Question

In: Finance

An office uses 1,000 photocopies per working day and there are 200 working days per year....

An office uses 1,000 photocopies per working day and there are 200 working days per year. Brand A copier costs $3,000 and will produce a total of one million copies before it wears out. Brand B’s copier costs $5,000 and will produce 2 million copies over its life. Maintenance and materials cost 3 cents per copy with either machine, and neither machine will have any salvage value. The required return is 10 percent per year. Which machine should the company acquire.
Please solve with out using excel. and show steps please.

Expert Solution

Annual requirement of photocopies = Daily required photocopy x working days per year

=1,000 x 200 = 200,000

Useful life of Brand A copier = Total capacity / Annual requirement

= 1,000,000/200,000 = 5 years

Useful life of Brand B copier = Total capacity / Annual requirement

= 2,000,000/200,000 = 10 years

We can compute EAC of both copiers to analyze and choose best option as they have unequal life span.

EAC = Asset price x Discount rate/ [1-(1+Discount rate)^{-Number of periods}] + Annual expense

EAC of Copier A = $ 3,000 x 0.1 / [(1 – (1+0.1)^-5 ]+ $ 0.03 x 200,000

= $ 3,000 x 0.1 / [(1 – (1.1)^-5 ]+ $ 6,000

= $ 300 / [(1 – (1.1)^-5 ]+ $ 6,000

= $ 300 / (1 – 0.620921323059155) + $ 6,000

= $ 300 / 0.379078676940845 + $ 6,000

= $ 791.392442384236 + 6,000 = $ 6,791.39244238424 or $ 6,791.39

EAC of Copier B = $ 5,000 x 0.1 / [(1 – (1+0.1)^-10 ]+ $ 0.03 x 200,000

= $ 5,000 x 0.1 / [(1 – (1.1)^-10 ]+ $ 6,000

= $ 500 / [(1 – (1.1)^-10 ]+ $ 6,000

= $ 500 / (1 – 0.385543289429531) + $ 6,000

= $ 500 / 0.614456710570469 + $ 6,000

= $ 813.726974412558 + 6,000 = $ 6,813.72697441256 or $ 6,813.73

Copier A should be acquired as its equivalent annual cost is less than that of Copier B.

jeff jeffy answered 8 months ago

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