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chap023

# chap023 - Chapter 23 Options and Corporate Finance...

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Unformatted text preview: Chapter 23: Options and Corporate Finance: Extensions and Applications 23.1 d1 = [(r + 2) t]/ 2 t = [(0.06 + (0.25)2 ) 4]/ N(d1) = 0.7673 d2 = d1 2 t = 0.73 ( 0.25) 2 ( 4) = 0.73 ( 0.25) 2 ( 4) = 0.23 N(0.23) = 0.5910 C = 50(0.7673) 50e-0.06 4 (0.5910) = \$38.365 \$23.245 = \$15.12 Total Value: \$15.12 \$1 million = \$302,400 \$50 23.2 Option A: use discount rate of 6% 4 Total pay value = \$1mil 0.06 + 1.2096 million Option B: 4 Total pay value = \$1.25 mil 0.06 The question is whether the incremental \$1.25 mil straight pay value is greater or lower than the options value of \$1.2096 mil. If we use the riskless rate of 6%, the cost of additional \$0.25 mil is \$0.8663 mil (As opposed to \$1.2096 mil). Holding everything else constant, Mr. Hurt is right and the Board is wrong. It's cheaper for the firm to pay Mr. Hurt a \$1.25 mil straight pay without opitons. However, diversification may make the \$1.25 mil straignt pay better off for Mr. Hurt. From the bounding effect, the firm will be better off to offer Mr. Hurt the options. 23.3 Fixed plant: r = 12% 150,000( \$20) { 0.5 (150,000) ( \$20) + 0.5 (150,000 / 2)( \$20) } 9.12 0 NPV = -1million + + 1 1 (1 + 0.12) (1 + 0.12) = -1million + \$2,678,571.43 + \$10,704,073.24 = \$12,382,644.67 Flexible plant: NPV = -1.5million + 150,000( \$10) (1 + 0.12) 1 + {0.5 (150,000) ( \$10) (1 + 0.12) 9 0.12 + 0.5 (150,000)( \$15) 9.12 0 1 } = -1.5million + \$1,339,285.71 + \$8,920,061.03 = \$8,759,346.74 TGC should choose the fixed plant since it has a larger NPV. Answers to End-of-Chapter Problems B-203 23.4 If rate = 11%; \$55 = -\$0.4505 million < 0 NPV = - \$50 + 1.11 If rate = 9%; \$55 = \$0.4588 million NPV = - \$50 + 1.09 NPV = 0.5 (0) + 0.5 (0.4588 million) = \$229,400 > \$500 He should not take the offer to sell his option. 23.5 a. b. NPV = -7 million + (10,000 \$200) 0.15 = -\$295,689.80 4 \$100,000 = C 0.15 C = \$35,026.54 ( level of sales) (\$200) = \$35,026.54 =175.13 units 176 units 5 23.6 9 NPV = -7 mil +(10,000 \$200 /1.15) +[(0.5 15,000 \$200 0.15 ) +(0.5 100,000)]/1.15 = -7 mil + \$1,739,130.43 + \$6,267,283.37 = \$1,006,413.80 B-204 Answers to End-of-Chapter Problems ...
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