*Payback period is the time required for positive project cash flow to recover negative project cash flow from the acquisition and/or development years. Payback can be calculated either from the start of a project or from the start of production.*

Payback period is commonly calculated based on undiscounted cash flow, but it also can be calculated for Discounted Cash Flow with a specified minimum rate of return. The intuition behind payback period measure is that the investor prefers to recover the invested money as quickly as possible.

One of the disadvantages of the payback period is that it doesn’t analyze the project in its lifetime; whatever happens after investment costs are recovered won’t affect the payback period. For example, if two investment alternatives have 10-year lifetimes, and investment alternatives A and B have 4 and 6 year payback periods, alternative A is more desirable from the payback period point of view, and it is not important how profitable alternative A would be after the 4^{th} year and B after the 6^{th} year.

Payback period can be useful when the investor has some time constraints and wants to know the fastest time that s/he can get her money back on the investment.

#### Example 9-1

Calculate the payback period for an investment with following cash flow.

C=\$200 | C=\$250 | I=\$150 | I=\$180 | I=\$220 | I=\$200 |

0 | 1 | 2 | 3 | 4 | 5 |

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
---|---|---|---|---|---|---|

ATCF | -200 | -250 | 150 | 180 | 220 | 200 |

Cummulative ATCF | -200 | -450 | -300 | -120 | 100 | 300 |

As you can see, in year 4, the cumulative cash flow sign changes from negative to positive, meaning that at some point between year 3 and 4, costs (the summation of 200 at time zero and 250 dollars investments in year 1) would be recovered by generated profit. So, the payback period is somewhere in third year. To calculate the fraction, we can simply divide the 120 (cumulative cash flow in year 3) by 220 (cash flow in year 4). Therefore the payback period equals: 3 + 120/220 = 3.55 years.

Note that payback period can be reported from the beginning of the production. In this case, the payback period for the above example is 3.55 - 2 = 1.55 years after production begins, because production starts from year 2.

As explained, payback period can be calculated for discounted cash flow as well. The following example includes these calculations.

#### Example 9-2

Calculate the discounted payback for the cash flow in example 9-1 considering a minimum rate of return of 15%.

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
---|---|---|---|---|---|---|

ATCF | -200 | -250 | 150 | 180 | 220 | 200 |

DCF | -200 | -217.39 | 113.42 | 118.35 | 125.79 | 99.44 |

Cummulative DCF | -200 | -417.39 | -303.97 | -185.62 | -59.83 | 39.60 |

Similar to the calculations in Example 9-1, the discounted payback period equals 4 + 59.83/99.44 = 4.6 years. And the discounted payback period from the beginning of production (year 2) equals 2.6 years.

### Mutually exclusive investments and payback analysis

#### Example 9-3

Consider two mutually exclusive investments with the following cash flows. Which project is more economically satisfactory assuming a minimum rate of return of 15%?

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
---|---|---|---|---|---|---|

A | -$200 | $600 | ||||

B | -$200 | $80 | $80 | $80 | $80 | $80 |

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
---|---|---|---|---|---|---|

ATCF | -200 | 0 | 0 | 0 | 0 | 600 |

CumulativeATCF | -200 | -200 | -200 | -200 | -200 | 400 |

Payback period = 4+200/600=4.33

NPV_{A} = 98.31 dollars at i*=15%

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
---|---|---|---|---|---|---|

ATCF | -200 | 80 | 80 | 80 | 80 | 80 |

Cumulative ATCF | -200 | -120 | -40 | 40 | 120 | 200 |

Payback period = 2+40/80=2.5

NPV_{B} = 68.17 dollars at i*=15%

Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
---|---|---|---|---|---|

0 | -80 | -80 | -80 | -80 | 520 |

For project A-B:

NPV_{A-B}= 30.13 dollars at i*=15%

ROR_{A-B}= 20.40%

So, we can conclude that project A is more economically satisfactory than project B. Note that although project B has a lower payback period, project A is better for investment and has better return. It could be concluded by comparing the NPVs as well.

Italicized sections are from *Economic Evaluation and Investment Decision Methods *by Stermole and Stermole*.*