Question

Suppose a machine costs $500,000 and requires $75,000 in pre-tax annual operating costs. The machine will be fully depreciated on a straight-line basis over its useful life of 10 years, a#er which it will have zero salvage value. If the required return is 12% and the tax rate is 22%, then what is the equivalent annual cost of the machine?

A)$146,992.08

B) $135,992.08

C) $152,492.08

D) $88,492.08

E) $40,992.08

Answer 1

In the given case, we have

Initial cost of machine = $500000

Annual pre tax operating cost = 75000

Tax rate = 22%

Required return = 12%

we need to determine Equivalent annual cost of machine i.e cost to be incurred each year

so for this we need to use following formula

Pv of cost of machine = Annual cost of machine incurred * PVAF(12%,10)

Here PVAF(12%,10) is Present value annuity factor with required rate of return is 12% with no. of period is 10 years i.e 5.650

Calculation of PV of cost of machine is as follow

1. Initial cost of machine = $500000

2. Pv of operating cost= Annual post tax operating cost * PVAF(12%,10)

Here Annual post tax operating cost is 75000(1-tax) = 75000 * 0.78 = 58500

Thus Pv of operating cost = 58500 * 5.650 = 330525

Thus PV of cost of machine = Initial cost of machine + Pvt of operating cost

i.e Pv of cost of machine = 500000+330538 = 830538

Now for calculating Annual cost of machine (Equivalent annual cost of machine) we will calculate

PV of cost of machine/PVAF(12%,10)

i.e 830538/5.65022302825 = $146992.0737

Thus Ans is (A)