# Question

Pointless Luxuries Inc. (PLI) produces unusual gifts targeted at wealthy consumers. The company is analyzing the possibility of introducing a new device designed to attach to the collar of a cat or dog. This device emits sonic waves that neutralize airplane engine noise, so that pets traveling with their owners can enjoy a more peaceful ride. PLI estimates that developing this product will require up-front capital expenditures of $10 million. These costs will be depreciated on a straight-line basis for five years. PLI believes that it can sell the product initially for $250. The selling price will increase to $260 in years 2 and 3 before falling to $245 and $240 in years 4 and 5, respectively. After five years the company will withdraw the product from the market and replace it with something else. Variable costs are $135 per unit. PLI forecasts sales volume of 20,000 units the first year, with subsequent increases of 25% (year 2), 20% (year 3), 20% (year 4), and 15% (year 5). Offering this product will force PLI to make additional investments in receivables and inventory. Projected end-of-year balances appear in the following table.

The firm faces a tax rate of 34 percent. Assume that cash flows arrive at the end of each year, except for the initial $10 million outlay.

a. Calculate the project’s contribution to net income each year.

b. Calculate the project’s cash flows each year.

c. Calculate two NPVs, one using a 10 percent discount rate and one using a 15 percent discount rate.

d. A PLI financial analyst reasons as follows: “With the exception of the initial outlay, the cash flows from this project arrive in more or less a continuous stream rather than at the end of each year. Therefore, by discounting each year’s cash flow for a full year, we are understating the true NPV. A better approximation is to move the discounting six months forward (e.g., discount year-1 cash flows for six months, year-2 cash flows for 18 months, and so on), as if all the cash flows arrive in the middle of each year rather than at the end.” Recalculate the NPV (at 10% and 15%) maintaining this assumption. How much difference does it make?

The firm faces a tax rate of 34 percent. Assume that cash flows arrive at the end of each year, except for the initial $10 million outlay.

a. Calculate the project’s contribution to net income each year.

b. Calculate the project’s cash flows each year.

c. Calculate two NPVs, one using a 10 percent discount rate and one using a 15 percent discount rate.

d. A PLI financial analyst reasons as follows: “With the exception of the initial outlay, the cash flows from this project arrive in more or less a continuous stream rather than at the end of each year. Therefore, by discounting each year’s cash flow for a full year, we are understating the true NPV. A better approximation is to move the discounting six months forward (e.g., discount year-1 cash flows for six months, year-2 cash flows for 18 months, and so on), as if all the cash flows arrive in the middle of each year rather than at the end.” Recalculate the NPV (at 10% and 15%) maintaining this assumption. How much difference does it make?

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