Question

You are considering expanding your product line that currently consists of skateboards to include gas-powered skateboards, and you feel you can sell 10,000 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 $100 each with variable costs of $40 for each one produced, while annual fixed costs associated with production would be $160,000. In addition, there would be a $1,000,000 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 $50,000 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 34%. 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 10% required rate of return?

Answer 1

a) The Initial cash outlay will be:

Expenditure for Equipment 1,000,000 + Working Capital Investment 50,000 = 1,050,000

b) Annual Net Cash Flow for years 1 through 9:

Sales (10000 x 100)	1,000,000
Variable Cost (10000 x 40)	400,000
Fixed Cost	160,000
Depreciation (Since initial investment is depreciated using straight line method down to 0, annual depreciation = 1,000,000/10	100,000
Profit Before Tax	340,000
Tax @ 34%	115,600
Profit After Tax	224,400
Add Back Depreciation (as it is a non-cash cost, it does not cause any cash flow)	100,000
Free Annual Cash Flow	324,400

c) Terminal Cash Flow for year 10 = Free Annual Cash Flow + Working capital invested earlier, free after project shut down = 324,400 + 50,000 = 374,400

d) NPV (Net Present Value) for the project will be the Net Present value i.e. value as on date of investment of all Inflow/outflow of the project.

- 1,050,000	Initial Cash Outflow
1,868,220	Present Value for cash inflow year 1 to 9, formula for calculation is:   Annual Inflow x Annuity Factor (10%,9) 324,400 x 5.759 = 1,868,220 Note: Annuity Factor can be used if the annual cash flow is equal and regular in all years. Annuity factor will be the sum total of PV factor for 9 years. Alternately, one can multiply annual cash flow with respective year PV Factor to arrive at same value. For eg. Year 1 - 324400 x 0.9091 Year 2 - 324400 x 0.8624 Year 3 - 324400 x 0.7513 and so on till year 9.
144,331	Present Value of Cash Flow for Year 10 Terminal Cashflow x PV Factor (10%, 10) 374,400 x 0.3855 = 144,331
962,551	Projects' Net Present Value at 10% required rate of return.

# Present Value Factor = 1 / (1+r)^n, where r = required rate of return, and n = number of year.