Question

You are considering a new product launch. The project will cost $1,450,000, have a 4-year life, and have no salvage value; depreciation is straight-line to 0. Sales are projected at 160 units per year; price per unit will be $17,000; variable cost per unit will be $10,000; and fixed costs will be $440,000 per year. The required return on the project is 12%, and the relevant tax rate is 32%.

a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10%. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 3 decimal places.

c. What is the cash break-even level of output for this project (ignoring taxes)? (Round the final answers to the nearest whole unit.)

d-1. What is the accounting break-even level of output for this project? (Round the final answers to the nearest whole unit.)

d-2. What is the degree of operating leverage at the accounting break-even point? (Round the final answer to 4 decimal places.)

Answer 1

a	Details	Base Case	Best Case	Worst Case
	Unit sales	160	176	144
	Price per unit	17,000	17,000	17,000
	Unit Variable cost	10,000	9,000	11,000
	Fixed cost	440,000	396,000	484,000
	NPV -Base Case	Year 0	Year 1	Year 2	Year 3	Year 4
	Investment	(1,450,000)
	Sales revenue		2,720,000	2,720,000	2,720,000	2,720,000
	Variable cost		-1,600,000	(1,600,000)	(1,600,000)	(1,600,000)
	Fixed cost		(440,000)	(440,000)	(440,000)	(440,000)
	Depreciation=		(362,500)	(362,500)	(362,500)	(362,500)
	Taxable Income		317,500	317,500	317,500	317,500
	Tax @32%		101,600	101,600	101,600	101,600
	Post Tax Income		215,900	215,900	215,900	215,900
	Add back depreciation		362,500	362,500	362,500	362,500
	Net Cash flow		578,400	578,400	578,400	578,400
	PV factor @12%	1	0.893	0.797	0.712	0.636
	PV of Cash flows	(1,450,000)	516,429	461,097	411,694	367,584
	NPV =	$ 306,802.86
	NPV -Best Case	Year 0	Year 1	Year 2	Year 3	Year 4
	Investment	(1,450,000)
	Sales revenue		2,992,000	2,992,000	2,992,000	2,992,000
	Variable cost		-1,584,000	(1,584,000)	(1,584,000)	(1,584,000)
	Fixed cost		(396,000)	(396,000)	(396,000)	(396,000)
	Depreciation=		(362,500)	(362,500)	(362,500)	(362,500)
	Taxable Income		649,500	649,500	649,500	649,500
	Tax @32%		207,840	207,840	207,840	207,840
	Post Tax Income		441,660	441,660	441,660	441,660
	Add back depreciation		362,500	362,500	362,500	362,500
	Net Cash flow		804,160	804,160	804,160	804,160
	PV factor @12%	1	0.893	0.797	0.712	0.636
	PV of Cash flows	(1,450,000)	718,000	641,071	572,385	511,058
	NPV =	$ 992,514.85
	NPV -worst Case	Year 0	Year 1	Year 2	Year 3	Year 4
	Investment	(1,450,000)
	Sales revenue		2,448,000	2,448,000	2,448,000	2,448,000
	Variable cost		-1,584,000	(1,584,000)	(1,584,000)	(1,584,000)
	Fixed cost		(484,000)	(484,000)	(484,000)	(484,000)
	Depreciation=		(362,500)	(362,500)	(362,500)	(362,500)
	Taxable Income		17,500	17,500	17,500	17,500
	Tax @32%		5,600	5,600	5,600	5,600
	Post Tax Income		11,900	11,900	11,900	11,900
	Add back depreciation		362,500	362,500	362,500	362,500
	Net Cash flow		374,400	374,400	374,400	374,400
	PV factor @12%	1	0.893	0.797	0.712	0.636
	PV of Cash flows	(1,450,000)	334,286	298,469	266,491	237,938
	NPV =	$ -312,816.40
b	Sensitivity Analysis	Base case	Best case	Change
	NPV	306,803	992,515	685,712
	Fixed cost	440,000	396,000	-44,000
	Sensitivity= Change in NPV/Change in Fixed cost=	-1558.436%

c	Cash Break even (440000/7000)	63
d1	Accounting Break Even ((440000+362000)/7000	115	units
d2	Degree of Operating Leverage ((1+440000)/362500)	1.2138