Question

Reliable Machinery Inc. is considering expanding its operations in Thailand. The initial analysis of the project yields the following results:'

■ The project is expected to generate $85 million in after-tax cash flows every year for the next 10 years.

■ The initial investment in the project is expected to be $750 million.

■ The cost of capital for the project is 12%. If the project generates much higher cash flows than anticipated, you will have the exclusive right for the next 10 years (from a manufacturing license) to expand operations into the rest of Southeast Asia. A current analysis suggests the following about the expansion opportunity:

■ The expansion will cost $2 billion (in current dollars).

■ The expansion is expected to generate $150 million in after-tax cash flows each year for 15 years. There is substantial uncertainty about these cash flows, and the standard deviation in the present value is 40%.

■ The cost of capital for this investment is expected to be 12% as well. The risk-free rate is 6.5%.

a. Estimate the net present value of the initial investment.

b. Estimate the value of the expansion option.

Answer 1

a). NPV of the initial investment = initial investment + PV of the cost of expansion

= 750 + 2000/(1+risk-free rate)^10 = 750 + 2000/(1+6.5%)^10 = 750 + 1,065.45 = 1,815.45

b). Expansion option can be valued as a call option, using the Black Scholes model as follows:

Stock price (S) = PV of the expected cash flows from expansion: PMT = 150; N = 15; rate = 12%, CPT PV. PV = 1,021.63

This PV is at t = 10 so it has to be discounted back to t = 0: FV = 1,021.63; N = 10; rate = 12%, CPT PV. PV = 328.94

Standard deviation of the cash flows = 40%

Strike price = PV of the cost of expansion = 1,065.45

Time to exercise the option = 10

Risk-free rate = 6.5%

Using Black-Scholes model:

Inputs:
Current stock price (S)	328.94
Strike price (K)	1,065.45
Time until expiration(in years) (t)	10.000
volatility (s)	40.0%
risk-free rate (r)	6.50%

Formulae:
d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))
d2 = d1 - (s(t^0.5))
N(d1) - Normal distribution of d1
N(d2) - Normal distribution of d2
C = S*N(d1) - N(d2)*K*(e^(-rt))

Output:
d1	0.2172
d2	(1.0477)
N(d1)	0.5860
N(d2)	0.1474
Call premium (C)	110.7722

Value of the expansion option = $110.77 million