Question

​(Calculating project cash flows and​ NPV) You are considering new elliptical trainers and you feel you can sell 5 comma 000 of these per year for 5 years​ (after which time this project is expected to shut down when it is learned that being fit is​ unhealthy). The elliptical trainers would sell for ​$1 comma 000 each with variable costs of ​$500 for each one​ produced, and annual fixed costs associated with production would be ​$1 comma 000 comma 000. In​ addition, there would be a ​$5 comma 000 comma 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 5 years. This project will also require a​ one-time initial investment of ​$1 comma 000 comma 000 in net working capital associated with​ inventory, and it is assumed that this working capital investment will be recovered when the project is shut down. ​ Finally, assume that the​ firm's tax rate is 34 percent.

a.  What is the initial outlay associated with this​ project? b.  What are the annual net cash flows associated with this project for years 1 through 4​? c.  What is the terminal cash flow in year 5 ​(that is, the free cash flow in year 5 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 10 percent​?

Answer 1

A: initial outlay = Purchase price+ increase in working capital

= 5000000+1000000

=6000000

b: annual depreciation= (Purchase price+ installation cost)/Useful life

= 5000000/10 = 500000

Tax shield on Depreciation= 500000*34%=170000

after-tax cash flows in years 1 to 4= (sales-variable cost- fixed cost)*(1-tax rate)+ Tax shield Depreciation

=(5000*1000-5000*500-1000000)*(1-34%)+170000

=1160000

c: terminal cash flow in year 5= operating cash flow+ working capital recovery

=1160000+ 1000000 = 2160000

D: net present value= initial outlay + present value of after-tax cash flows from years 1-4+ present value of terminal cash flow

= -6000000+2160000*(1-1/(1+10%)^4)/10%+2160000/1.1^5

=2188099.42

The project should be undertaken since net present value is positive