Answer:
The payback period is 13 quarters, which is the same as 39 months.
Step-by-step explanation:
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.