Question

You are considering new elliptical trainers and you feel you can sell 6,000 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 $1000 each and have a variable cost of $500 each. The annual fixed costs associated with production would be $1,200,000. In addition, there would be a $6,000,000 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 5 years. This project will also require a one-time initial investment of $1,100,000 in net working capital associated with inventory, and that working capital investment will be recovered when the project is shut down. Finally, assume that the firm's marginal tax rate is 31percent

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

b. What are the annual free cash flows associated with this project for years 1 through 4?

c. What is the terminal cash flow in year 5(that is, what is the free cash flow in year 5 plus any additional cash flows associated with the termination of the project)?

d. What is the project's NPV given a required rate of return of 11 percent?

Answer 1

a.

Initial outlay associate with the project = Cost of production equipment + working capital

                                                        = $ 6,000,000 + $ 1,100,000 = $ 7,100,000

b.

Depreciation = Cost of equipment /Useful life = $ 6,000,000/5 = $ 1,200,000

Computation of annual cash flow:

Revenue ( 6,000 x $ 1,000)	$ 6,000,000
Less: Variable cost ($ 500 x 6,000)	$ 3,000,000
Contribution margin	$ 3,000,000
Less: Fixed cost	$ 1,200,000
Operating profit	$ 1,800,000
Less: Depreciation	$ 1,200,000
PBT	$ 600,000
Less: Tax @ 31 %	$ 186,000
Net profit	$ 414,000
Add: Depreciation	$ 1,200,000
Annual cash flow	$ 1,614,000

Annual free cash flow for year 1 through 4 is $ 1,614,000

c.

Terminal cash flow in year 5 = Annual cash flow + Working capital release

                                         = $ 1,614,000 + $ 1,100,000 = $ 2,714,000

d.

NPV = PV of cash inflow – Initial outlay

        = $ 1,614,000 x PVIFA (11 %, 5) + $ 1,100,000 x PVIF (11 %, 5) - $ 7,100,000

       = $ 1,614,000 x [1-(1.11)^-5/0.11] + $ 1,100,000 x (1.11)^-5 - $ 7,100,000

       = $ 1,614,000 x [(1-0.593451328058559)/0.11] + $ 1,100,000 x 0.593451328058559 - $ 7,100,000

       = $ 1,614,000 x (0.406548671941441/0.11) + $ 652,796.460864414 - $ 7,100,000

       = $ 1,614,000 x 3.69589701764947 + $ 652,796.460864414 - $ 7,100,000

       = $ 5,965,177.78648624 + $ 652,796.460864414 - $ 7,100,000

       = $ 6,617,974.24735065 - $ 7,100,000

       = - $ 482,025.752649345 or - $ 482,025.75

NPV of the project is - $ 482,025.75