Question

You are considering a new product launch. The project will cost $860,000, have a 4-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 520 units per year; price per unit will be $18,800, variable cost per unit will be $15,500, and fixed costs will be $890,000 per year. The required return on the project is 13 percent, and the relevant tax rate is 24 percent. a. The unit sales, variable cost, and fixed cost projections given above are probably accurate to within ±10 percent. 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? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your NPV answers to 2 decimal places, e.g., 32.16.) b. Calculate the sensitivity of your base-case NPV to changes in fixed costs. (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) c. What is the accounting break-even level of output for this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a]		Base Case	Upper Bound	Lower Bound
	Units per year	520	572	468
	Variable cost per unit	$                  15,500	$               17,050	$              13,950
	Fixed costs	$              8,90,000	$           9,79,000	$          8,01,000
	BASE CASH NPV:
	Sales = 520*18800 =	$            97,76,000
	Variable costs = 520*15500 =	$            80,60,000
	Fixed costs	$              8,90,000
	Depreciation = 860000/4 =	$              2,15,000
	NOI	$              6,11,000
	Tax at 24%	$              1,46,640
	NOPAT	$              4,64,360
	Add: Depreciation	$              2,15,000
	OCF	$              6,79,360
	PV of OCF = 679360*(1.13^4-1)/(0.13*1.13^4) =	$            20,20,737
	Less: Initial cost	$              8,60,000
	NPV	$            11,60,737
	BEST CASE NPV:
	Sales = 572*18800 =	$        1,07,53,600
	Variable costs =572*13950 =	$            79,79,400
	Fixed costs	$              8,01,000
	Depreciation = 860000/4 =	$              2,15,000
	NOI	$            17,58,200
	Tax at 24%	$              4,21,968
	NOPAT	$            13,36,232
	Add: Depreciation	$              2,15,000
	OCF	$            15,51,232
	PV of OCF =1551232*(1.13^4-1)/(0.13*1.13^4) =	$            46,14,095
	Less: Initial cost	$              8,60,000
	NPV	$            37,54,095
	WORST CASE NPV:
	Sales = 468*18800 =	$            87,98,400
	Variable costs = 468*17050 =	$            79,79,400
	Fixed costs	$              9,79,000
	Depreciation = 860000/4 =	$              2,15,000
	NOI	$            -3,75,000
	Tax at 24%	$                -90,000
	NOPAT	$            -2,85,000
	Add: Depreciation	$              2,15,000
	OCF	$                -70,000
	PV of OCF =70000*(1.13^4-1)/(0.13*1.13^4) =	$            -2,08,213
	Less: Initial cost	$              8,60,000
	NPV	$          -10,68,213
b]	Sensitivity of NPV to fixed costs = Change in NPV/Change in fixed costs = (3754095-1160737)/(810000-890000) =	$                  -32.42
	It means that for $1 change in fixed costs the NPV
	will change in the opposite direction by $32.42.
	A decrease of $89000 in fixed costs will increase
	NPV by 89000*32.42 =	$            28,85,380
c]	Accounting break even level of output = Fixed costs/CM per unit = (890000+215000)/(18800-15500) =	335	Units