Question

Growth Option: Option Analysis Fethe's Funny Hats is considering selling trademarked, orange-haired curly wigs for University of Tennessee football games. The purchase cost for a 2-year franchise to sell the wigs is $20,000. If demand is good (40% probability), then the net cash flows will be $25,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $5,000 per year for 2 years. Fethe's cost of capital is 10%. What is the expected NPV of the project? Round your answer to the nearest dollar. $ If Fethe makes the investment today, then it will have the option to renew the franchise fee for 2 more years at the end of Year 2 for an additional payment of $20,000. In this case, the cash flows that occurred in Years 1 and 2 will be repeated (so if demand was good in Years 1 and 2, it will continue to be good in Years 3 and 4). Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 0.3587 and that the risk-free rate is 7%. Do not round intermediate calculations. Round your answers to the nearest dollar. Use computer software packages, such as Minitab or Excel, to solve this problem. Value of the growth option: $ Value of the entire project: $

Answer 1

1).

	Probability (P)	Year 0	Year 1	Year 2	NPV (using NPV function)	P*NPV
Cash flows for good demand	40%	-20000	25000	25000	23388	9355
Cash flows for bad demand	60%	-20000	5000	5000	-11322	-6793
					Expected NPV	2562

Expected NPV of the project = $2,562

2). If the franchise is renewed after 2 years, the NPV of the cash inflows from the renewal will be:

	Probability (P)	Year 3	Year 4	NPV	P*NPV
Cash flows for good demand	40%	25000	25000	35858	14343
Cash flows for bad demand	60%	5000	5000	7172	4303
				Expected NPV	18646

NPV = $18,646 (This will be the price of the underlying asset for the Black-Scholes model.)

The strike price will be the investment of 20,000 at the end of Year 2 if the franchise is renewed.

Black-Scholes model:

Inputs:
Current stock price (S)	18,646.00
Strike price (K)	20,000.00
Time until expiration(in years) (t)	2.000
volatility (s)	59.9%
risk-free rate (r)	7.00%

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	0.5060
d2	(0.3410)
N(d1)	0.6936
N(d2)	0.3666
Call premium (C)	6,559

Value of the growth option is $6,559

Value of the entire project = Value of the initial project + value of the growth option

= 2,562 + 6,559 = $9,121