Question

A project has the following estimated data: price = $90 per unit; variable costs = $36.9 per unit; fixed costs = $7,700; required return = 15 percent; initial investment = $10,000; life = five years. Ignore the effect of taxes. Required: (a) What is the accounting break-even quantity? (Do not round your intermediate calculations.) (b) What is the cash break-even quantity? (Do not round your intermediate calculations.) (c) What is the financial break-even quantity? (Do not round your intermediate calculations.) (d) What is the degree of operating leverage at the financial break-even level of output? (Do not round your intermediate calculations.)

Answer 1

Depreciation = Initial Investment / Life = $10,000/5 = $2,000

a). Q_A = (FC + D) / (P - V)

= ($7,700 + $2,000) / ($90 - $36.9)

= $9,700 / $53.10 = 182.67

b). Q_C = FC / (P - V)

= $7,700 / ($90 - $36.9)

= $7,700 / $53.10 = 145.01

c). The PV of the OCF must be equal to this value at the financial breakeven since the NPV is zero, so

$10,000 = OCF(PVIFA15%,5)

$10,000 = OCF x 3.3522

OCF = $10,000/3.3522 = $2,983.12

Q_F = (FC + OCF) / (P - V)

= ($7,700 + $2,983.12) / ($90 - $36.9)

= $10,683.12 / $53.10 = 201.19

d). DOL = [Q(P - V)] / [{Q(P - V)} - FC]

= [201.19($90 - $36.9)] / [{201.19($90 - $36.9)} - $7,700]

= $10,683.12 / [$10,683.12 - $7,700]

= $10,683.12 / $2,983.12 = 3.58x