Question

Q:

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. NPV is the difference between present value of cash inflows and initial investment.

present value of cash inflows = Year 1 operating cash flow/(1+required rate of return) + Year 2 operating cash flow/(1+required rate of return)² + Year 3 operating cash flow/(1+required rate of return)³ + Year 4 operating cash flow/(1+required rate of return)⁴ ... + Year 10 operating cash flow/(1+required rate of return)¹⁰

	Years	0	1	2	3	4	5	6	7	8	9	10
	Initial investment	-$1,000,000	0	0	0	0	0	0	0	0	0	0
	Sales quantity	0	30,000	30,000	30,000	30,000	30,000	30,000	30,000	30,000	30,000	30,000
	Sales price/unit	0	$50.00	$50.00	$50.00	$50.00	$50.00	$50.00	$50.00	$50.00	$50.00	$50.00
	Variable cost/unit	0	$30.00	$30.00	$30.00	$30.00	$30.00	$30.00	$30.00	$30.00	$30.00	$30.00
	Sales	$0	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000	$1,500,000
Less:	Variable cost	$0	$900,000	$900,000	$900,000	$900,000	$900,000	$900,000	$900,000	$900,000	$900,000	$900,000
Less:	Fixed cost	$0	$300,000	$300,000	$300,000	$300,000	$300,000	$300,000	$300,000	$300,000	$300,000	$300,000
Less:	Depreciation	$0	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
	Pre-tax cash flow	$0	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000
Less:	Taxes @30%	$0	$60,000	$60,000	$60,000	$60,000	$60,000	$60,000	$60,000	$60,000	$60,000	$60,000
	After-tax cash flow	$0	$140,000	$140,000	$140,000	$140,000	$140,000	$140,000	$140,000	$140,000	$140,000	$140,000
Add back:	Depreciation	$0	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
	Operating cash flow	-$1,000,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000	$240,000
	NPV	$356,054

project NPV is $356,054 if all variables are as expected.

Calculations

b. NPV in the worst-case scenario

new sales = expected sales*(1-rate of fall) = 30,000*(1-0.30) = 30,000*0.70 = 21,000

% drop is sale price = (reduced sale price/expected sale price) - 1 = ($40/$50) - 1 = 0.8 - 1 = -0.2 or 20%

reduced variable cost per unit = expected variable cost*(1-% drop is sale price) = $30*(1-0.20) = $30*0.8 = $24

	Years	0	1	2	3	4	5	6	7	8	9	10
	Initial investment	-$1,000,000	0	0	0	0	0	0	0	0	0	0
	Sales quantity	0	21,000	21,000	21,000	21,000	21,000	21,000	21,000	21,000	21,000	21,000
	Sales price/unit	0	$40.00	$40.00	$40.00	$40.00	$40.00	$40.00	$40.00	$40.00	$40.00	$40.00
	Variable cost/unit	0	$24.00	$24.00	$24.00	$24.00	$24.00	$24.00	$24.00	$24.00	$24.00	$24.00
	Sales	$0	$840,000	$840,000	$840,000	$840,000	$840,000	$840,000	$840,000	$840,000	$840,000	$840,000
Less:	Variable cost	$0	$504,000	$504,000	$504,000	$504,000	$504,000	$504,000	$504,000	$504,000	$504,000	$504,000
Less:	Fixed cost	$0	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000	$200,000
Less:	Depreciation	$0	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
	Pre-tax cash flow	$0	$36,000	$36,000	$36,000	$36,000	$36,000	$36,000	$36,000	$36,000	$36,000	$36,000
Less:	Taxes @30%	$0	$10,800	$10,800	$10,800	$10,800	$10,800	$10,800	$10,800	$10,800	$10,800	$10,800
	After-tax cash flow	$0	$25,200	$25,200	$25,200	$25,200	$25,200	$25,200	$25,200	$25,200	$25,200	$25,200
Add back:	Depreciation	$0	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
	Operating cash flow	-$1,000,000	$125,200	$125,200	$125,200	$125,200	$125,200	$125,200	$125,200	$125,200	$125,200	$125,200
	NPV	($292,592)

NPV in the worst-case scenario is -$292,592.