Question

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 $24,000 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%. 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 7%.

   Select the correct decision tree.

Answer 1

Part (a)

If demand is good (40% probability), then the net cash flows will be $24,000 per year for 2 years.

NPV_g = - C0 + C / (1 + r) + C / (1 + r)² = -20,000 + 24,000 / (1 + 10%) + 24,000 / (1 + 10%)² = $  21,652.89

p_g = 40%

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If demand is bad (60% probability), then the net cash flows will be $5,000 per year for 2 years.

NPV_b = - C0 + C / (1 + r) + C / (1 + r)² = -20,000 + 5,000 / (1 + 10%) + 5,000 / (1 + 10%)² = $   -11,322.31

p_b = 60%

Hence, the expected NPV = p_g x NPV_g + p_b x NPV_b = 40% x 21,652.89 + 60% x (-11,322.31) = $  1,867.77

Part (b)

The correct decision tree is:

NPV_g = - C0 + C / (1 + r) + C / (1 + r)² - C₀ / (1 + r*)² + C / (1 + r)³ + C / (1 + r)⁴ = -20,000 + 24,000 / (1 + 10%) + 24,000 / (1 + 10%)² - 20,000 / (1 + 7%)² + 24,000 / (1 + 10%)³ + 24,000 / (1 + 10%)⁴ = $ 38,608.00

Hence, the expected NPV = p_g x NPV_g + p_b x NPV_b = 40% x 38,608.00 + 60% x (-11,322.31) = $   8,649.81