Question

Seth Fitch owns a small retail ice cream parlor. He is considering expanding the business and has identified two attractive alternatives. One involves purchasing a machine that would enable Mr. Fitch to offer frozen yogurt to customers. The machine would cost $7,980 and has an expected useful life of three years with no salvage value. Additional annual cash revenues and cash operating expenses associated with selling yogurt are expected to be $6,080 and $800, respectively. Alternatively, Mr. Fitch could purchase for $9,720 the equipment necessary to serve cappuccino. That equipment has an expected useful life of four years and no salvage value. Additional annual cash revenues and cash operating expenses associated with selling cappuccino are expected to be $8,300 and $2,260, respectively. Income before taxes earned by the ice cream parlor is taxed at an effective rate of 20 percent.

Required
Determine the payback period and unadjusted rate of return (use average investment) for each alternative.

Answer 1

* For the machine investment decision:

+ Payback period: 1.68 years

+ Unadjusted rate of return: 26.27%

* For the equipment investment decision:

+ Payback period: 1.83 years

+ Unadjusted rate of return: 29.71%

Step-by-step explanation:

* For the machine investment decision:

Payback calculation:

+ Incremental in yearly cashflow = ( Increase in revenue - Increase in operating expenses ) x ( 1 - tax rate) + Tax shield from increase in depreciation (which is Depreciation in one year x Tax rate) = (6080 - 800 ) * 0.8 + (7980/3)*0.2 = $4756

+ Payback period = Increase in yearly cashflow / Initial investment = 7980 /4756 = 1.68 years

Unadjusted rate of return:

+ Increamental profit in one-year= ( Increase in revenue - Increase in operating expenses - Increase in depreciation) x ( 1 - tax rate) = (6080 - 800 - 7980/3) * 0.8 = $2096

+ Unadjusted rate of return = Increamental profit in one-year / Initial investment = 2096 / 7980 = 26.27%

* For the equipment investment decision:

Payback calculation:

+ Incremental in yearly cashflow = ( Increase in revenue - Increase in operating expenses ) x ( 1 - tax rate) + Tax shield from increase in depreciation (which is Depreciation in one year x Tax rate) = (8300 - 2260 ) * 0.8 + (9720/4)*0.2 = $5318

+ Payback period = Increase in yearly cashflow / Initial investment = 9720 /5318 = 1.83 years

Unadjusted rate of return:

+ Increamental profit in one-year= ( Increase in revenue - Increase in operating expenses - Increase in depreciation) x ( 1 - tax rate) = (8300 - 2260 - 9720/4) * 0.8 = $2888

+ Unadjusted rate of return = Increamental profit in one-year / Initial investment = 2888 / 9720 = 29.71%