Office Automation, Inc, must choose between two copiers, the XX40 of the RH45. T

Question

Office Automation, Inc, must choose between two copiers, the XX40 of the RH45. The XX40 costs $1,500 and will last for three years. The copier will require a real after-tax cost of $120 per year after all relevant expenses. The RH45 costs $2,300 and will last five years. The real after-tax cost for the RH45 will be $150 per year. All cash flows occur at the end of the year. The inflation rate is expected to be 5 percent per year, and the nominal discount rate is 14 percent. Which copier should the company choose?

Explanation / Answer

XX40:

Cost of XX40 = $1,500

Number of years = 3 years

After-tax cost = $120 per year

RH45:

Cost of RH45 = $2,300

Number of years = 5 years

After-tax cost = $150 per year

Inflation rate (h) = 5% per year

Nominal Discount rate = 14%

Calculating Real Interest rate (r):

1+Nominal interest rate = (1+Real interest rate) * (1+Inflation rate)

Rearranging terms, we have

Real interest rate = [(1+Nominal interest rate) / (1+Inflation rate)] – 1

Real interest rate = [(1+0.14) / (1+0.05)] - 1

Real interest rate = [(1.14 / 1.05)] – 1

Real interest rate = 1.0857 – 1

Real interest rate = 0.0857 (or) 8.57%

Real interest rate (r) = 8.5%

Calculating Present Value Costs of both copiers:

XX40:

EAC = $1,500 (A/P, 3, 8.57%) + $120 (A/F, 3, 8.57%)

EAC = [$1,500 * 0.3920] + [$120 * 0.168530]

EAC = [$588 + $20.22]

EAC = $608.22

RH45:

EAC = $2,300 (A/P, 5, 8.57%) + $150 (A/F, 5, 8.57%)

EAC = [$2,300 *0.2542] + [$150 * 0.168530]

EAC = $584.66 + $25.27

EAC = $609.93

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