Question

A firm decides to invest in a new piece of machinery which is expected to produce
an additional revenue of $8000 at the end of every year for ten years. At the end of
this period the firm plans to sell the machinery for scrap, for which it
expects to receive $5000. What is the maximum amount that the firm should pay
for the machine if it is not to suffer a net loss as a result of this
investment? You may assume that the discount rate is 6% compounded
annually.

Answer 1

We need to find the present worth of the additional revenue and salvage value at an interest rate of 6%.

PW = 8000*(A/P,10,6%) + 5000(P/F,10,6%)

If you have access to time value of money tables you can look these up. Otherwise,

\[P = A\left[ (1+i)^n - 1 \over i(i+i)^n \right]\]and\[P = F \left[ 1 \over (1+i)^n \right]\]where A is the annual revenue, F is the salvage value, i is the interest rate, and n is the number of compounding periods.
The maximum acceptable price of the machine is equal to the PW of the machine. This will mean the company breaks even on the investment.