Principles of Corporate Finance_ 12th Edition

A-6 Appendix Answers to Select Basic Problems

bre44380_app_A1-A10 6 10/09/15 08:14 PM

If stock price is $620.59, buy δ =1 share and borrow

the PV of exercise price: 620.59 – _____^450

1.005

= 172.83. If

stock price is $452.64, buy δ =.558 shares and borrow

the PV of 215.71: .558 × 452.64 – ______ 215.71

1.005

= 37.9. The

option delta at start is:

δ = ______________ 172.83 – 37.9

620.59 – 452.64

= .803

Buy .803 shares for .803 × 530, borrow PV

of 325.59: .803 × 530 – ______ 325.59

1.005

= 101.62. The

6-month put can be valued by put-call parity: 101.62

+ _______^450

(1.0 05)^2

• 530 = 17.15.

b. Delta =

spread of option prices

___________________

spread of stock prices

=

8

____

14.7

= .544.

c.
Current
Cash Flow

Possible Future

Cash Flows

Buy call equals − 3.8 (^0) + 8.0
Buy .544 shares −21.8 −18.2 + 26.2
Borrow 18.0 +18.0 −18.2 −18.2
− 3.8 0 − 8.0
d. Possible stock prices with call option prices in
parentheses:
40
(4.0)
33.3 48.0
(0) (8.4)
27.8 57.6
(0) (0)(17.6)
Option prices were calculated as follows:
Month 1: (i)
(.48 × 0) + (.52 × 0)

1.01
= 0
(ii)
(.48 × 17.6) + (.52 × 0)

1.01
= 8.4
Month 0: =
(.48 × 8.4) + (.52 × 0)

1.01
= 4.0
e. Delta =
spread of option prices

spread of stock prices
= ____8.4
14.7
= .571

3. In Figure 21.3, p = .4764, 1 – p = .5236, interest rate =
   .5% per 3-month period. At month 6, the call pays off
   $276.55 at stock price = $726.55, $80 at stock price =
   $530, zero at stock price = $386.57.
   Using the risk-neutral method, call value at month 3 is:

____.4764 × 276.55 + .5236 × 80
1.005

= 172.77

or ____ .4764 × 80 + .5236 × 0
1.005

= 37.9

Call value at start is:

__.4764 × 172.77 + .5236 × 37.9
1.005

= 101.64

Now use replication. The results are identical, but
small rounding errors will crop up. The option
deltas at month 3 are δ = ___276.55 – 80
726.55 – 530

= 1 and

δ = ___________80 – 0

530 – 386.57

= .558.

5. a. Delta = 100/(200 − 50) = .667.
   b.

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

d. Value of call =

(.4 × 100) + (.6 × 0)

_________________

1.10

= 36.36.

e. No. The true probability of a price rise is almost cer-

tainly higher than the risk-neutral probability, but it

does not help to value the option.

7. True; as the stock price rises, the risk of the option falls.

CHAPTER 22

1. a. Increase value.
   b. Increase value.
   c. Reduce value.


2. The life of a project is not fixed ahead of time. IM&C
   has the option to abandon the guano project after 2 or
   3 years if performance is poor. If performance is great,
   exercise of the abandonment option could be delayed
   well beyond the estimated 7-year life.


3. Gas turbines can be started up on short notice when
   spark spreads are high. The turbines’ value comes from
   flexibility in production.


4. (a) True; (b) True; (c) True; (d) True; (e) True—the
   series of smaller plants generates real options, but the
   large plant may nevertheless be more efficient.

CHAPTER 23

1. Promised yield = 12.77%; expected yield = 9.42%.

Current

Cash Flow

Possible Future

Cash Flows

Buy call equals −36.36 0 + 100

Buy .667 shares −66.67 +33.33 +133.33

Borrow 30.30 +30.30 −33.33 − 33.33

−36.36^0 + 100