Question

​(Related to Checkpoint​ 12.1)  ​(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 9 comma 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 ​$130 each with variable costs of ​$30 for each one​ produced, and annual fixed costs associated with production would be ​$180 comma 000. In​ addition, there would be a ​$1 comma 300 comma 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 comma 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 37 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 9 percent​?

a.  The initial cash outlay associated with this project is ​$

(Round to the nearest​ dollar.)

b.  The annual net cash flows associated with this project for years 1 through 9 are ​$

​(Round to the nearest​ dollar.)

c.  The terminal cash flow in year 10 ​(that is, the free cash flow in year 10 plus any additional cash flows associated with termination of the​ project) is ​$

​(Round to the nearest​ dollar.)

d.  Given a required rate of return of 9​%, the​ project's NPV is ​$

​(Round to the nearest​ dollar.)

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			9000	9000	9000	9000	9000	9000	9000	9000	9000	9000
Profits	=no. of units sold * (sales price - variable cost)		900000	900000	900000	900000	900000	900000	900000	900000	900000	900000
Fixed cost			-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000	-180000
-Depreciation	Cost of equipment/no. of years		-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000	-130000
=Pretax cash flows			590000	590000	590000	590000	590000	590000	590000	590000	590000	590000
-taxes	=(Pretax cash flows)*(1-tax)		371700	371700	371700	371700	371700	371700	371700	371700	371700	371700
+Depreciation			130000	130000	130000	130000	130000	130000	130000	130000	130000	130000
=b. after tax operating cash flow			501700	501700	501700	501700	501700	501700	501700	501700	501700	501700
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		-1360000	501700	501700	501700	501700	501700	501700	501700	501700	501700	561700 c.
Discount factor=	(1+discount rate)^corresponding period	1	1.09	1.1881	1.295029	1.4115816	1.538624	1.6771001	1.828039	1.9925626	2.171893	2.367364
Discounted CF=	Cashflow/discount factor	-1360000	460275	422270.9	387404.45	355416.93	326070.58	299147.32	274447.1	251786.31	230996.6	237268.2
d. NPV=	Sum of discounted CF=	1885084