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# CH23 - CHAPTER 23 Warrants and Convertibles Answers to...

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CHAPTER 23 Warrants and Convertibles Answers to Practice Questions 1. a. Exercise later. By exercising now, you gain a dividend of \$3. However, you forgo the interest you could have earned on the exercise price: (0.10 × \$40) = \$4. Also, by exercising now, you give up the option to own the bond and not own the stock. b. If the dividend is \$5, you pick up \$1 of extra income by exercising, but you 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 relative to the value of the firm, so the dilution adjustment is correspondingly important. Total equity value after the warrant issue (V) is (\$40 million + \$5 million) = \$45 million. Thus, (V/N) = (\$45 million/1 million shares) = 45. P = (V/N) = 45 EX = 30 σ = 0.20 t = 5.0 r f = 0.08 1.5435 ) 5.0 (0.20 1.9907 t σ d d 1.9907 /2 ) 5.0 (0.20 ) 5.0 )]/(0.20 /1.08 log[45/(30 /2 t σ t X)]/σ log[P/PV(E d 1 2 5 1 = × - = - = = × + × = + = N(d 1 ) = N(1.9907) = 0.9767 N(d 2 ) = N(1.5435) = 0.9386 Call value = [N(d 1 ) × P] – [N(d 2 ) × PV(EX)] = [0.9767 × 45] – [0.9386 × (30/1.08 5 )] = \$24.79 b. The market value of each share of common stock is: (\$45 - \$12.395) = \$32.605 212 \$12.395 2 \$24.79 value) (Call q 1 1 value Warrant = = × + =

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3. a. An approximate solution can be derived here by assuming that the warrant holder pre-commits to exercising at a specified future date. For example, suppose the warrants are not exercised before year five. Warrant holders would then lose the first four dividends. We recalculate the warrant value as follows: P = (V/N) – PV(dividends) = 45 – 11.27 = 33.73 EX = 30 σ = 0.20 t = 5.0 r f = 0.08 .8989 ) 5.0 (0.20 1.3461 t σ d d 1.3461 /2 ) 5.0 (0.20 ) 5.0 )]/(0.20 (30/1.08 log[33.73/ /2 t σ t X)]/σ log[P/PV(E d 1 2 5 1 0 = × - = - = = × + × = + = N(d 1 ) = N(1.3461) = 0.9109 N(d 2 ) = N(0.8989) = 0.8156 Call value = [N(d 1 ) × P] – [N(d 2 ) × PV(EX)] = [0.9109 × 33.73] – [0.8156 × (30/1.08 5 )] = \$14.07 b. The market value of each share of common stock is: (\$45 - \$7.035) = \$37.965 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. With a \$1,000 face value for the bonds, a bondholder can convert one bond into: (1,000/25) = 40 shares. The conversion value is: (40 × \$30) = \$1,200 b. A convertible sells at the conversion value only if the convertible is certain to be exercised. You can think of owning the convertible as equivalent to owning forty shares plus an option to put the shares back to the company in exchange for the value of the bond. The price of the convertible bond
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CH23 - CHAPTER 23 Warrants and Convertibles Answers to...

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