Question

At​ present, Solartech Skateboards is considering expanding its product line to include​ gas-powered skateboards;​ however, it is questionable how well they will be received by skateboarders. Although you feel there is a 40 percent chance you will sell 11,000 of these per year for 10 years​ (after which time this project is expected to shut down because​ solar-powered skateboards will become more​ popular), you also recognize that there is a

30 percent chance that you will only sell 3,000

and also a

30 percent chance you will sell 15,000.

The gas skateboards would sell for

$120 each and have a variable cost of

​$35 each. Regardless of how many you​ sell, the annual fixed costs associated with production would be ​$140,000.

In​ addition, there would be an initial expenditure of ​$1,200,000 associated with the purchase of new production equipment which will be depreciated using the bonus depreciation method in year 1.

Because of the number of stores that will need​ inventory, the working capital requirements are the same regardless of the level of sales. This project will require a​ one-time initial investment of

$70,000 in net working​ capital, and​ working-capital investment will be recovered when the project is shut down.​ Finally, assume that the​ firm's marginal tax rate is 24 percent.

a. What is the initial outlay associated with the​ project?

b. What are the annual free cash flows associated with the project for years​ 1, and 2 through 9 under each sales​ forecast? What are the expected annual free cash flows for year​ 1, and years 2 through​ 9?

c. What is the terminal cash flow in year 10​ (that is, what is the free cash flow in year 10 plus any additional cash flows associated with the termination of the​ project)?

d. Using the expected free cash​ flows, what is the​ project's NPV given a required rate of return of

9 ​percent? What would the​ project's NPV be if 11,000 skateboards were​ sold?

Answer 1

[a]

Initial outlay = Cost of equipment + Investment in working capital

Initial outlay = $1,200,000 + $70,000 = $1,270,000

[b] , [c] and [d]

Operating cash flow (OCF) each year = income after tax + depreciation

Free cash flow in year 0 = -initial outlay

Free cash flow in year 10 = OCF + terminal cash flow

terminal cash flow = recovery of working capital investment

NPV is calculated using NPV function in Excel

11,000 units per year

NPV is $1,344,347

3,000 units per year

NPV is -$665,824

15,000 units per year

NPV is $2,349,433

Project NPV =  (probability of each outcome * NPV of each outcome)

Project NPV = (40% * $1,344,347) + (30% * (-$665,824)) + (30% * $2,349,433)

Project NPV = $1,042,822

Project NPV = $1,042,822