Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

63 485 chapter 24 b 486 the value of a single warrant

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Unformatted text preview: profit by purchasing the warrant, exercising it immediately, and selling the stock. Here, the warrant holder pays less than $18 while receiving the $18 difference between the price of three shares and the exercise price. 480 CHAPTER 24 B-481 6. Since a convertible bond gives its holder the right to a fixed payment plus the right to convert, it must be worth at least as much as its straight value. Therefore, if the market value of a convertible bond is less than its straight value, there is an opportunity to make an arbitrage profit by purchasing the bond and holding it until expiration. In Scenario A, the market value of the convertible bond is $1,000. Since this amount is greater than the convertible’s straight value ($900), Scenario A is feasible. In Scenario B, the market value of the convertible bond is $900. Since this amount is less than the convertible’s straight value ($950), Scenario B is not feasible. a. Using the conversion price, we can determine the conversion ratio, which is: Conversion ratio = $1,000 / $34 Conversion ratio = 29.41 So, each bond can be exchanged for 29.41 shares of stock. This means the conversion price of the bond is: Conversion price = 29.41($29) Conversion price = $852.94 Therefore, the minimum price the bond should sell for is $852.94. Since the bond price is higher than this price, the bond is selling at the straight value, plus a premium for the conversion feature. b. A convertible bond gives its owner the right to convert his bond into a fixed number of shares. The market price of a convertible bond includes a premium over the value of immediate conversion that accounts for the possibility of increases in the price of the firm’s stock before the maturity of the bond. If the stock price rises, a convertible bondholder will convert and receive valuable shares of equity. If the stock price decreases, the convertible bondholder holds the bond and retains his right to a fixed interest and principal payments. 7. 8. You can convert or tender the bond (i.e., surrender the bond in exchange for the call price). If you convert, you get stock worth 21.50 × $52 = $1,118. If you tender, you get $1,100 (110 percent of par). It’s a no-brainer: convert. a. Since the stock price is currently below the exercise price of the warrant, the lower bound on the price of the warrant is zero. If there is only a small probability that the firm’s stock price will rise above the exercise price of the warrant, the warrant has little value. An upper bound on the price of the warrant is $51, the current price of the common stock. One would never pay more than $51 to receive the right to purchase a share of the company’s stock if the firm’s stock were only worth $51. If the stock is trading for $58 per share, the lower bound on the price of the warrant is $3, the difference between the current stock price and the warrant’s exercise price. If warrants were selling for less than this amount, an investor could earn an arbitrage profit by purchasing warrants, exercising them immediately, and selling the stock. As always, the upper bound on the price of a warrant is the current stock price. In this case, one would never pay more than $58 for the right to buy a single share of stock when he could purchase a share outright for $58. 9. b. 481 CHAPTER 24 B-482 Intermediate 10. a. The minimum convertible bond value is the greater of the conversion price or the straight bond price. To find the conversion price of the bond, we need to determine the conversion ratio, which is: Conversion ratio = $1,000 / $130 Conversion ratio = 7.69 So, each bond can be exchanged for 7.69 shares of stock. This means the conversion price of the bond is: Conversion price = 7.69($26) Conversion price = $200 And the straight bond value is: P = $30({1 – [1/(1 + .055)]60 } / .055) + $1,000[1 / (1 + .055)60] P = $563.75 So, the minimum price of the bond is $563.75 b. If the stock price were growing by 13 percent per year forever, each share of its stock would be worth approximately $26(1.13)t after t years. Since each bond is convertible into 7.69 shares, the conversion value of the bond equals ($26)(7.69)(1.13)t after t years. In order to calculate the number of years that it will take for the conversion value to equal $1,100, set up the following equation: ($26)(7.69)(1.13)t = $1,100 t = 13.95 years 11. a. The percentage of the company stock currently owned by the CEO is: Percentage of stock = 750,000 / 5,000,000 Percentage of stock = .1500 or 15.00% b. The conversion price indicates that for every $34 of face value of convertible bonds outstanding, the company will be obligated to issue a new share upon conversion. So, the new number of shares the company must issue will be: New shares issued = $30,000,000 / $34 New shares issued = 882,352.94 So, the new number of shares of company stock outstanding will be: New total shares = 5,000,000 + 882,352.94 New total shares = 5,882,352.94 482 CHAPTER 24 B-483 After the conversion, the percentage of company stock...
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