Principles of Corporate Finance Chapters 19, 20, 21 Solutions

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• Published : May 13, 2012

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Problem Set #3
All questions are in “Principals of Corporate Finance” by Brealey, Myers, and Allen(10 ed.). Due date is Thursday March 12 by 5pm. Drop box will be in front of Gail Keenan’s office.
Chapter #19: Financing and Valuation
Problems: #7, 8, 17, 19
Chapter #20: Understanding Options
Problems: #10, 16, 18, 19
Chapter #21: Valuing Options
Problems: #1, 5, 6, 12
Chapter #19: Financing and Valuation
7. a. 12%, of course.
b. rE = .12 + (.12 - .075)(30/70) = .139, WACC = .075(1 - .35)(.30) + .139(.70) = .112, or 11.2%.
8. a. Base-case NPV = -1,000 + 1200/1.20 = 0
b. PV tax shield = (.35 X .1 X .3(1000))/1.1 = 9.55. APV = 0 + 9.55 = \$9.55
17. a. Base-case NPV = –\$1,000,000 + (\$95,000/0.10) = –\$50,000 PV(tax shields) = 0.35 × \$400,000 = \$140,000
APV = –\$50,000 + \$140,000 = \$90,000
b. PV(tax shields, approximate) = (0.35 × 0.07 × \$400,000)/0.10 = \$98,000 APV = –\$50,000 + \$98,000 = \$48,000
The present value of the tax shield is higher when the debt is fixed and therefore the tax shield is certain. When borrowing a constant proportion of the market value of the project, the interest tax shields are as uncertain as the value of the project, and therefore must be discounted at the project’s opportunity cost of capital. 19. a. Base-case \$0.11

1.12
\$1.75
NPV 10
10
1t
t
= − + ∑ −=
=
\$ or – \$110,000
APV = Base-case NPV + PV(tax shield)
PV(tax shield) is computed from the following table:
Year
Debt Outstanding
at Start of Year
Interest
Interest
Tax Shield
Present Value
of Tax Shield
1 \$5,000 \$400 \$140 \$129.63
2 4,500 360 126 108.02
3 4,000 320 112 88.91
4 3,500 280 98 72.03
5 3,000 240 84 57.17
6 2,500 200 70 44.11
7 2,000 160 56 32.68
8 1,500 120 42 22.69
9 1,000 80 28 14.01
10 500 40 14 6.48
Total 575.74
APV = –\$110,000 + \$575,740 = \$465,740
b. APV = Base-case NPV + PV(tax shield) – equity issue costs = –\$110,000 + \$575,740 – \$400,000 = \$65,740
Chapter #20: Understanding Options
10. The call price (a) increases; (b) decreases; (c) increases; (d) increases; (e) decreases; (f) decreases.
16. From put-call parity:
C + [EX/(1 + r)] = P + S
P = –S + C + [EX/(1 + r)] = –55 + 19.55 + [45/(1.025)] = \$8.45 18. a. The payoffs at expiration for the two options are shown in the following position diagram:
Taking into account the \$100 that must be repaid at expiration, the net payoffs are: b. Here we can use the put-call parity relationship: Value of call + Present value of exercise price = Value of put + Share price The value of Mr. Colleoni’s position is:

Value of put (EX = 150) – Value of put (EX = 50) – PV (150 – 50) Using the put-call parity relationship, we find that this is equal to: Value of call (EX = 150) – Value of call (EX = 50)
Thus, one combination that gives Mr. Colleoni the same payoffs is:  Buy a call with an exercise price of \$150
 Sell a call with an exercise price of \$50
Similarly, another combination with the same set of payoffs is:  Buy a put with an exercise price of \$150
 Buy a share of stock
 Borrow the present value of \$150
 Sell a call with an exercise price of \$50
19. Statement (b) is correct.
Chapter #21: Valuing Options
1. a. Using risk-neutral method, (p X 20) + (1 - p)(-16.7) = 1, p = .48. Value of call =
( ) ( )
8.3
01.1
48. 8 52. 0
=
× + ×

b. Delta =
= 544.
7.14
8
=

c.

d. Possible stock prices with call option prices in parentheses: Option prices were calculated as follows:

e. Delta =
= 544.
7.14
8
=
5. a. Delta = 100/(200 - 50) = .667.
b.

c. ( ) ( )( ) p ×100 + 1− p − 50 = 10 , p = 4.

a. Value of call =
( ) ( )
36.36
10.1
4. 100 6. 0
=
× + ×

e. No. The true probability of a price rise is -almost certainly higher than the risk...