Question

You are considering a new product launch. The project will cost $2,100,000, 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 $27,000; variable cost per unit will be $16,500; and fixed costs will be $570,000 per year. The required return on the project is 14%, 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? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final NPV answers to 2 decimal places. Omit $ sign in your response.)

Scenario	Unit Sales	Variable Cost	Fixed Costs	NPV
Base		$	$	$
Best		$	$	$
Worst		$	$	$

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. Omit $ sign in your response.)

ΔNPV/ΔFC           $

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

Cash break–even            units

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

Accounting break–even            units

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

Degree of operating leverage           

Answer 1

H PBT I J K L M N O P Depreciat Operating Total cash PVIF@ Tax@32% PAT lion cash flows Investment flows 14% Present value (2,100,000) (2,100,000) 1.000 $(2,100,000.00); 187,200 397,800 525,000 922,800 922,800 0.877 $ 809,473.68 187,200 397,800 525,000 922,800 922,800 0.769 $ 710,064.64 187,200 397,800 525,000 922,800 922,800 0.675 $ 622,863.72 187,200 397.800 525.000 922,800 922,800 0.592 $ 546,371.68 585,000 585,000 585,000 585,000 G3 - X r fix =+M2*-0.25 A B C D E F G Sales Sale Variable Contributi Fixed Deprecia 1 Year units price cost on per unit costs tion 2 0 3 1 160 27,000 16,500 10,500 570,000 525,000 4 2 160 27,000 16,500 10,500 570,000 525,000 5 3 160 27,000 16,500 10,500 570,000 525,000 6 41 160 27,000 16,500 | 10,500 570,000 525,000 7 8 9 Sales Sale Variable Contributi Fixed Deprecia 10 Year units price cost on per unit costs tion 11 0 12 1 160 27,000 16,500 10,500 580,000 525,000 13 2 160 27,000 16,500 10,500 580,000 525,000 14 3 160 27,000 16,500 10,500 580,000 525,000 15 4 160 27,000 16,500 10,500 580,000 525,000 Base case NPV $ 588,773.71 PBT 575,000 575,000 575,000 575,000 Depreciat Operating Total cash PVIF@ Tax@32% PAT lion cash flows Investment flows 14% Present value |(2,100,000) (2,100,000) 1.000 $(2,100,000.00) 184,000 391,000 525,000 916,000 916,000 0.877 $ 803,508.77 184,000 391,000 525,000 916,000 916,000 0.769 $ 704,832.26 184,000 391,000 525,000 916,000 916,000 0.675 $ 618,273.91 184,000 391,000 525,000 916,000 916,000 0.592 $ 542,345.53 16 NPV with FC change $ 568,960.47 Variable cost Contributi Fixed on per unit costs Deprecia tion PBT Tax@32% PAT ion Sales Sale 19 Year units price 20 0 21 1 176 27,000 22 2 176 27,000 23 3 176 27,000 24 4 176 27,000 14,850 14,850 14,850 14,850 12,150 12,150 12,150 12,150 513,000 525,000 513,000 525,000 513,000 525,000 513,000 525,000 1,100,400 1,100,400 1,100,400 1,100,400 352,128 352,128 352,128 352,128 748,272 748,272 748,272 748,272 Depreciat Operating Total cash PVIF@ cash flows Investment flows 14% Present value (2,100,000) (2,100,000) 1.000 $(2,100,000.00) 525,000 1,273,272 1,273,272 0.877 $ 1,116,905.26 525,000 1,273,272 1,273, 272 0.769 $ 979,741.46 525,000 1,273,272 1,273,272 0.675 $ 859,422.33 525,000 1,273,272 1,273,272 0.592 $ 753,879.24 26 Best case NPV $ 1,609,948.29

H I D Variable cost E F Contributi on per unit Fixed costs G Deprecia tion PBT Tax@32% A B C Sales Sale 28 Year units price 29 0 30 1 144 27,000 31 2 144 27,000 32 3 144 27,000 33 4 144 27,000 J K L M N O P Depreciat Operating Total cash PVIF@ PAT lion cash flows Investment flows 14% Present value (2,100,000) (2,100,000) 1.000 $(2,100,000.00) 83,232 525,000 608,232 608,232 0.877 $ 533,536.84 83,232 525,000 608,232 608,232 0.769 $ 468,014.77 83,232 525,000 608,232 608,232 0.675 $ 410,539.28 83,232 525,000 608,232 608,232 0.592 $ 360,122.17 $ 18,150 $ 18,150 $ 18,150 $ 18,150 $ $ $ $ 8,850 8,850 8,850 8,850 627,000 525,000 627,000 525,000 627,000 525,000 627,000 525,000 122,400 122,400 122,400 122,400 39,168 39,168 39,168 39,168 34 Worst case NPV $ (327,786.94) 35 36 Unit Variable 37 Scenario sales cost Fixed costs NPV 38 Base 160 $ 16,500 $ 570,000 $ 588,773.71 39 Best 176 $ 14,850 $ 513,000 $ 1,609,948.29 40 Worst 144 $ 18,150 $ 627,000 $327,786.94 41 42 ANPV/AFC -$1.98 =(P17-P8)/10000 43 Cash break-even 54.29 =F3/(E3) 44 Accounting break-even 104.29 =(F3+G3)/E3 45 Degree of operating leverage 2.0857 =1+F3/G3 46 Financial break-even 180.16 =((PMT(12%,4,-1950000,0)-(1950000/4)*21%)/(1-21%)+560000)/(17500-10600)

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