Question

(Calculating free cash flows) 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 $1,000 each and have a variable cost of $500 each. The annual fixed costs associated with production would be $1,000,000. In addition, there would be a $7,000,000 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 33 percent. 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 12 percent?

Answer 1

a.

Initial outlay = Cost of equipment + Working capital investment

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

= $ 8,100,000

b.

Annual revenue ($ 1,000 x 6,000)	$6,000,000
Less: Variable cost ($ 500 x 6,000)	3,000,000
Contribution margin	3,000,000
Less: Fixed cost	1,000,000
Less: Depreciation ($ 7000000/5)	1,400,000
PBT	600,000
Less: Tax @ 33 %	198,000
Net income	402,000
Add: Depreciation	1,400,000
Annual cash flow	$ 1,802,000

Annual free cash flow associate with the project for year 1 through 4 is $ 1,802,000

c.

Terminal cash flow = Annual free cash flow + Working capital recovery

                                  = $ 1,802,000 + $ 1,100,000 = $ 2,902,000

d.

NPV = FV of cash inflows – Initial cash layout

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 12 % (F)	PV (C x F)
0	-$8,100,000	1/ (1+0.12)0	1	-$8,100,000
1	1,802,000	1/ (1+0.12)1	0.8928571428571	1,608,928.57143
2	1,802,000	1/ (1+0.12)2	0.7971938775510	1,436,543.36735
3	1,802,000	1/ (1+0.12)3	0.7117802478134	1,282,628.00656
4	1,802,000	1/ (1+0.12)4	0.6355180784048	1,145,203.57729
5	2,902,000	1/ (1+0.12)5	0.5674268557186	1,646,672.73530
			NPV	-$980,023.74207

NPV of the project is -$ 980,023.74