Chapter 19: Convertibles, Warrants, and Derivatives
Chapter 19
Convertibles, Warrants, and Derivatives
Discussion Questions
19-1.
What are the basic advantages to the corporation of issuing convertible securities?
The advantages to the corporation of a convertible security are:
a. The interest rate is lower than on a straight issue.
b. This type of security may be the only device for allowing a small firm access to the capital markets.
c. The convertible allows the firm to effectively sell stock at a higher price than that possible when the bond was initially issued (but perhaps at a lower price than future price potential might provide).
d. If the bond can be called at a price above its conversion price, the bond will be converted to stock and the debt-to-asset ratio will decline.
Why are investors willing to pay a premium over the theoretical value (pure bond value or conversion value)?
Investors are willing to pay a premium over the theoretical value for a convertible bond issue because of the future prospects for the associated common stock. Thus, if there are many years remaining for the conversion privilege, the investor will be able to receive a reasonably high interest rate and still have the option of converting the convertible bond to common stock if circumstances justify.
Why is it said that convertible securities have a floor price?
The floor price of a convertible is based on the pure bond value associated with the interest payments on the bond as shown in Figure 19-1. Regardless of how low the associated common stock might go, the semiannual interest payments will set a floor price for the bond.
19-2.
19-3.
Chapter 19: Convertibles, Warrants, and Derivatives
19-4.
19-5.
19-6.
19-7.
The price of Haltom Corporation 5? 2024 convertible bonds is $1,380. For the Williams Corporation, the 6? 2024 convertible bonds are selling at $725.
a. Explain what factors might cause their prices to be different from their par value of $1,000.
b. What will happen to each bond’s value if long-term interest rates decline?
Convertible bond pricing
a. Haltom bonds are well above par value because its common stock has
probably increased substantially. In the case of Williams, it is reasonable to assume that its common stock has declined. Also, its interest rate is probably well below the going market rate because of its low bond price.
b. With the Haltom Corporation, there would be little or no impact. It is clearly controlled by its common stock value. With the Williams Corporation, its potential value is somewhat associated with interest rates (rather than just conversion), so it is likely to go up somewhat in value.
How can a company force conversion of a convertible bond?
A firm may force conversion of a bond issue through the use of the call
privilege. If a bond has had a substantial gain in value due to an increase in price of the underlying common stock, the bondholder may prefer to convert to
common stock rather than trade in the bond at some small premium over par as stipulated in a call agreement.
What is meant by a step-up in the conversion price?
A “step-up” in conversion price will increase with the passage of time and likewise the conversion ratio will decline. Before each step-up, there is an inducement for bondholders to convert to common at the more desirable price.
Explain the difference between basic earnings per share and diluted earnings per share.
Basic earnings per share do not consider the potentially dilative effects of convertibles, warrants, and other securities that can generate new shares of
common stock. Diluted earnings per share consider all dilutive effects regardless of their origin.
Chapter 19: Convertibles, Warrants, and Derivatives
19-8.
Explain how convertible bonds and warrants are similar and different.
Convertible bonds and warrants are similar in that they give the security holder a future option on the common stock of the corporation. They are dissimilar in that a convertible bond represents a debt obligation of the firm as well. When it is converted to common stock, corporate debt will actually be reduced and the capitalization of the firm will not increase. A warrant is different in that it is not a valuable instrument on its own merits, and also its exercise will increase the overall capitalization of the firm.
Explain why warrants are issued. (Why are they used in corporate finance?)
Warrants may be used to sweeten a debt offering or as part of a merger offer or a bankruptcy proceeding. They also offer the potential of future cash flow to the corporation if the warrants are used to buy new shares of common stock.
What are the reasons that warrants often sell above their intrinsic value?
Warrants may sell above their intrinsic value because the investor views the associated stock’s prospects optimistically. Also, the longer the time to
expiration, the higher the speculative premium because the possibility of a rising stock price increases. Warrants also allow for the use of leveraged investing.
What are the differences between a call option and a put option?
A call option is an option to buy at a set price for a given period of time, and a put option is an option to sell at a set price for a given period of time.
Suggest two areas where the use of futures contracts is most common. What percent of the value of the underlying security is typical as a down payment in a futures contract?
Futures contracts are most common for commodities and interest rate securities, especially government bonds.
Five percent is a typical down payment (margin) in a futures contract. This
allows the holder of the contract to control an amount of securities 20 times more than the down payment. For this reason, futures contracts have very volatile prices.
19-9.
19-10.
19-11.
19-12.
Chapter 19: Convertibles, Warrants, and Derivatives
19-13.
You buy a stock option with an exercise price of $50. The cost of the option is $4. If the stock ends up at $56, indicate whether you have a profit or loss with a call option? With a put option?
With a call option, you would have a profit of $2. You bought the option for $4 and the market value is $6 over the exercise value. With a put option, you would have a loss. It is worthless to have the right to sell a stock for $50, when the cost of the stock is $56. You would lose your $4 investment.
Chapter 19
Problems
1.
Value of warrants (LO19-4) Preston Toy Co. has warrants outstanding that allow the holder to purchase a share of stock for $22 (exercise price). The common stock is currently selling for $28, while the warrant is selling for $9.25 per share. a. What is the intrinsic (minimum) value of this warrant? b. What is the speculative premium on this warrant?
19-1. Solution:
Preston Toy Company
a.
I = (M – E) × N
Where: I = Intrinsic value of a warrant M = Market value of common stock E = Exercise price of a warrant N = Number of shares each warrant entitles the holder to purchase
I = ($28 – $22) × 1 = $6
b.
S = W – I
Where: S = Speculative premium W = Warrant price I = Intrinsic value
S = $9.25 – $6.00 = $3.25
Chapter 19: Convertibles, Warrants, and Derivatives
2.
Value of warrants (LO19-4) Quantum Inc. has warrants outstanding that allow the holder to purchase 1.5 shares of stock per warrant at $30 per share (exercise price). Thus, each individual share can be purchased at $30 with the warrant. The common stock is currently selling for $36. The warrant is selling for $12.
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?
19-2. Solution:
Quantum Inc.
a.
I = (M – E) × N
Where: I = Intrinsic value of a warrant M = Market value of common stock E = Exercise price of a warrant N = Number of shares each warrant entitles the holder to purchase S = W – I Where
I = ($36 – $30) × 1.5 = $9.00 S = W = I = S =
Speculative premium Warrant price Intrinsic value $12 – $9 = $3.00
b.
c. The speculative premium should decrease and approach $0
as the expiration date nears.
Chapter 19: Convertibles, Warrants, and Derivatives
3.
Breakeven on warrants (LO19-4)The warrants of Integra Life Sciences allow the holder to buy a share of stock at $11.75 and are selling for $2.85. The stock price is currently $8.50. To what price must the stock go for the warrant purchaser to at least be assured of breaking even?
19-3. Solution:
Integra Life Sciences
The stock price must go to $14.60. At that point, the warrant will be worth at least $2.85 ($14.60 – $11.75), which equals the cost of the warrant.
$11.75 + 2.85 $14.60 Exercise price
Speculative premium Breakeven price
4.
Breakeven on warrants (LO19-4) The warrants of Dragon Pet Co. allow the holder to buy a share of stock at $26.20 and are selling for $14.10. The stock price is currently $23.50. To what price must the stock go for the warrant purchaser to at least be assured of breaking even?
19-4. Solution:
Dragon Pet Company
The stock price must go to $40.30. At that point, the warrant will be worth at least the current price of $14.10.
I = (M – E) × N
Where: I = Intrinsic value of a warrant M = Market value of common stock E = Exercise price of a warrant N = Number of shares each warrant entitles the holder to purchase
$14.10 = (M – $26.20) × 1
Chapter 19: Convertibles, Warrants, and Derivatives
5.
M = $40.30
Features of a convertible bond (LO19-1) Plunkett Gym Equipment Inc. has a $1,000 par value convertible bond outstanding that can be converted into 25 shares of common stock. The common stock is currently selling for $34.75 a share, and the convertible bond is selling for $960.
a. What is the conversion value of the bond? b. What is the conversion premium? c. What is the conversion price?
19-5. Solution:
Plunkett Gym Equipment Inc.
a. $34.74 stock price × 25 shares = $868.75
b. $960 bond price – $868.75 conversion value = $91.25
conversion premium c. $1,000/25 conversion ratio = $40 conversion price
(Assume all bonds in the following problems have a par value of $1,000.) 6.
Features of a convertible bond (LO19-1) O’Reilly Moving Company has a $1,000 par value convertible bond outstanding that can be converted into 20 shares of common stock. The common stock is currently selling for $43.10 a share, and the convertible bond is selling for $900.00.
a. What is the conversion value of the bond? b. What is the conversion premium? c. What is the conversion price?
Chapter 19: Convertibles, Warrants, and Derivatives
19-6. Solution:
O’Reilly Moving Company
a. $43.10 stock price × 20 shares = $862.00 Conversion value b.
$900.00 Bond price
– $862.00 Conversion value $ 38.00 Conversion premium
c. $1,000/20 conversion ratio = $50.00 conversion price
7. Price of a convertible bond (LO19-2) The bonds of Goniff Bank & Trust have a
conversion premium of $90. Their conversion price is $20. The common stock price is $16.50. What is the price of the convertible bonds?
19-7. Solution:
Goniff Bank & Trust
The conversion ratio is equal to the par value divided by the conversion price:
Par value/Conversion price = Conversion ratio $1,000/$20 = 50 conversion ratio
Common stock price × Conversion ratio = Conversion value $16.50 × 50 Shares = $825 conversion value Conversion value + Conversion premium = Convertible bond price $825 + $90 = $915
8.
Price of a convertible bond (LO19-2) The bonds of Generic Labs Inc. have a conversion premium of $70. Their conversion price is $25. The common stock price is $22.50. What is the price of the convertible bond?
Chapter 19: Convertibles, Warrants, and Derivatives
19-8. Solution:
Generic Labs Inc.
The conversion ratio is equal to the $1,000 par value divided by the conversion price:
Par value/Conversion price = Conversion ratio $1,000/$25 = 40 conversion ratio
Common stock price × Conversion ratio = Conversion value $22.50 × 40 shares = $900 conversion value
$900 Conversion value + 70 Conversion premium $970 Convertible bond price
9.
Conversion premium for bond (LO19-2) Sherwood Forest Products has a convertible bond quoted on the NYSE bond market at 90. (Bond quotes represent the 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 5? percent. The conversion ratio is 25, and the common stock is currently selling for $33 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?
19-9. Solution:
Sherwood Forest Products
First calculate the bond price = 90% × $1,000 par value
= $900 bond price A. $33 common stock price × 25 shares = $825 conversion value
$900 bond price – $825 = $75 conversion premium
Chapter 19: Convertibles, Warrants, and Derivatives
B. $900 bond price/25 shares = $36.00 stock price where
conversion value and bond price $900 are equal.
10. Conversion value and pure bond value (LO19-1) Reynolds Technology has a convertible
bond outstanding, trading in the marketplace at $835. The par value is $1,000, the coupon rate is 9 percent, and the bond matures in 25 years. The conversion ratio is 20, and the company’s common stock is selling for $41 per share. Interest is paid semiannually. a. What is the conversion value? b. If similar bonds, which are not convertible, are currently yielding 12 percent, what is
the pure bond value of this convertible bond? (Use semiannual analysis as described in Chapter 10.)
19-10. Solution:
Reynolds Technology
a. $41.00 stock price × 20 shares = $820 conversion value b. Pure bond value $763.57 N 50
I/Y 6 PV CPT PV –763.57 PMT 45 FV 1,000 11. Pure bond value and change in interest rates (LO19-3) Pittsburgh Steel Company has a
convertible bond outstanding, trading in the marketplace at $960. The par value is $1,000, the coupon rate is 10 percent, and the bond matures in 20 years. The conversion price is $55 and the company’s common stock is selling for $48 per share. Interest is paid
semiannually. If non-convertible bonds of similar risk are currently yielding 12 percent, what will be the pure bond value of the Pittsburgh Steel Company bonds? (Use semiannual analysis.)
19-11. Solution:
Pittsburgh Steel Company
N 40 Pure bond value $849.54
I/Y 6 PV CPT PV –849.54 PMT 50 FV 1,000 Chapter 19: Convertibles, Warrants, and Derivatives
12. Current yield on a convertible bond (LO19-1) 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 7 percent a year. The firm’s common stock is currently selling for $41.30 per share. The current bond price has a conversion premium of $10 over the conversion value. a. b. c.
19-12. $1,331.60 bond price
What is the current price of the bond? What is the current yield on the bond (annual interest divided by the bond’s market
price)?
If the common stock price goes down to $23.40 and the conversion premium goes up
to $100, what will be the new current yield on the bond?
Solution:
Olsen Mining Company
a. $41.30 stock price × 32 shares =
$1,321.60 conversion value + 10.00 conversion premium b. 7% × $1,000 = $70 annual interest
Annual interest$70Bond price?$1,331.60?5.26%
c. $23.40 stock price × 32 shares = $748.80 conversion value
+100.00 conversion premium $848.80 bond price
Annual interestBond price?$70$848.80?8.25%
Chapter 19: Convertibles, Warrants, and Derivatives
13. Conversion value versus pure bond value (LO19-1) Standard Olive Company of
California has a convertible bond outstanding with a coupon rate of 5 percent and a
maturity date of 20 years. It is rated Aa, and competitive, nonconvertible bonds of the same risk class carry a 10 percent return. The conversion ratio is 15. Currently the common stock is selling for $35 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. Calculate the crossover point at which the pure bond value equals conversion value.
19-13. Solution:
Standard Olive Company of California
a. $1,000 par/15 conversion ratio = $66.67 conversion price b.
c. N 40 $ 35 × 15 $ 525
I/Y 5 Stock price
Conversion ratio Conversion value
PV CPT PV –571.02 PMT 25 FV 1,000 Answer: 571.02
d.
Chapter 19: Convertibles, Warrants, and Derivatives
19-13. (Continued)
e. At a stock price of $35 per share, the price of the bond will
be influenced more by the pure bond value (floor price) of $570.98. If interest rates move up, the pure bond value will fall, and if they move down, the pure bond value will rise. As the stock rises from $35 per share to the crossover point of $38.07 ($570.98/15) the market price of the bond will react directly to stock price changes and the market price of the bond will rise with the stock price. The biggest premium over the pure bond value will occur at $38.07 where the pure bond value equals the conversion value.
14. Call feature with a convertible bond (LO19-1) Defense Systems Inc. has convertible
bonds outstanding that are callable at $1,070.
The bonds are convertible into 33 shares of common stock. The stock is currently selling for $39.25 per share. a. If the firm announces it is going to call the bonds at $1,070, 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 33 down to 30 after 5 years and down to 27 after 10 years. If the bonds have been outstanding for four years and 11 months, what will the price of the bonds be if the stock price is $40? Assume the bonds carry no conversion premium.
c. Further assume that you anticipate that the common stock price will be up to $42.50 in
two months. Considering the conversion feature, should you convert now or continue to hold the bond for at least two more months?
19-14. Solution:
Defense Systems Inc.
a. They will probably convert the bonds to common stock.
With a conversion ratio of 33 shares and a common stock price of $39.25, the value of the converted securities would be $1,295.25. This is substantially above the call value of $1,070. Thus, there is a strong inducement to convert.
Chapter 19: Convertibles, Warrants, and Derivatives
b. Bond price = Stock price × Conversion ratio
$40 × 33 = $1,320
c. Bond price in two months = Stock price × Conversion ratio $42.50 × 30 = $1,275
You should convert now rather than hold on to the bonds for two more months. The overall value will be $45 less at that point in time.
15. Convertible bond and rates of return (LO19-2) Vernon Glass Company has $15 million
in 10 percent convertible bonds outstanding. The conversion ratio is 40, the stock price is $17, and the bond matures in 10 years. The bonds are currently selling at a conversion premium of $45 over their conversion value.
If the price of the common stock rises to $23 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 $45 to $20.
19-15. Solution:
Vernon Glass Company
First, find the price of the convertible bond. The conversion value is $680 ($17 × 40). The conversion value of $680, plus the conversion premium of $45, equals $725, the current market price of the convertible bond.
Next, you find the price of the convertible bond on this day next year.
$23 stock price × 40 conversion ratio = $920 conversion value
$920 conversion value + $20 premium = $940 market value of the convertible bond
Chapter 19: Convertibles, Warrants, and Derivatives
The bond has also paid $100 interest over the year (10% × $1000).
Then determine the rate of return.
($940 – $725 + $100)/$725 = $315/$725 = 43.45%
16. Price appreciation with a warrant (LO19-4) Assume you can buy a warrant for $6 that
gives you the option to buy one share of common stock at $14 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 $29 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 buy the stock and the warrant at the prices stated here? Explain this relationship.
19-16. Solution:
a. ($18 stock price – $14 exercise price) × 1 share per
warrant = $4 intrinsic value b. $6 warrant price – $4 intrinsic value = $2 speculative
premium c. Percentage change if stock is purchased at $18 $29?$18$11??61.11% increase in stock price $18$18
Percentage change if warrant is purchased at $6 New intrinsic value = ($29 – $14) × 1 = $15 $15?$6$9??150% increase in warrant price $6$6
The warrant is leveraged. A movement in the stock price will cause the warrant to rise on a smaller initial investment; therefore, the percentage gain is larger for the warrant than
Chapter 19: Convertibles, Warrants, and Derivatives
for the stock. If there were still time to expiration, the warrant would still have a premium and the increase in price would be even greater.
17. Profit potential with a warrant (LO19-4) The Redford Investment Company bought 100
Cinema Corp. warrants one year ago and would like to exercise them today. The warrants were purchased at $24 each, and they expire when trading ends today (assume there is no speculative premium left). Cinema Corp. common stock is selling today for $50 per share. The exercise price is $30 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 the Redford Investment Company’s
dollar profit or loss be?
b. What is the Redford Investment Company’s percentage rate of return?
19-17. Solution:
The Redford Investment Company
a. Intrinsic value of a warrant = (Market value of common
stock – Exercise price of warrant) × No. of shares each warrant entitles holder to purchase.
($50 – $30) × 2 = $40 intrinsic value $40 × 100 warrants = $4,000 proceeds from sale $24 × 100 warrants = $2,400 purchase price Profit = Proceeds from sale – Purchase price = $4,000 – $2,400 = $1,600
b. $1,600/$2,400 = 66.7% return
18. Comparing returns on warrants and common stock (LO19-4) The Gifford Investment
Company bought 90 Cable Corporation warrants one year ago and would like to exercise them today. The warrants were purchased at $25 each, and they expire when trading ends today. (Assume there is no speculative premium left.) Cable Corporation common stock was selling for $49 per share when Gifford Investment Company bought the warrants. The exercise price is $41, and each warrant entitles the holder to purchase two shares of stock, each at the exercise price. a. What was the intrinsic value of a warrant at that time?
Chapter 19: Convertibles, Warrants, and Derivatives
b. What was the speculative premium per warrant when the warrants were purchased? The purchase price, as indicated earlier, was $25.
c. What would Gifford’s total dollar profit or loss have been had they invested the $2,250 directly in Cable Corporation’s common stock one year ago at $49 per share? Cable Corporation common stock is selling today for $59 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 when the common stock was selling for $59 per share.
19-18. Solution:
Gifford Investment Company (Continued) a. ($49 stock price – $41 exercise price) × 2 shares = $16
intrinsic value b. $25 purchase price – $16 intrinsic value = $9 speculative
premium per warrant c. $2,250 investment / $49 per share = 46 shares
46 shares × ($59 – $49) = $460 d. Intrinsic value of a warrant = (Market value of common stock – Exercise price of warrant) × No. of shares each warrant entitles holder to purchase ($59 - $41) × 2 = $36 intrinsic value
$36 × 90 warrants = $3,240 proceeds from sale $25 × 90 warrants = $2,250 purchase price Profit = Proceeds from sale – Purchase price =$3,240 – $2,250 =$990
$990/$2,250 = 44.00% return
Chapter 19: Convertibles, Warrants, and Derivatives
$460/$2,250 = 20.44% return. This is clearly less than the
44.00% return on the warrant.
19. Return calculations with warrants (LO19-4) 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 $10, 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 $40, what would be his total dollar and percentage
return on the stock?
c. At the time the stock goes to $40, 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 returns 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 from $40 before the warrant has no value?
19-19. Solution:
Comet Airlines
a.
$1,000?100 warrants $10b. $ 40 New price – 20 Old price $ 20 Gain × 50 Shares (if he bought $1,000 worth of stock) $1,000 Total dollar gain
19-19. (Continued)
c. $ 40 Stock price – 18 Exercise price
$20$1,000?100.00% or ?100.00% $20$1,000Chapter 19: Convertibles, Warrants, and Derivatives
$ 22 Intrinsic value (0 speculative premium) $ 22 New price of warrant – 10 Old price of warrant $ 12 Gain × 100 Warrants $1,200 Total dollar gain
$12$1,200?120.00%牋or ?120.00% $10$1,000d. With an $18 exercise price, at a stock price of $14.50, the warrant would have a negative intrinsic value of $3.50. With a speculative premium of only $3.50, the warrant would be worthless. Under the problem as described, the warrant would be worthless at stock values of $14.50 or less.
20. Earnings per share with warrants (LO19-5) Online Network Inc. has a net income of
$650,000 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 $1.6 million. The $1.6 million is represented by 1,600 different $1,000 bonds. Each $1,000 bond pays 6 percent interest. The conversion ratio is 10. The firm is in a 30 percent tax bracket. a. Compute basic earnings per share. b. Compute diluted earnings per share.
19-20. Solution:
Online Network Inc.
a. Basic earnings per share
Earnings$650,000???$6.50 Shares100,000b. Diluted earnings per share
Adjusted earnings after taxes ?Shares outstanding + All convertible securitiesChapter 19: Convertibles, Warrants, and Derivatives
$650,000?$67,200* ?100,000?16,000**$717,200??$6.18 116,000*Interest savings × (1 – Tax rate) = $96,000 (1 – .30)
= $96,000 (.70) = $67,200 in reduced aftertax interest exp. **= 16,000 in additional shares from conversion 1,600 convertible bonds × 10 conversion ratio
21. Earnings per share with convertibles (LO19-5) Myers Drugs Inc. has 1.20 million shares
of stock outstanding. Earnings after taxes are $9 million. Myers also has warrants
outstanding that 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 following formula:
Earnings after taxesShares outstanding + Assumed net increase in shares from the warrants
19-21. Solution:
Myers Drugs Inc.
a. Basic earnings per share
Earnings$9,000,000???$7.50 Shares1,200,000b. Diluted earnings per share
Chapter 19: Convertibles, Warrants, and Derivatives
Earnings after taxes?Shares outstanding + Assumed net increase in shares from the warrants$9,000,000 ?1,200,000?70,000*$9,000,000??$7.09 1,270,000
* 1. New shares created
2. Reduction in shares from cash proceeds
(computed below)
Cash proceeds 100,000 @ $15 = $1,500,000
Current price of stock $50
Assumed reduction in shares outstanding from purchase of shares with cash received
Proceeds = $1,500,000/$50 = 30,000 shares
100,000 30,000
3. Assumed net increase in shares from exercise of warrants
______ 70,000
22. Conversion value and changing pure bond value (LO19-3) Tulsa Drilling Company has
$1.3 million in 12 percent convertible bonds outstanding. Each bond has a $1,000 par value. The conversion ratio is 40, the stock price is $36, and the bonds mature in 10 years. The bonds are currently selling at a conversion premium of $60 over the conversion value. a. Today, one year later, the price of Tulsa Drilling Company common stock has risen to
$46. What would your rate of return be if you had purchased the convertible bond one year ago and sold it today? Assume that on the date of sale, the conversion premium has shrunk from $60 to $10. (Hint: Don’t forget to include the interest payment for the first year)
Chapter 19: Convertibles, Warrants, and Derivatives
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?
19-22. Solution:
Tulsa Drilling Company
a. First find the price of the convertible bond. The conversion
value is $1,440 ($36 × 40). The conversion value, $1,440, plus the $60 premium, equals $1,500, the current market price of the convertible bond.
Next, find the price of the convertible bond one year later
(today).
$46 stock price × 40 shares = $1,840 conversion value $1,840 conversion value + $10 premium = $1,850 market price of the convertible bond
The bond has also paid $120 interest over the year (12% × $1,000)
b.
($1,850 + 120 – $1,500)/$1,500 = $470/$1,500 = 31.33% total return
Pure bond value after one year (nine years remaining). Answer: $1,253.19
N 18 I/Y 4 PV CPT PV –1,253.19 PMT 60 FV 1,000 No, because the pure bond value of $1,253.54 is still well below
the conversion value of $1,840 and the market value of $1,850. It would not have a significant effect on valuation. The stock price is the major factor determining the convertible bond price.
23. Falling stock prices and pure bond value (LO19-3) Manpower Electric Company has
6 percent convertible bonds outstanding. Each bond has a $1,000 par value. The conversion ratio is 20, the stock price $36, and the bonds mature in 16 years.
Chapter 19: Convertibles, Warrants, and Derivatives
a. What is the conversion value of the bond?
b. Assume after one year that the common stock price falls to $30.50. What is the conversion value of the bond?
c. Also assume that after one year interest rates go up to 10 percent on similar bonds. There are 15 years left to maturity. What is the pure value of the bond? Use semiannual analysis.
d. Will the conversion value of the bond (part b) or the pure value of the bond (part c) have a stronger influence on its price in the market?
e. If the bond trades in the market at its pure bond value, what would be the conversion premium (stated as a percentage of the conversion value)?
19-23. Solution:
a. 20 shares × $36 per share = $720 conversion value b. 20 shares × $30.50 per share = $610.00 conversion value c. Pure bond value
Answer: $692.55
N 30 I/Y 5 PV CPT PV –692.55 PMT 30 FV 1,000
d. For the time being, the pure bond value ($692.55) will have
the stronger influence than the stock price. The conversion value of $610.00 is $82.55 less than the pure bond value. As the stock price gets closer to the parity point ($692.55/20 shares) of $34.63, the stock will start to exert more influence than the pure bond value. e. Market price of bond = Pure bond value = $692.55 Conversion value = –610.00 Conversion premium = $ 82.55
$82.55/$610.00= 13.53% conversion premium
Chapter 19: Convertibles, Warrants, and Derivatives
COMPREHENSIVE PROBLEM
Comprehensive Problem 1.
Fondren Exploration Ltd. (rates of return on convertible bond investments) (LO19-1) Fondren Exploration Ltd. has 1,000 convertible bonds ($1,000 par value) outstanding, each of which may be converted to 50 shares of stock. 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 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, and a zero conversion premium. 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 conversion value be greater than the pure bond value, based on the interest rates stated here? (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
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.
CP 19-1. Solution:
Fondren Exploration Limited
a. Diluted earnings per share
Adjusted Shares = 150,000 + 50,000* = 200,000 Adj. Shares
*(1,000 bonds × 50 shares per bond) = 50,000 new shares
Adjusted earnings after taxes = $270,000 actual earnings + ($1,000,000 × .12 coupon rate) × (1 – .35 tax rate) Adj. earnings after taxes = $270,000 actual earnings
Chapter 19: Convertibles, Warrants, and Derivatives
+ ($120,000 × .65) = $ 78,000 aftertax interest savings = $348,000 adj. earnings aftertax
$348,000/200,000 = $1.74 diluted earnings per share b. Current conversion value = 50 × $26 =
Premium Current value
$ 1,300 × 1.05 $ 1,365
Future conversion value = 50 × $37 = $1,850 $1,850?$1,365$485Rate of return???35.53%
$1,365$1,365c. Conversion value = 50 × $16 = $800.00
Pure bond value (see Table 16-3 for 12 percent interest rate
and 14 percent market rate on $862.06 for 25 years) The conversion value is less than the pure bond value ($800 < $862.06).
d. Conversion value × Premium $800 × 1.15 = $920 e.
The convertible would be trading for greater than the pure bond value: ($920 > $862.06). Conversion value = 50 × $23 = Premium (6%) Current value
Pure bond value (10% market value) = Differential
$1,150.00 1.06 $1,219.00 1,182.36 $ 36.64
Chapter 19: Convertibles, Warrants, and Derivatives
Comprehensive Problem 2.
United Technology Corp. (a call decision with convertible bonds) (LO19-1) 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 bonds 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 bonds 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 basic 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.
CP 19-2. Solution:
United Technology Corporation (UTC)
Interest expense 11% × $40 million = $4,400,000 million
Shares created from conversion = 30 × 40,000 bonds = 1,200,000 new shares
Conversion value = 30 shares × $41 per share = $1,230 Call price = $1,000 × 1.09 = $1,090
a. If the bond is called, it will be converted because the conversion value is greater than the call price ($1,230 > $1,090).
The convertibles are not included in basic earnings per share.
We will compute basic EPS before and after the conversion. Basic EPS after the conversion would be the same as diluted EPS before conversion.
Chapter 19: Convertibles, Warrants, and Derivatives
Basic EPS before conversion = NI/Shares outstanding = $38 million/6 million shares = $6.33 Basic EPS after conversion or diluted EPS before conversion
Adjusted earnings after taxes ?Shares outstanding?New shares issued
$38,000,000 + $4,400,000 (1?.25) ?6,000,000 + 1,200,000$38,000,000 + $3,300,000?7,200,000
$41,300,000??$5.747,200,000There is a reduction in basic EPS from $6.33 to $5.74.
b. With the elimination of the convertible bond, UTC has
reduced its debt and increased its equity financing. This provides more flexibility in the way of debt issues for the future. With the current interest rate at 8 percent, UTC
could sell a new issue of straight debt and repurchase shares of common stock in the open market. This would serve the purpose of a partial refunding which would result in a lower outlay for interest and dividends. Flexibility is improved. c. Aftertax dividend expense = 1,200,000 × $3.50 = $4,200,000 Aftertax interest expense = $4,400,000 (1 – .25) = $3,300,000 Aftertax net cash loss $900,000
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