Question

​(Calculating project cash flows and​ NPV) You are considering expanding your product line that currently consists of skateboards to include​ gas-powered skateboards, and you feel you can sell 7,000 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 ​$70 each with variable costs of ​$50 for each one​ produced, and annual fixed costs associated with production would be ​$190,000 . In​ addition, there would be a ​$1,300,000 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 $ 60,000 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 35 percent.

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 required rate of return of 8 percent​?

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Cost of new machine		-1300000
Initial working capital		-60000
=a. Initial Investment outlay		-1360000
Unit sales			7000	7000	7000	7000	7000	7000	7000	7000	7000	7000
Profits	=no. of units sold * (sales price - variable cost)		140000	140000	140000	140000	140000	140000	140000	140000	140000	140000
Fixed cost			-190000	-190000	-190000	-190000	-190000	-190000	-190000	-190000	-190000	-190000
-Depreciation	Cost of equipment/no. of years		-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000
=Pretax cash flows			-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000
-taxes	=(Pretax cash flows)*(1-tax)		-117000	-117000	-117000	-117000	-117000	-117000	-117000	-117000	-117000	-117000
+Depreciation			130000	130000	130000	130000	130000	130000	130000	130000	130000	130000
=b. after tax operating cash flow			13000	13000	13000	13000	13000	13000	13000	13000	13000	13000
reversal of working capital												60000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												60000
c.Total Cash flow for the period		-1360000	13000	13000	13000	13000	13000	13000	13000	13000	13000	73000
Discount factor=	(1+discount rate)^corresponding period	1	1.08	1.1664	1.259712	1.360489	1.4693281	1.5868743	1.713824	1.8509302	1.999005	2.158925
Discounted CF=	Cashflow/discount factor	-1360000	12037.04	11145.4	10319.819	9555.3881	8847.5816	8192.2051	7585.375	7023.4955	6503.237	33813.12
d. NPV=	Sum of discounted CF=	-1244977.333