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 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 ​$70 each with variable costs of ​$30 for each one​ produced, and annual fixed costs associated with production would be $180,000. In​ addition, there would be a $1,200,000 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 30 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 13 percent​?

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Cost of new machine		-1200000
Initial working capital		-60000
=Initial Investment outlay a.		-1260000
Unit sales			8000	8000	8000	8000	8000	8000	8000	8000	8000	8000
Profits	=no. of units sold * (sales price - variable cost)		320000	320000	320000	320000	320000	320000	320000	320000	320000	320000
Fixed cost			-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000
-Depreciation	Cost of equipment/no. of years		-120000	-120000	-120000	-120000	-120000	-120000	-120000	-120000	-120000	-120000
=Pretax cash flows			20000	20000	20000	20000	20000	20000	20000	20000	20000	20000
-taxes	=(Pretax cash flows)*(1-tax)		14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
+Depreciation			120000	120000	120000	120000	120000	120000	120000	120000	120000	120000
=after tax operating cash flow b.			134000	134000	134000	134000	134000	134000	134000	134000	134000	134000
reversal of working capital												60000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												60000
Total Cash flow for the period		-1260000	134000	134000	134000	134000	134000	134000	134000	134000	134000	c. 194000
Discount factor=	(1+discount rate)^corresponding period	1	1.13	1.2769	1.442897	1.6304736	1.8424352	2.0819518	2.352605	2.65844	3.004042	3.394567
Discounted CF=	Cashflow/discount factor	-1260000	118584.07	104941.656	92868.722	82184.71	72729.831	64362.683	56958.13	50405.4	44606.57	57150.14
d. NPV=	Sum of discounted CF=	-515208.0733