Question

 You are considering expanding your product line that currently consists of skateboards to include​ gas-powered skateboards, and you feel you can sell 8,000 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 ​$90 each with variable costs of ​$35 for each one​ produced, and annual fixed costs associated with production would be ​$150,000. 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 $70,000 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 32 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 99​?

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 11 percent​?

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Cost of new machine		-1300000
Initial working capital		-70000
=a. Initial Investment outlay		-1370000
Unit sales			8000	8000	8000	8000	8000	8000	8000	8000	8000	8000
Profits	=no. of units sold * (sales price - variable cost)		440000	440000	440000	440000	440000	440000	440000	440000	440000	440000
Fixed cost			-150000	-150000	-150000	-150000	-150000	-150000	-150000	-150000	-150000	-150000
-Depreciation	Cost of equipment/no. of years		-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000
=Pretax cash flows			160000	160000	160000	160000	160000	160000	160000	160000	160000	160000
-taxes	=(Pretax cash flows)*(1-tax)		108800	108800	108800	108800	108800	108800	108800	108800	108800	108800
+Depreciation			130000	130000	130000	130000	130000	130000	130000	130000	130000	130000
=b. after tax operating cash flow			238800	238800	238800	238800	238800	238800	238800	238800	238800	238800
reversal of working capital												70000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												70000
c. Total Cash flow for the period		-1370000	238800	238800	238800	238800	238800	238800	238800	238800	238800	308800
Discount factor=	(1+discount rate)^corresponding period	1	1.11	1.2321	1.367631	1.5180704	1.6850582	1.8704146	2.07616	2.3045378	2.558037	2.839421
Discounted CF=	Cashflow/discount factor	-1370000	215135.1	193815.4	174608.5	157304.96	141716.18	127672.23	115020	103621.65	93352.84	108754.6
d. NPV=	Sum of discounted CF=	61001.51777