are currently selling at a conversion premium of $70 over the conversion value. 

a.   If the price of Tulsa Drilling Company common stock rises to $42 on this date next year, what would your rate of return be if you bought a convertible bond today and sold it in one year? Assume that n this date next year, the conversion premium has shrunk from $70 to $20.

b.   Assume the yield on similar nonconvertible bonds has fallen to 8 percent at the time of sale. What would the pure bond value be at that point? (Use semiannual analysis.) Would the pure bond value have a significant effect on valuation then? 

 

Comprehensive Problems

CP 19-1.

Fondren Exploration, Ltd., has 1,000 convertible bonds ($1,000 par value) outstanding, each of which may be converted to 50 shares. The $1 million worth of bonds has 25 years to maturity. The current price of the stock is $26 per share. The firm's net income in the most recent fiscal year was $270,000. The bonds pay 12 percent interest. The corporation has 150,000 shares of common stock outstanding. Current market rates on long-term nonconvertible bonds of equal quality are 14 percent. A 35 percent tax rate is assumed. 

a.   Compute diluted earnings per share.

b.   Assume the bonds currently sell at a 5 percent conversion premium over straight conversion value (based on a stock price of $26). However, as the price of the stock increases from $26 to $37 due to new events, there will be an increase in the bond price, but the conversion premium will be zero. Under these circumstances, determine the rate of return on a convertible bond investment that is part of this price change, based on the appreciation in value.

c.   Now assume the stock price is $16 per share because a competitor introduced a new product. Would the straight conversion value be greater than the pure bond value, based on the interest rates stated above? (See Table 16-3 in Chapter 16 to get the bond value without having to go through the actual computation.)

d.   Referring to part c, if the convertible traded at a 15 percent premium over the straight conversion value, would the convertible be priced above the pure bond value?

e.   If long-term interest rates in the market go down to 10 percent while the stock price is at $23, with a 6 percent conversion premium, what would the difference be between the market price of the convertible bond and the pure bond value? Assume 25 years to maturity, and once again use Table 16-3 for part of your answer.

f.    If Fondren were able to retire the convertibles and replace them with 50,000 shares of common stock selling at $26 per share and paying a 5 percent dividend yield (dividend to price ratio), would the aftertax cash outflow related to the original convertibles be greater or less than the cash outflow related to the stock? 

 

 

CP 19-2.

United Technology Corporation (UTC) has $40 million of convertible bonds outstanding (40,000 bonds at $1,000 par value) with a coupon rate of 11 percent. Interest rates are currently 8 percent for bond of equal risk. The bonds have 15 years left to maturity. The bonds may be called at a 9 percent premium over par. They are convertible into 30 shares of common stock. The tax rate for the company is 25 percent. 

The firm's common stock is currently selling for $41 and it pays a dividend of $3.50 per share. The expected income for the company is $38 million with 6 million shares outstanding. 

Thoroughly analyze the bond and determine whether the firm should call the bond at the 9 percent call premium. In your analysis, consider the following: 
a.   The impact of the call on base and diluted earnings per share (assume the call forces conversion).

b.   The consequences of your decision on financing flexibility.

c.   The net change in cash outflows to the company as a result of the call and conversion.