Question

Calculate the payback period considering the time-value of money.

Accusoft Systems is offering small business owners a software package that keeps track of many accounting functions from bank transactions to sales invoices. The site license will cost $46,000 to install and will require a fee of $3500 every 3 months. If your company can save $13,500 every quarter and have the security of managing its books in-house, how long will it take for you to recover the investment at an interest rate of 11% per quarter?

The time taken to recover the investment is determined to be

Answer 1

ANSWER:

I = 11% per quarter

Benefits per quarter = savings per quarter - install fee every 3 months = $13,500 - $3,500 = $10,000

initial cost = $46,000

n = ?

in order to find the time taken to recover the investment the present worth will have to be zero.

pw = initial cost + benefits per quarter(p/a,i,n)

0 = -46,000 + 10,000(p/a,11%,n)

46,000 = 10,000(p/a,11%,n)

46,000 / 10,000 = (p/a,11%,n)

4.6 = (p/a,11%,n)

looking into the compounding factor tables we get that n is between 6 and 7 quarters and solving further we get that i is 6.75 quarters

so the time taken to recover the investment is 6.75 quarters.