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We are evaluating a project that costs $604,100, has a seven-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 90,000 units per year. Price per unit is $44, variable cost per unit is $31, and fixed costs are $710,000 per year. The tax rate is 23 percent, and we require a return of 12 percent on this project.
A. Calculate the accounting break-even point?
B. What is the degree of operating leverage at the accounting break-even point?
C. Calculate the base-case cash flow and NPV?
D. What is the sensitivity of NPV to changes in the quantity sold?
E. What is the sensitivity of OCF to changes in the variable cost figure?

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Answer:

A) 61254 units

C) $1102984. 83

D) 3.728%

E) −8.889%

Explanation:

Project cost = $604,100

Tenure = 7 Years

Depreciation = $604,100/7 = $ 86,300

Price per unit = $44

Variable cost per unit = $31

Contribution margin = $44 - $31 = $13

Fixed cost = $710,000

Production in unit = 90,000 units per year

Salvage value = 0

Tax rate = 23%

Required rate of return = 12%

A.) Contribution margin :

Break-even point = (Fixed cost + depreciation )/ contribution margin

=($710,000 +$86,300)/ $13

= 61253.84 units

= 61254 units

C.) Net income = (90,000 × 13) - $710,000 - $86,300 × (1 - 0.23)

=$287,749

OCF = Net income + Depreciation added back

=$287,749 + $86,300

=$374,049

NPV =$374,049*PVIFA(12%, 7 years ) - $604,100

=($374,049 × 4.5638) - $604,100

=$1102984. 83

C.) We found NPV with existing production of 90,000 units = $1102984.83

Now, we increase the production for 1% with result = 90000 * 1.01 = 90900 units

Net income =( 90900*$13 - $710,000 - $ 86300)*(0.77)

=$296758

OCF = Net income + Depreciation added back

= $296758 + $ +86,300

=$383,058

NPV =$383,058 × PVIFA(12%, 7 years ) - $604,100

=($383,058 × 4.5638) - $604,100

=$1144100.10

So NPV increased = ($ 1144100.10 - $1102984.83)/$1102984.83 = 3.7276%

So, the sensitivity = 3.728%

E.) We assume the expected variable cost is increased 1% to $31*(1.01) = $ 31.31

Contribution margin = $44 - $31.31 = $12.69

Net income = (90,000 × 12.69 - $710,000 - $86,300) × 0.77

=$266,266

OCF = Net income + Depreciation added back

=$266,266 + $86,300

=$352,566

NPV =$352,566 × PVIFA(10%, 5 years ) - 604,100

=$352,566 × 4.5638 - $604,100

=$1004940.71

NPV changed = ($1004940.71 -$1102984.83)/$1102984.83 = -3.431%

So sensitivity of variable cost = −8.889%

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