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# CH22 - CHAPTER 22 Warrants and Convertibles Answers to...

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CHAPTER 22 Warrants and Convertibles Answers to Practice Questions 1. a. Later—by exercising now you gain a dividend of \$3, but you give up the interest you could have earned on the exercise price, \$4 (i.e., .10 40). You also give up the option not to own the stock. b. If the dividend is \$5, you pick up \$1 of extra income by exercising, but you would still give up the option. If the stock has low variability, it is unlikely that the share price will change very much. In that case, the income gain may outweigh the loss from shortening the option life. If the stock has high variability, it may be better to keep the option alive because of the higher option value. 2. a. The Moose Stores warrant issue is large, and the dilution adjustment is correspondingly important. Total equity value after issue is V, which is equal to [40 +5] = \$45 million. Thus, V/N is 45. Also, which does not have to be adjusted because there is not debt, and From Appendix Table 6, the Black-Scholes value of a call on shares selling for \$45 would be: and b. The market value of each share of common stock is: 3. a. Suppose the warrants are not exercised before year five. Warrant holders would lose the first four dividends. We recalculate the warrant value as follows: 247 45 . 5 20 . time = = σ 20 . 2 08 . 1 / 30 45 ) ( / 5 = = price Exercise PV N V 57 . 24 \$ 45 546 . ) ( = = Call PV 29 . 12 \$ 2 57 . 24 ) Call ( PV q 1 1 ) Warrant ( V P = = + = 71 . 32 \$ 29 . 12 45 = - 45 . 5 20 . = = time σ

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and The Black-Scholes value of a call on shares selling for \$45 would be: and b. Therefore, the market value of each share of common stock is: The following table shows warrant values assuming (a pre-commitment to) exercise at various dates. Clearly, there is a strong incentive to exercise early. Exercise Year PV (Dividends Lost) PV (Call) PV (Warrant) Stock Price 0 \$0 \$15.0 \$7.5 \$37.5 1 0 17.2 8.6 36.4 2 1.85 17.6 8.8 36.2 3 4.42 17.1 8.5 36.5 4 7.60 15.9 7.9 37.1 5 11.27 14.0 7.0 38.0 4. The cost of extending the warrant life is the same as issuing a new warrant with maturity equal to the time of extension. In essence, the new warrants are given to the old warrant holders at no charge. 5. a. Assume a \$1,000 face value for the bonds. This would allow a bondholder to convert one bond into 40 shares (i.e., 1,000 divided by 25). The conversion value is, therefore, equal to \$1,200 (i.e., 40 times 30). 248 65 . 1 08 . 1 / 30 27 . 11 45 ) price Exercise ( PV ) Dividends ( PV ) N / V ( 5 = - = - 03 . 14 \$ ) 27 . 11 45 ( 416 . ) Call ( PV = - = 2 03 . 14 ) Call ( PV q 1 1 ) Warrant ( PV = + = 02 . 7 \$ ) Warrant ( PV = 98 . 37 \$ 02 . 7 45 = -
b. The convertible would only sell at the conversion value if it were certain to be exercised. You can think of owning the convertible as equivalent to owning 40 shares plus an option to put the shares back to the company in exchange for the value of a bond. The price exceeds the conversion value by the value of this put.

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