Finance Chapter 3 Solve the following simultaneous equations

Revised Shockley, Chapter 3 Answers:

Problem 1:

a.

Economy:

Market Index:

Risk-free

Option:

b. Solve the following simultaneous equations:

c. The return on the firm is:

Problem 2:

a. First, find the expected cash flow given the state of the economy.

b. Solve the following simultaneous equations:

Boom:

Stagnant:

Recession:

Expected Return:

c. The value of the firm is 5,200*$315.79 + 23,800*$94.34 + 0*$6.58 =

Problem 3:

a. First, find the expected cash flow given the state of the economy.

Subtract the expected cash flow for each state of the economy from the

associated cash flows for Events 1 and 2 within each state.

b. Solve the following simultaneous equations:

Problem 4:

b. Boom: $100,000.00 + 75%*$3,000,000.00 + 25%*$1,600,000.00 =

c. Because the conditional mean cash flows are the same for each state of the

Problem 5:

a. Find the conditional mean contingent values:

Solve the following simultaneous equations:

$53,794.20

The discount rate is ($63,000.00 ÷ $53,794.20) – 1 = 17.11%

Or

Problem 6:

a. Find the conditional mean contingent values:

Solve the following simultaneous equations:

b. Find the expected value of the project cash flows: 20%*$75,000.0 +

Or

Problem 7:

a. Conditional mean asset values:

Solve the following simultaneous equations:

The value of the firm is 14,400*$315.79 + (-19,400)*$94.34 + 31,200*$6.58

= $2,922,476.00

Problem 8:

a. Solve the following simultaneous equations:

The return on the firm is:

Problem 9:

a. 50%*$80,000.00 + 50%*$50,000.00 = $65,000.00 (Boom)

b. Subtract the mean value for each state from the associated event cash flows:

c. Value the cash flows using tracking portfolio:

Solve the following simultaneous equations:

Problem 10:

a. When considering the call option with a strike of $20,000.00, the cash flows from

Future Economy:

Event 1

(Probability = 50%):

Event 2

(Probability = 50%):

Conditional

Mean:

Value the cash flows using tracking portfolio:

Solve the following simultaneous equations:

Problem 11:

No, the position in the index option implies that the project’s cash flows are non-linear

Problem 12:

One can verify this by solving the following simultaneous equations:

Because the tracking portfolio does not require a holding in the index option, the project

must be linear relative to the market index and the risk-free security.