You are the project manager for Insomniacs International. Since you don't sleep much, you get a lot of project work done. You're considering recommending a project that costs $575,000; expected inflows are $25,000 per quarter for the first two years and then $75,000 per quarter thereafter. What is the payback period?

The Payback Period (PBP) represents how long will it take a project to recover the initial investment. It is a tool that can be used for one or multiple projects to compare which one will return the initial investment first.

To find the answer, we will lay out a table with the information provided in the problem:

Starting the project we have an initial investment of $575.000 and we will write it down as quarter 0.
From then on, for 2 years we will quarterly earnings of $25.000.
After 2 years have passed, we will have quarterly earning of $75.000.
We will add up the inflows of each quarter until we have a cumulative inflow of $0. This means that, by this quarter, the earnings will be the same as the initial investment.

Q Inflows Cumulative inflows

0 -$ 575.000 -$ 575.000

1 $ 25.000 -$ 550.000

2 $ 25.000 -$ 525.000

3 $ 25.000 -$ 500.000

4 $ 25.000 -$ 475.000

5 $ 25.000 -$ 450.000

6 $ 25.000 -$ 425.000

7 $ 25.000 -$ 400.000

8 $ 25.000 -$ 375.000

9 $ 75.000 -$ 300.000

10 $ 75.000 -$ 225.000

11 $ 75.000 -$ 150.000

12 $ 75.000 -$ 75.000

13 $ 75.000 $ -

Where Q = Quarter

We can see that by quarter 13, the initial investment is equal to the cumulative inflows, as it amounts to $0.
To find the answer in months, we will proceed to multiply the quarters by 3, as each quarter has 3 months.
13 quarters x 3 months = 39 months.

In conclusion, the payback period is 39 months.