Question

You are considering a proposal to produce and market a new sluffing machine. The most likely outcomes for the project are as follows:

Expected sales: 30,000 units per year

Unit price: $50

Variable cost: $30

Fixed cost: $300,000

The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 30%, and the required rate of return is 12%.

However, you recognize that some of these estimates are subject to error. Sales could fall 30% below expectations for the life of the project and, if that happens, the unit price would probably be only $40. The good news is that fixed costs could be as low as $200,000, and variable costs would decline in proportion to sales.

a. What is project NPV if all variables are as expected? (Do not round intermediate calculations. Enter your answer in thousands not in millions and round your answer to the nearest whole dollar amount.)

b. What is NPV in the worst-case scenario? (Do not round intermediate calculations. Enter your answer in thousands not in millions and round your answer to the nearest whole dollar amount. Negative amount should be indicated with a minus sign.)

Answer 1

a

Time line		0	1	2	3	4	5	6	7	8	9	10
Cost of new machine		-1000000
=Initial Investment outlay		-1000000
													100.00%
Unit sales			30000	30000	30000	30000	30000	30000	30000	30000	30000	30000
Profits	=no. of units sold * (sales price - variable cost)		600000	600000	600000	600000	600000	600000	600000	600000	600000	600000
Fixed cost			-300000	-300000	-300000	-300000	-300000	-300000	-300000	-300000	-300000	-300000
-Depreciation	Cost of equipment/no. of years		-100000	-100000	-100000	-100000	-100000	-100000	-100000	-100000	-100000	-100000	0	=Salvage Value
=Pretax cash flows			200000	200000	200000	200000	200000	200000	200000	200000	200000	200000
-taxes	=(Pretax cash flows)*(1-tax)		140000	140000	140000	140000	140000	140000	140000	140000	140000	140000
+Depreciation			100000	100000	100000	100000	100000	100000	100000	100000	100000	100000
=after tax operating cash flow			240000	240000	240000	240000	240000	240000	240000	240000	240000	240000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-1000000	240000	240000	240000	240000	240000	240000	240000	240000	240000	240000
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194	1.7623417	1.9738227	2.210681407	2.4759632	2.773079	3.105848
Discounted CF=	Cashflow/discount factor	-1000000	214285.71	191326.53	170827.26	152524.34	136182.45	121591.47	108563.8117	96931.975	86546.41	77273.58
NPV=	Sum of discounted CF=	356053.53

NPV = 356 (in thousands)

b

Time line		0	1	2	3	4	5	6	7	8	9	10

NPV = -791 (in thousands)