Question

The operating cost for a machine is $40,000 for year 1 and then it increases by $5,000per year through year 10. The equivalent uniform annual cost for the machine (years 1–10) at an interest rate of 9% per year is calculated as:

Answer 1

Introduction: On looking at the problem it is evident that there is a gradient series with the operating cost increased by a constant sum of $5000, the same being an arithmetic gradient. The same gradient is to be converted to an equivalent uniform annual cost. The same is computed as follows,

Given Data

A' = $40000

G = $5000

N = 10 years

i = 9%

To Find

EUAC = A = ?

A = A' + G(A/G,i,n)

A = 40000 + 5000(A/G,9%,10)

Using DCIF tables

A = 40000 + 5000(3.7978)

A = $58989

The EUAC for the machine is $58989