a.Luke Athletics Inc. has purchased a $200,000 machine to produce tennis balls.
ID: 2722135 • Letter: A
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.
1.What is the present value of the break-even point?
2.What will be the impact of an increase in the tax rate from 25% to 34% on the breakeven point?
3.What will be the impact of a decrease in the cost of capital from 12% to 10% on the project breakeven point?
4.How is it different from accounting breakeven point?
Explanation / Answer
Equivalent Annual Cost of Machine Machine Purchase Cost (A) $200,000.00 Annuity Factor for 5 years at 12% (B) 3.6048 EAC (A/B) $55,481.95 Present Value of Breakeven Point = EAC of Machine + Fixed Cost * (1-tax rate) - Depreciation * tax rate / (Sale Price - Variable Cost) * (1 - tax rate) = 55481.95 + 325000 * (1-0.25) - 40000 * 0.25 / (35 - 15) * ( 1 - 0.25) = (55481.95 + 243750 - 10000) / 15 = 289231.95 / 15 = 19282.13 Increase in tax rate from 25% to 34% = 55481.95 + 325000 * (1-0.34) - 40000 * 0.34 / (35 - 15) * ( 1 - 0.34) = (55481.95 + 214500 - 13600) / 13.20 = 256381.95 / 13.20 = 19422.87 Decrease in Cost of Capital from 12% to 10% EAC of machine changes to Machine Purchase Cost (A) $200,000.00 Annuity Factor for 5 years at 12% (B) 3.7908 EAC (A/B) $52,759.50 = 52759.50 + 325000 * (1-0.25) - 40000 * 0.25 / (35 - 15) * ( 1 - 0.25) = (52759.50 + 243750 - 10000) / 15 = 286259.50 / 15 = 19083.97 Accounting BreakEven Point (Fixed Cost + Depreciation) / (Sales Price - Variable Cost) = 325000 + 40000 / 20 = 365000 / 20 = 18250 units
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