Luke Athletics Inc. has purchased a $200,000 machine to produce tennis balls. Th

Question

Luke Athletics Inc. has purchased a $200,000 machine to produce tennis balls. The machine will be fully depreciated by the straight-line method for its economic life of five years and will be worthless after its life. The firm expects that the sales price of the toy is $35 while its variable cost is $15. The firm should also pay $325,000 as fixed costs each year. The corporate tax rate for the company is 25 percent, and the appropriate discount rate is 12 percent.

I.What is the present value of the break-even point?

II.What will be the impact of an increase in the tax rate from 25% to 34% on the breakeven point?

III.What will be the impact of a decrease in the cost of capital from 12% to 10% on the project breakeven point?

IV.How is it different from accounting breakeven point?

Explanation / Answer

EAC                        = Initial Investment / ATr

                = $200,000 / A50.12

                                                                = $55,481.95

                Calculate the annual depreciation expense.

                                Depreciation      = $200,000 / 5

                                                                = $40,000

                Present-value break-even point=

                [EAC+(Fixed Costs) (1 - Tc) – (Depr.) (Tc)] / [(Sales Price – Variable Cost) (1 – Tc)]                = BEP

                [$55,481.95 + ($325,000) (0.75) – ($40,000) (0.25)] / [($35 - $15) (0.75) = 19,282.13 units

The present value break-even point is 19,282 units.

Present-value break-even point

[EAC+(Fixed Costs) (1 - Tc) – (Depr.) (Tc)] / [(Sales Price – Variable Cost) (1 – Tc)]                = BEP

55,481.95 + ($325,000) (0.66) – ($40,000) (0.34)] / [($35 - $15) (0.66) =19,422.88 units

EAC                        = Initial Investment / ATr

                = $200,000 / A50.10

                                                                = $52,757.92

Present-value break-even point=

                [EAC+(Fixed Costs) (1 - Tc) – (Depr.) (Tc)] / [(Sales Price – Variable Cost) (1 – Tc)]                = BEP

[$52,757.92 + ($325,000) (0.75) – ($40,000) (0.25)] / [($35 - $15) (0.75)=19100.53 units

Difference between present value of break even point and accounting break even point

The main difference is that the present value of break even calculation considers discounted cash flows using the cost of capital while the accounting break even point does not take the time value of money into consideration.

Accounting break even does not make use of the discounted cash flow.

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