Question

Most businesses replace their computers every two to three years. Assume that a computer costs $2,000 and that it fully depreciates in 3 years, at which point it has no resale value and is thrown away.
If the interest rate for financing the equipment is equal to I, show how to compute the minimum annual cash flow that a computer must generate to be worth the purchase.

Answer 1

Answer:

$2000=Z/(1+i)^1+Z/(1+i)^2+Z/(1+i)^3

Explanation:

let Z be the annual minimum cash flow

The internal rate of approach can be used here, in other words, the rate of return at which capital outlay of $2000 is equal present values of future cash flows

In year 1, present value of cash =X/discount factor

year 1 PV=Z/(1+i)^1

year 2 PV=Z/(1+i)^2

year 3=Z/(1+i)^3

Hence,

$2000=Z/(1+i)^1+Z/(1+i)^2+Z/(1+i)^3

Solving for Z above would give the minimum annual cash flow that must be generated for the computer to worth the purchase

Assuming i, interest rate on financing is 12%=0.12

Z can be computed thus:

$2000=Z(1/(1+0.12)^1+(1/(1+0.12)^2+(1+0.12)^3)

$2000=Z*3.09497902

Z=$2000/3.09497902

Z=$646.21