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Question : Pointless Luxuries Inc. (PLI) produces unusual gifts targeted at wealthy

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 amits 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 at $135/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 it receivables and inventory. Projected en-of-year balances appear in the following table:

Accounts Receivable (Year 0) $0 (Year 1) $200,000 (Year 2) $250,000 (Year 3) $300,000 (Year 4) $150,000 (Year 5) $0

Inventory (Year 0) 0 (Year 1) 500,000 (Year 2) 650,000 (Year 3) 780,000 (Year 4) 600,000 (Year 5) 0

The firm faces a tax rate of 34%. Assume that cash flows arrive at the end of ear 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% discount rate and the other using a 15% 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 streat rather than at the end of each year. Therefore, by discounting each eyar's cash flow for a full year, we are understanding the true NPV. A better approximation is to move the discounting siz months forward (e.g., discount year I cash flows for six months, year 2 cash flows for eighteen months, and so on), as if all cash flows arrive in the middle of each year rather than at the end." Recalculate the NPV (at 10% and 15%) maintining this assumption. How much difference does it make?