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

Question

a. 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

Break Even Point = Fixed Cost / contribution per unit

Fixed cost = 325000 per year for 5 years + Depreiation of 40000

Fixed cost cash flow for 5 years = (325000*.75)-(40000*.25) = 233750 (Tax savings due to theses expenses are considered)

PV factor for 5 year at 12% is 3.6048

PV of fixed costs = 233750*3.6048 = 842622

Contribution per unit = (35-15)*(1-.25) = 20*.75 = 15 per unit

Break Even Point = 842622/15 = 56175 units.

If the tax rate had been 34%, the Fixed cash outflows would have been

(325000*.66)-(40000*.34) = 214500-13600 = 200900

PV of fixed costs would be 200900*3.6048 = 724204

Break Even Point = 724204/15 = 48280 units.

If discount rate had been 10%, the PV of fixed cost would be 3.7908*233750 = 886100

BEP would be 886100/15 = 59073 units

Accounting BEP is ((325000*5)+(40000*5))/20 = 91250 units

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