Unformatted text preview: Chapter 24: Warrants and Convertibles 24.1 a. time. b. a 24.2 a. (Note that some warrants are perpetual.) A convertible is a security, usually a bond, which gives its holder the right, though not the obligation, to exchange the security for common stock at a fixed ratio for specific period. Warrant is a security which gives its holder the right, though not the obligation, to buy common stock from the issuing firm at a fixed price for a given period of If the stock price is below the exercise price, it would be foolish to exercise the warrant. Exercise would require payment of the high exercise price. For that price you would receive a share of stock worth less than what you paid. If you want to own the stock it is cheaper to buy the shares in the market. Thus, the warrant is worthless at expiration; its value is zero. Prior to expiration, the warrant will have value as long as there is some probability that the stock price will rise above the exercise price in the time remaining until expiration. b.If the stock price is above the exercise price, the warrant has a value. That value is the difference between the stock price and the exercise price. If the warrant were priced below [stock price - exercise price], an investor could earn arbitrage profit by acquiring the warrant for less than [stock price - exercise price], exercising it for exercise price, and immediately selling the stock for stock price. c. Even when the exercise price is zero, if the warrant is priced above the stock price, it would be cheaper to purchase the stock than to exercise the warrant. The primary difference between warrants and calls is that the firm issues warrants while calls are issued between individuals. The implication of the difference is that when a call is exercised, the number of shares outstanding does not change. There is simply a transfer of the shares between different parties. Also, when the call is exercised, the firm receives no additional funds. Neither of these facts is true about warrants. When a warrant is exercised, the number of outstanding shares increases by one. This effect is called dilution. The firm also receives the exercise price of the warrant. Before the warrant is sold, the price of GR stock is the value of its assets, seven ounces of platinum, divided by the two shares outstanding. (7 $500) / 2 = $1,750 Mrs. Fiske will exercise when the price of a share of GR Company reaches the exercise price of the warrant, $1,800. Solve for the price of platinum. (7 Price of platinum) / 2 = $1,800 Price of platinum = $514.29 i. 7 $520 = $3,640 ii. Mrs. Fiske will exercise her warrant. The new price of GR stock will be the new value of the firm divided by the number of shares outstanding. The number of shares outstanding rose to three when Mrs. Fiske exercised her warrant. There are two ways to compute the value of the firm. Method one: The new value of the firm is the old value plus the exercise price that Mrs. Fiske paid to receive her share of stock. 24.3 a. b. 24.4 a. b. c. iii. Answers to End-of-Chapter Problems B-205 d. e. Value of GR = (7 $520) + $1,800 = $5,440 Thus, the price per share is $1,813.33 [= $5,440 / 3]. Method two: With the $1,800 from Mrs. Fiske, GR Company will buy 3.46154 [= $1,800 / $520] ounces of platinum. The total holdings of platinum by GR Company are 7 + 3.46154 = 10.46154 ounces. After the purchase the value of the firm is 10.46154 $520 = $5,440. Again, the price per share is $1,813.33 [= $5,440 / 3]. iv. Mrs. Fiske's gain is the value of the share she now owns less the exercise price that she paid. Gain = $1,813.33 - $1,800 = $13.33 If Mrs. Fiske had bought a call from Mr. Gould, she would have exercised it when the price of platinum jumped to $520 per ounce. Mrs. Fiske would have received Mr. Gould's share of stock, so the number of shares outstanding would remain unchanged. When platinum is $520 per ounce, the price of GR stock is (7 $520) / 2 = $1,820. Upon exercise of her call, Mrs. Fiske would receive stock worth $1,820 for which she paid $1,800. Thus, her gain would have been $20. The reason the gains are different is that the warrant dilutes the value of the stock. After exercise of a warrant, there are more shareholders making claims against the assets of the firm. Dilution does not occur with the exercise of a call. Lower limit = $0 Upper limit = 0.25 $8 = $2 Lower limit = 0.25 ($12 - $10) = $0.5 Upper limit = 0.25 $12 = $3 24.5 a. b. 24.6 Total value of equity before the exercise = 10 million $17 = $170 million Number of shares being increased = 5 200,000 = 1 million Total value of equity after the exercise = $170 million + 200,000 $15 x 5 = $185 million Thus, stock price after the exercise = $185 million / (10 + 1) million = $16.82 24.7 No, the market price of the warrant will not be zero. Unless the warrant will expire momentarily, the remaining period to expiration has value. If there is a positive probability that the market price of the stock will rise above $21 during the remaining period to expiration, the warrant is still valuable. Thus, the market price of the warrant would be greater than zero. 24.8 Warrant price = [4 million / (4 + 0.5) million] call price = 0.8889 call price d1 = [ln($22 / $20) + (0.05 + 0.005 / 2)] / 0.0050.5 = 2.0904 d2 = 2.0904 - 0.0050.5 = 2.0197 B-206 Answers to End-of-Chapter Problems N(d1) = 0.9817 N(d2) = 0.9783 C = $22 0.9817 - $20 e-0.05 0.9783 = $2.9856 Thus, warrant price = 0.8889 $2.9856 = $2.654 24.9 #sh = 1.5 million #w = 100,000 5 = 0.5 million #sh / (#sh + #w) = 1.5 / (1.5 + 0.5) = 0.75 Therefore, warrant price = $4.70 0.75 = $3.525 a. b. 24.11 Minimum value of warrant X = 3 ($30 - $20) = $30 Minimum value of warrant Y = 2 ($40 - $30) = $20 24.10 B is more likely. Convertible bond price is the maximum of straight bond value and the conversion value. Bond A's conversion value = $1,000 > Bond A's offering price. This is not feasible. a. Conversion value: Conversion ratio = $1,000 / $25 = 40 Conversion value = 40 $24 = $960 Straight bond value < $950. Therefore, minimum value = conversion value = $960 Since the bond is not callable, the option of being able to wait to convert the bond has value. Bondholders can wait until it is most advantageous to convert their bonds without the fear that the firm will call the bonds. That feature has value and will account for the premium of the market value of the convertible debenture over its conversion value. 24.12 b. 24.13 Ownership before the call = 500,000 / 4,000,000 = 0.125 = 12.5% Total number of shares outstanding after the call: 4 million + ($1,000 / $20) ($20 million / $1,000) = 5 million Therefore, ownership after the call = 500,000 / 5,000,000 = 0.10 = 10% Her ownership dropped from 12.5% to 10%. The conversion ratio is the number of shares a bondholder receives if he converts. For the Ryan bonds, that is 28. The conversion price is the face value, $1,000, divided by the conversion ratio. It is $35.71. The conversion premium is the conversion price divided by the stock price minus one. For Ryan it is $35.71 / $31.25 - 1 = 0.1427 = 14.27%. The conversion ratio is unchanged when the bond price changes. It is still 28.
B-207 24.14 a. i. ii. iii. b. i. Answers to End-of-Chapter Problems ii. iii. c. d. The conversion price is only meaningful if the bond is selling at par. Since this bond no longer is selling at par, this price is meaningless. The conversion premium is only meaningful if the bond is selling at par. Since this bond no longer is selling at par, this price is meaningless. The conversion value is the conversion ratio times the current stock price. 28 $31.25 = $875. There are two ways to find the new conversion value. Method one: Multiply the new price by the conversion ratio. 28 $33.25 = $931. Method two: The conversion ratio tells you how much the conversion value will increase for every $1 increase in the price of the stock. Since the price two dollars, the conversion value should rise by $56 [= $2 28]. The new price is then $931 [= $875 + $56]. increased 24.15 a. b. c. Straight bond value = $1,000 / 1.110 = $385.54 Conversion value = 25 $12 = $300 Option value = $400 - $385.54 = $14.46 24.16 The conversion value is ($1,000 / $180) $60 = $333.33 24.17 a.
b. c. Straight Bond value = $60 0.10 +
30 (1 + 0.10) 30 $1,000 = $622.92 $1,000 $35 = $280 Conversion value = $125 35 (1 + 15%)t = $1,100 t = 24.67 years, other things being equal, it's about 25 years. If the conversion value exceeds 1,100 then, it will be called. B-208 Answers to End-of-Chapter Problems ...
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