5. El Paso Company is planning to get a machine that will cost $14,000 and is ex

Question

5. El Paso Company is planning to get a machine that will cost $14,000 and is expected to last for 7 years. The company uses straight-line depreciation. The tax rate of El Paso is 31% and the proper discount rate in this case is 12%.Find the minimum pretax earnings per year that the machine must generate to become profitable.The machine is expected to have $4000 pretax earnings annually, with a standard deviation of $1000. Calculate the probability that the machine will turn out to be profitable. Show solutions.

Explanation / Answer

Machine cost = 14000

Annual Depreciation Expenses = (Machine cost - Salvage Value)/Useful Life

Annual Depreciation Expenses = (14000-0)/7

Annual Depreciation Expenses = 2000

Minimum Annual cash Flow = Machine cost / PVIFA(12%,7)

Minimum Annual cash Flow = 14000/4.563757

Minimum Annual cash Flow = $ 3067.65

Minimum pretax earnings per year = (Minimum Annual cash Flow - Annual Depreciation Expenses*tax rate )/(1-tax rate)

Minimum pretax earnings per year = (3067.65-2000*31%)/(1-31%)

Minimum pretax earnings per year = $ 3547.32

Z = (Minimum pretax earnings per year - Expected pretax earnings per year )/standard deviation

Z = (3547.32-4000)/1000

Z = -0.45268

Using Excel Formula

Probability = 1 -normsdist(z)

Probability = 1- normsdist(-0.45268)

Probability = 67.46%

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