Question

You are about to buy a machine for $100,000 and you will need $22,000 as an operating cost in the first year then it will increase by $1,000 per year, if the life time of the machine is only five years, the equivalent uniform annual cost at an interest rate of 8% per year is closest to:

A.$40250 per year
B.$55920 per year
C.$35235 per year
D.$48890 per year

Answer 1

Initial Cost = 100,000

Operating Cost in the first year 22,000 and increases by 1,000 per year

Life = 5 years

Interest rate = 8%

Calculate equivalent uniform annual cost.

Step 1 – Calculate the Present Worth

PW = 100,000 + [22,000 (P/A, 8%, 5) + 1,000 (P/G, 8%, 5)]

PW = 100,000 + [22,000 (3.99271) + 1,000 (7.3724)] = 195,212

Step 2 – Calculate equivalent uniform annual cost

EUAC = PW (A/P, 8%, 5)

EUAC = 195,212 (A/P, 8%, 5)

EUAC = 195,212 (0.25046)

EUAC = 48,892.7

The closest answer will be D.$48,890 per year.