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 $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%.

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 0.3397 and that the risk-free rate is 6%. Do not round intermediate calculations. Round your answers to the nearest dollar.
Value of the growth option:
Value of the entire project:
We are examining a new project. We expect to sell 5,600 units per year at $70 net cash flow apiece for the next 10 years. In other words, the annual cash flow is projected to be $70 × 5,600 = $392,000. The relevant discount rate is 18 percent, and the initial investment required is $1,550,000. After the first year, the project can be dismantled and sold for $1,270,000. Suppose you think it is likely that expected sales will be revised upward to 8,600 units if the first year is a success and revised downward to 4,200 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project is a success. This implies that if the project is a success, projected sales after expansion will be 17,200. Note that abandonment is still an option if the project is a failure.
If success and failure are equally likely, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Value of the growth option: $3374.47Value of the entire project: $5,227.74First, we need to calculate the value of the growth option. Here are the steps:Step 1: Calculate the price of the underlying asset.For a two-year investment, the initial outlay is $20,000. In year 1, the cash flow will be either $5,000 or $25,000. In year 2, if the option is exercised, the cash flow will be either $5,000 or $25,000. The present value of these cash flows can be calculated as follows:Pv1Good demand = $25,000 / (1+10%)^1 = $22,727.27Pv1Bad demand = $5,000 / (1+10%)^1 = $4,545.45Pv2Good demand = $25,000 / (1+10%)^2 = $20,661.16Pv2Bad demand = $5,000 / (1+10%)^2 = $4,132.23Step 2: Calculate the variance of the project’s rate of return.The variance is given as 0.3397.Step 3: Calculate d1 and d2.d1 = [ln($22,727.27/$20,000) + (0.06 + 0.3397/2) x 1]/[0.5826] = 1.56d2 = d1 - 0.5826 = 0.98Step 4: Calculate the value of the growth option.The value of the growth option can be calculated using the Black-Scholes formula as follows:Value of the growth option = $20,000 x [0.7533 x N(1.56) - 0.5715 x N(0.98)] = $3374.47Next, we need to calculate the value of the entire project. Here are the steps:Step 1: Calculate the present value of the annual cash flows.The present value of the annual cash flows can be calculated as follows:PV of annual cash flows = $70 x 5,600 x [(1 - 1/(1 + 18%)^10) / 0.18] = $356,451.22Step 2: Calculate the present value of the terminal value.The present value of the terminal value can be calculated as follows:PV of terminal value = $1,270,000 / (1 + 18%)^1 = $1,075,423.73Step 3: Calculate the NPV.The NPV can be calculated as follows:NPV = - $1,550,000 + $356,451.22 + $1,075,423.73 + $3374.47 = $5,227.74Therefore, the NPV of the project is $5,227.74.