Question

The manager of a canned-food processing plant has two mutually exclusive labeling machine options. On the basis of a rate of return analysis with a MARR of 9% per year, determine which model is economically better
Model X Y

First cost, $ -50,000 -90,000

AOC, $ per year -6,000 -4,000

Salvage value, $ 10,000 15,000

Life, years 5 10

Answer 1

As the two machines have unequal lives, the EAC of each machine should be compared to determine which model is economically better.

EAC = (NPV * r) / (1 - (1 + r)-n)

where NPV = net present value

r = MARR

n = life of machine in years

NPV = sum of present values of machine's cash flows

present value of each cash flow = cash flow / (1 + MARR)t

where t = number of years after which the cash flow occurs.

The NPV and EAC of machine are calculated as below :

Cash outflow in year 0 = initial cost

Cash outlflow in years 1 to 9 = AOC

Cash inflow in year 10 = salvage value - AOC

As Machine X has a higher EAC (lower negative EAC), Model X is economically better