Discount rate

%

Initial investment

$

Steady cash flow

Annual cash flow

$

Payback period

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mos

Discounted payback period

yrs

mos

Irregular cash flow

Cash flow - year 1

$

Cash flow - year 2

$

Cash flow - year 3

$

Cash flow - year 4

$

Cash flow - year 5

$

Discounted payback period

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yrs

…

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This payback period calculator is a tool that lets you estimate the number of years required to break even from an initial investment. You can use it when analyzing different possibilities to invest your money and combine it with other tools, such as the Net Present Value or Internal Rate of Return metrics.

In this article, we will explain the difference between the regular payback period and the discounted payback period. You will also learn the payback period formula and analyze a step-by-step example of calculations.

Imagine that you are going to invest $100,000 and purchase an apartment. You are going to rent it to tenants for $24,000 a year. How many years do you need for this investment to pay back?

The period from now to the moment when your investment will be recovered is called the **payback period**. Intuitively, you can say that it is equal to the total investment sum divided by the annual cash inflow:

`PP = I / C`

where

**PP**is the payback period in years,**I**is the total sum you invested, and**C**is the annual cash inflow - the money you earn.

In the apartment example, you could estimate the payback period with this equation:

`PP = $100,000 / $24,000 = 4.17 years`

The situation gets a bit more complicated if you'd like to take the time value of money into account. After all, your $100,000 will not be worth the same after ten years; in fact, they will be worth a lot less. Every year, your money will depreciate by a certain percentage, called the **discount rate**.

Unlike the regular payback period, the discounted payback period metric takes this depreciation of your money into consideration. The value obtained with the use of the discounted payback period calculator will be closer to reality, although undoubtedly more pessimistic.

If the cash flows are regular (each year you gain the same amount of money), it's quite easy to compute this metric. All you have to do is apply the following formula:

`DPP = - ln(1 - I * R / C) / ln(1 + R)`

where

**DPP**is the discounted payback period in years,**R**is the discount rate,**I**is the total sum you invested, and**C**is the annual cash inflow - the money you earn.

You can check the difference between the PP and DPP of the apartment example. Let's assume a discount rate of 5%:

`DPP = - ln(1 - $100,000 * 0.05 / $24,000) / ln(1 + 0.05) = 4.79 years`

Now, suppose that your project will not bring you a steady cash flow. Let's analyze the example with the apartment more closely. For instance, you can say that you will not be able to find long-term tenants the first two years and will only assume $15,000 of annual income. Additionally, during the fifth year, you will have to renovate the apartment and hence decrease your total profit to $10,000. If you assume a discount rate of 5%, what will be the discounted payback period?

To answer this question, you need to follow the steps below.

- First, you need to write down your cash flow for each year. We suggest you construct a table:

time | Cash flow |
---|---|

initial investment | $100,000 |

year 1 | $15,000 |

year 2 | $15,000 |

year 3 | $24,000 |

year 4 | $24,000 |

year 5 | $10,000 |

year 6 | $24,000 |

year 7 | $24,000 |

year 8 | $24,000 |

- Then, you need to calculate the present value of each of these cash flows. You should use the following formula:

`PVi = Ci / (1 + R) ^ i`

where

**R**is the discount rate - in this case, 5%,**PVi**is the present value of the cash flow in year**i**,**Ci**is the future value of the cash flow in year**i**, and**i**is the year. It is equal to zero for the moment of investing, to one for year 1, etc.

Again, put all of your results in a table.

time | Cash flow | Present value |
---|---|---|

initial investment | $100,000 | $100,000 |

year 1 | $15,000 | $14,286 |

year 2 | $15,000 | $13,605 |

year 3 | $24,000 | $20,732 |

year 4 | $24,000 | $19,745 |

year 5 | $10,000 | $7,835 |

year 6 | $24,000 | $17,909 |

year 7 | $24,000 | $17,056 |

year 8 | $24,000 | $16,244 |

- In this step, find out the cumulative value of your cash flows. You can find it by adding the amount of cash flow in year
**i**to the sum of all cash flows that occurred in the preceding years. Remember that the initial investment is actually an expense, so it should be considered negative in this step.

After you're finished with the calculations, create your final table with results.

time | Cash flow | Present value | Cumulative present value |
---|---|---|---|

initial investment | $100,000 | $100,000 | $ -100,000 |

year 1 | $15,000 | $14,286 | $ -85,714 |

year 2 | $15,000 | $13,605 | $ -72,109 |

year 3 | $24,000 | $20,732 | $ -51,377 |

year 4 | $24,000 | $19,745 | $ -31,632 |

year 5 | $10,000 | $7,835 | $ -23,797 |

year 6 | $24,000 | $17,909 | $ -5,887 |

year 7 | $24,000 | $17,056 | $ 11,169 |

year 8 | $24,000 | $16,244 | $ 27,413 |

- Look at the table above. You will break even at the moment when the cumulative present value will change from a negative to positive number - in this case, sometime between year 6 and 7. To find the exact time, use the following discounted payback period formula:

`DPP = X + Y / Z`

where:

**X**is the year before which DPP occurs - in other words, the last year with a negative balance.**Y**is the cumulative cash flow in the year**Y**(expressed as a positive value), and**Z**is the discounted cash flow in the year following year**Y**.

In our example, you have to input the following values:

`DPP = 6 + $5,887 / $17,056`

`DPP = 6.35 years`

- Oof, that was a lot of calculations! The discounted payback period can be estimated as 6.35 years for this specific investment. You can, of course, save yourself a lot of effort if you input all of the initial data directly into this payback period calculator and let it do all the work. Go ahead and try it! :)

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