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%.

1. What is the expected NPV of the project? Round your answer to the nearest dollar.

   $ 2562 ?

2. 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 0.3683 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

A.

Cost of wigs (Outflow) = $20,000

Net cash flow per year (40% probability of good demand) = $25,000

Net cash flow per year (60% probability of bad demand) = $5000

Cost of capital = 10%

Time period in both cases = 2 years

Cash outflow = $20,0000

Total cash inflow for one year = good demand probability x net cash flow + bad demand probability and net cash flow

                                           = 0.4 x 25,000 + 0.6 X 5000

                                           = 13,000

Annual cash flow ( flow for one year) = $13,000

Present Value Factor = {1 / ( 1+ r ) n }where r = cost of capital and n = Nth year number

r = 0.1

Present Value factor for Year 0 = {1 / ( 1+ 0.1 ) 0 } = 1

Present Value factor for Year 1 = {1 / ( 1+ 0.1 ) 1 } = 0.9090909

Present Value factor for Year 2 = {1 / ( 1+ 0.1 ) 2 } = 0.826446281

Net Present Value = Present Value factor of Year 0 X Net Annual cash flow + Present Value factor of Year 1 X Net Annual cash flow + Present Value factor of Year 2 X Net Annual cash flow

Net Present Value = 1 X -20,000 + 0.9090909 X 13,000 + 0.826446281 X 13,000 = 2561.98

Net Present Value = $2561.98

Rounding of to nearest dollar we get,

Net Present Value = $2562

B.

Initial cost ( Outflow ) = $20,000

Time Period = 4 years

Cash inflow for each of 4 years = $25,000

Investment at end of second year = $20,000

Variance of rate of return = 0.3683

Risk free rate = 7%

Strike Price is cost to extend the franchise = $20,000

Time to expiration = 2 years

V = PV of all expected future cash flows if the project is repeated starting in year 2

PV ( Good Demand ) = 25,000 / 1.13 + 25,000/1.14 = 35858.21

PV ( Bad Demand ) = 5000/ 1.13 + 5,000/1.14 = 7171.64

Total Value = 35858.21 x 0.4+ 7171.64 x 0.6 = 18,646

Total Value = $18,646

Volatility = Variance0.5 = 0.36830.5 = 0.606877253

Value of entire project = 20,000 + 18,646 = 38,646