# Payback Period

## Definition

Payback Period is the duration that an investment takes to recover its cost.

Topic Contents:

## Formula

Payback Period | = (A - 1) + | Cost - Cumulative Cash Flow^{( A - 1)} |

Cash Flow^{A} |

Where:

A | = | Year in which the cumulative cash flows from investment exceed the initial cost. |

A - 1 | = | The year prior to A. |

Cash Flow^{A} | = | Net cash flow in Year A. |

Cumulative Cash Flow^{( A - 1)} | = | Cumulative Cash Flows from investment at the end of the Year (A - 1). |

Cost | = | The initial cost of investment. |

## Explanation

Payback Period is the duration needed to recover the cost of investment.

All other things equal, the investment with a shorter payback period should be preferred.

Long payback periods increase the riskiness of investments because the uncertainty increases with the length of time.

Consider the following two investments.

- Investment A has NPV of $2,000,000 and payback period of 3 years.
- Investment B has NPV of $2,100,000 and payback period of 15 years.

Now, even though Investment B is slightly more profitable, Investment A is probably the better bargain because of the fact that a lot could go wrong in the 12 additional years required for investment B to recover its cost.

There are several factors that create uncertainty over a period of time such as changes in macro-economic factors, technology, legislation, competitive environment, consumer tastes, political environment and tax laws, all potentially affecting the feasibility of investments.

## Example 1

Mr. A is considering to invest in a poultry farm.

The project will require an initial investment of $250,000 and is expected to generate the following cash flows thereafter:

Year | $ |

1 | (50,000) |

2 | 80,000 |

3 | 130,000 |

4 | 110,000 |

5 | (100,000) |

6 | 160,000 |

7 | 200,000 |

**Calculate the payback period and comment on your answer.**

## Solution

Year A | Cash Flows $ | Cumulative Cash Flows $ |

1 | (50,000) | (50,000) |

2 | 80,000 | 30,000 |

3 | 130,000 | 160,000 |

4 | 110,000 | 270,000 |

5 | (100,000) | 170,000 |

6 | 160,000 | 320,000 |

7 | 200,000 | 480,000 |

The cumulative cash flows from investment exceed the initial investment of $250,000 in the year 4 (Year A).

Payback Period | = (A - 1) + | Cost - Cumulative Cash Flow^{( A - 1)} |

Cash Flow^{A} | ||

= 3 + | 250,000 - 160,000 | |

110,000 | ||

= 3.82 years or 3 years and 299 days* |

* 0.82 x 365 = 299

**Note:**

*You may think of the cash outflow of $50,000 incurred in the first year of operation as part of the initial investment cost. In that case, you should consider the cost of investment in the payback period calculation as $300,000 ($250,000 + $50,000) and calculate the cumulative cash flows excluding the $50,000. [3 + (300,000 - 210,000) ÷ 110,000] Your answer will be the same as above.*

**Comment**

The initial investment in poultry farm will be recovered in approximately 4 years which seams a reasonable payback duration for the type of investment.

Mr. A should compare the payback period from the poultry farm business with that of any other investment option.

The relative importance of payback period in comparison to other investment appraisal methods depends on the circumstances of Mr. A such as his appetite for risk, liquidity, business plan and personal preferences. In any case, his decision should be primarily based on the more theoretically sound appraisal methods such as NPV or IRR.

## Modified Payback Period

It may be noted from the example above that in the Year 5, a cash outflow of $100,000 is expected which could be due to further capital investment or trading losses. The result of the cash outflow in year 5 is that the cumulative cash inflows again drop below the cost of investment.

To solve this anomaly, we may calculate a modified payback period that calculates the length of time required to recover the entire cash outflows of the proposed investment.

Modified Payback Period | = (A - 1) + | Cost - Cumulative Cash Flow^{( A - 1)} |

Cash Flow^{A} |

Where:

A | = | Year in which the cumulative positive cash flows from investment exceed the total negative cash flows. |

A - 1 | = | Year prior to A. |

Cash Flow^{A} | = | Net cash flow in Year A. |

Cumulative Cash Flow^{( A - 1)} | = | Cumulative Cash Flows from investment at the end of the Year (A - 1). |

Cost | = | Total negative cash flows investment. |

## Example 2

(Same information from Example 1 is reproduced here)

Mr. A is considering to invest in a poultry farm.

The project will require an initial investment of $250,000 and is expected to generate the following cash flows thereafter:

Year | $ |

1 | (50,000) |

2 | 80,000 |

3 | 130,000 |

4 | 110,000 |

5 | (100,000) |

6 | 160,000 |

7 | 200,000 |

**Calculate the modified payback period.**

## Solution

Year A | Positive Cash Flows $ | Cumulative Positive Cash Flows $ |

1 | - | - |

2 | 80,000 | 80,000 |

3 | 130,000 | 210,000 |

4 | 110,000 | 320,000 |

5 | - | 320,000 |

6 | 160,000 | 480,000 |

7 | 200,000 | 680,000 |

Cost = 250,000 (initial cost) + 50,000 (year 1) + 100,000 (year 5)

= $400,000

The cumulative positive cash flows from investment exceed the total negative cash flows of $400,000 in the year 6 (Year A)

Modified Payback Period | = (A - 1) + | Cost - Cumulative Cash Flow^{( A - 1)} |

Cash Flow^{A} | ||

= 5 + | 400,000 - 320,000 | |

160,000 | ||

= 5.5 years or 5 years and 6* months |

* 0.5 x 12 = 6

## Advantages

- Payback Period allows investors to assess the risk of an investment attributable to the length of its investment life.
- Easy to calculate and understand.

## Limitations

- Basic payback period ignores the time value of money. This limitation can be overcome by applying the discounted payback period.
- Payback period does not take into account the level of cash flows of an investment
**after**the payback period. In other words, payback period ignores the overall profitability of investments. - Basic payback period can be difficult to calculate where multiple negative cash flows are incurred during the investment period. This problem can be solved by calculating the modified payback period as discussed above.
- Payback period does not provide a theoretically absolute decision rule like other appraisal methods (e.g. all investments with positive NPV should be accepted) and is therefore susceptible to subjective interpretation.