Question

  You are considering expanding your product line that currently consists of skateboards to include​ gas-powered skateboards, and you feel you can sell12,000

of these per year for 10 years​ (after which time this project is expected to shut down with​solar-powered skateboards taking​ over). The gas skateboards would sell for

​$120 each with variable costs of $50 for each one​ produced, and annual fixed costs associated with production would be ​$140,000. In​ addition, there would be a ​$1,300,000

initial expenditure associated with the purchase of new production equipment. It is assumed that this initial expenditure will be depreciated using the simplified​ straight-line method down to zero over 10 years. The project will also require a​one-time initial investment of $80,000 in net working capital associated with​ inventory, and this working capital investment will be recovered when the project is shut down. ​ Finally, assume that the​ firm's marginal tax rate is 37 percent.

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

b.  What are the annual net cash flows associated with this project for years 1 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 termination of the​ project)?

d.  What is the​ project's NPV given a required rate of return of 8 percent​?

Answer 1

a.

The initial outlay includes the cost associated with the purchase of new production equipment as well as the investment in working capital:

=​$1,300,000+$80,000=​$1,380,000

b.

Depreciation= (Purchase Price of Asset-Approximate Salvage Value)/Estimated Useful Life of Asset

= (1300000-0)/10=130000

Earnings before interest/taxes:
EBIT = No. of skateboards sold*(sales - variable costs)- (fixed costs)- (depreciation)

=12000*(120-50) - 140000 - 130000

=$ 570,000

After taxes, this results in net income = 570,000 (1-0.37) =$ 359100

Add back depreciation to this to find the annual free cash flow:

Annual free cash flows for years 1 through 9 = 359100 +130000

=$489,100

c.

Total terminal cash flow in year 10=$489,100 + $80,000 {Recapture of working capital associated with termination of the​ project}

=$569,100

d.

NPV=$489,100 (PVIFA _{8%,9 yr.}) + $569,100(PVIFA _{8%, 10 yr.}) - ​$1,380,000

=489,100 *6.2469 + 569,100 *6.7101 - ​1,380,000

=$5,494,077