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 ​$1,500
each and have a variable cost of ​$750 each. The annual fixed costs associated with production would be ​$1,100,000.
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 ​$1,000,000
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 31 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 9 percent?

Answer 1

Time line		0	1	2	3	4	5
Cost of new machine		-7000000
Initial working capital		-1000000
=a. Initial Investment outlay		-8000000
								100.00%
Unit sales			6000	6000	6000	6000	6000
Profits	=no. of units sold * (sales price - variable cost)		4500000	4500000	4500000	4500000	4500000
Fixed cost			-1100000	-1100000	-1100000	-1100000	-1100000
-Depreciation	Cost of equipment/no. of years		-1400000	-1400000	-1400000	-1400000	-1400000	0	=Salvage Value
=Pretax cash flows			2000000	2000000	2000000	2000000	2000000
-taxes	=(Pretax cash flows)*(1-tax)		1380000	1380000	1380000	1380000	1380000
+Depreciation			1400000	1400000	1400000	1400000	1400000
=b. after tax operating cash flow			2780000	2780000	2780000	2780000	2780000
reversal of working capital							1000000
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							1000000
Total Cash flow for the period		-8000000	2780000	2780000	2780000	2780000	c. 3780000
Discount factor=	(1+discount rate)^corresponding period	1	1.09	1.1881	1.295029	1.4115816	1.538624
Discounted CF=	Cashflow/discount factor	-8000000	2550458.716	2339870.381	2146670.075	1969422.1	2456740.6
d. NPV=	Sum of discounted CF=	3463161.90