A four year project costs $1.7 million and has straight-line depreciation. Sales

Question

A four year project costs $1.7 million and has straight-line depreciation. Sales of 190 units per year are projected, with a unit sales price of $18,000. Variable costs per unit are $11,200, and fixed costs are $410,000 per year. The required return is 12%, and the tax rate is 35%.

a. What is the cash break-even level of output (ignoring taxes)?

b. What is the accounting break-even level of output? 122

c. What is the degree of operating leverage at the accounting break-even point?

d. What is the base case NPV for the project?

e. How sensitive is NPV to changes in fixed costs?

f. If estimates can be +/- 10%, what would be the best case and worst case NPVs?

Explanation / Answer

a)The cash breakeven is:
QC = FC/(P – v)
QC = $410,000/($18,000 – 11,200)
QC = 60

b) The accounting breakeven is:
QA = (FC + D)/(P – v)
QA = [$410,000 + ($1,700,000/4)]/($18,000 – 11,200)
QA = 122. 79 123

c) At the accounting breakeven, the DOL is:
DOL = 1 + FC/OCF
DOL = 1 + ($410,000/$425,000) = 1.9647
This means for each 1% increase in unit sales, OCF will increase by 1.9647%.

Scenario Unit sales Variable cost          Fixed cost

Base 190 $11,200 $410,000

Best 209 $10,080 $369,000

Worst 171 $12,320            $451,000

d) Using the tax shield approach, the OCF and NPV for the base case estimate is:

OCFbase = [($18,000 – 11,200)(190) – $410,000](0.65) + 0.35($1,700,000/4)

OCFbase = $722,050

   NPVbase = –$1,700,000 + $722,050(PVIFA12%,4)

NPVbase = $493,118.10

e) To calculate the sensitivity of the NPV to changes in fixed costs we choose another level of fixed costs. We will use fixed costs of $420,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get:

   OCF = [($18,000 – 11,200)(190) – $410,000](0.65) + 0.35($1,700,000/4)

               OCF = $715,550

   And the NPV is:

   NPV = –$1,700,000 + $715,550(PVIFA12%,4)

               NPV = $473,375.32

   The sensitivity of NPV to changes in fixed costs is:

   NPV/FC = ($493,118.10 – 473,375.32)/($410,000 – 420,000)

NPV/FC = –$1.974

    For every dollar FC increase, NPV falls by $1.974.

f) The OCF and NPV for the worst case estimate are:

   OCFworst = [($18,000 – 12,320)(171) – $451,000](0.65) + 0.35($1,700,000/4)

OCFworst = $486,932

   NPVworst = –$1,700,000 + $486,932(PVIFA12%,4)

NPVworst = –$221,017.41

And the OCF and NPV for the best case estimate are:

   OCFbest = [($18,000 – 10,080)(209) – $369,000](0.65) + 0.35($1,700,000/4)

OCFbest = $984,832

   NPVbest = –$1,700,000 + $984,832(PVIFA12%,4)

NPVbest = $1,291,278.83

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