Aem 4570 Week 1

Problem Set #3
AEM 4570: Advanced Corporate Finance
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 neutral probability, but it does not help to value the option.
6. a. Call value = $3.44. b. Put value = call value + PV(exercise price) - stock price =
$1.67.
12.
a. The possible prices of Buffelhead stock and the associated call option values (shown in parentheses) are:
Let p equal the probability of a rise in the stock price. Then, if investors are risk-neutral: p (1.00) + (1 – p) × (–0.50) = 0.10 p = 0.4
If the stock price in month 6 is $110, then the option will not be exercised so that it will be worth:
[(0.4 × $55) + (0.6 × $0)]/1.10 = $20
Similarly, if the stock price is $440 in month 6, then, if it is exercised, it will be worth ($440 - $165) = $275. If the option is not exercised, it will be worth:
[(0.4 × $715) + (0.6 × $55)]/1.10 = $290
Therefore, the call option will not be exercised, so that its value today is:
[(0.4 × $290) + (0.6 × $20)]/1.10 = $116.36
b. (i) If the price rises to $440:
(ii) If the price falls to $110:
c. The option delta is 1.0 when the call is certain to be exercised and is zero when it is certain not to be exercised. If the call is certain to be exercised, it is equivalent to buying the stock with a partly deferred payment. So a one-dollar change in the stock price must be matched by a one-dollar change in the option price. At the other extreme, when
1.0
880 220
715 55
Delta =
−
−
=
0.33
220 55
55 0
Delta =
−
−
=the call is certain not to be exercised, it is valueless, regardless of the change in the stock price.
d. If the stock price is $110 at 6 months, the option delta is 0.33. Therefore, in order to replicate the stock, we buy three calls and lend, as follows:
Initial Stock Stock
Outlay Price = 55 Price = 220
Buy 3 calls -60 0 165
Lend PV(55) -50 +55 +55
-110 +55 +220
This strategy Is equivalent to:
Buy stock -110 +55 +220