Question

Growth Option: Decision-Tree 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 $27,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $7,000 per year for 2 years. Fethe's cost of capital is 10%. Do not round intermediate calculations.

1. What is the expected NPV of the project? Negative value, if any, should be indicated by a minus sign. Round your answer to the nearest dollar.
   $   
   
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). Write out the decision tree. Note: The franchise fee payment at the end of Year 2 is known, so it should be discounted at the risk-free rate, which is 4%.

   Select the correct decision tree.

Answer 1

NPV = - C₀ + C / r x [1 - (1 + r)^-n]

where C₀ = initial investment = 20,000

C = Annual cash flows which is dependent on two scenarios

r = cost of capital = 10%, n = term = 2 years

Case: When Demand is good; Probability P_G = 40%, C = 27,000

NPV_G = -20,000 + 27,000 / 10% x [1 - (1 + 10%)^-2] = $ 26,860

Case: When Demand is bad; Probability P_B = 60%, C = 7,000

NPV_B = -20,000 + 7,000 / 10% x [1 - (1 + 10%)^-2] = - $ 7,851

Part (a)

Expected NPV = P_G x NPV_G + P_B x NPV_B = 40% x 26,860 + 60% x (-7,851) = $  6,033

Part (b)

Please note that the option at the end of year 2 will be exercised only if demand had been good. There is no point exercising the option if the demand had been bad, as it results into negative NPV.

The decision tree will be as shown below.

Path 1: Good demand + Renew franchise

Probability, P₁ = 40%

The franchise fee payment at the end of Year 2 is known, so it should be discounted at the risk-free rate, which is 4%.

NPV₁ = NPV_G - 20,000 / (1 + 4%)² + 27,000 / (1 + 10%)³ + 27,000 / (1 + 10%)⁴ =  26,860 + 20,236 = $  47,095

Path 2: Bad demand + Don't Renew franchise

Probability, P₂ = 60%

NPV₂ = NPV_B = - $ 7,851

Hence, expected NPV with option = P₁ x NPV₁ + P₂ x NPV₂ = 40% x 47,095 + 60% x (-7,851) = $ 14,127

Hence, value of the option = NPV with option - NPV without option = 14,127 - 6,033 = $ 8,094