# Discounted Payback Period

## Definition

Discounted Payback Period is the duration that an investment requires to recover its cost taking into consideration the time value of money.

Topic Contents:

## Formula

**Discounted Payback Period:**

= (A - 1) + | Cost - Cumulative Present Value of Cash Flow^{( A - 1)} |

Present Value of Cash Flow^{A} |

Where:

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

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

Present Value of Cash Flow^{A} | = | Present value of Net cash flow in Year A. |

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

Cost | = | The initial cost of investment. |

## Explanation

Discounted Payback Period is the time required to recover the present value of cash flows equal to the cost of investment.

Simple payback period does not take into account the principles of time value of money. Why this can be a problem when analyzing the payback period can be explained through a simple example.

Consider the cash flow pattern of the following investments that have an initial cost of $100,000 each:

Year | Investment A $ | Investment B $ |

1 | 10,000 | 40,000 |

2 | 20,000 | 30,000 |

3 | 30,000 | 20,000 |

4 | 40,000 | 10,000 |

5 | 5,000 | 5,000 |

Total | 105,000 | 105,000 |

Both investments have a payback period of exactly 4 years. However, 70% of the recovery of investment A occurs in 3rd and 4th years whereas 70% of the amount in investment B is recovered in the first 2 years.

By investing in Investment A, the investor will have to sacrifice the additional gain he could have earned by simply re-investing a higher proportion of cash inflows **earlier** in other investment opportunities had he opted for Investment B.

Clearly, investment B has a better payback but the simple payback period fails to account for the timing of cash flows **within the payback period.**

As with simple payback period, the investments with shorter discounted payback period should be preferred as it reduces the risk and uncertainty associated with investments.

The calculation of discounted payback period is very similar to the simple payback period calculation.

## Example

Mr. A is considering to invest in a business.

The business will cost $100,000 to set up and is expected to generate the following yearly net cash flows:

Year | $ |

1 | (20,000) |

2 | 30,000 |

3 | 35,000 |

4 | 40,000 |

5 | 150,000 |

The cost of capital is 10%.

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

## Solution

Year | Cash Flows | Discount Factor @ 16% | Present Value of Cash Flows | Cummulative Present Value of Cash Flows |

$ | $ | $ | ||

1 | (20,000) | 0.909 | -18,180 | -18,180 |

2 | 30,000 | 0.825 | 24,780 | 6,600 |

3 | 35,000 | 0.751 | 26,285 | 32,885 |

4 | 40,000 | 0.683 | 27,320 | 60,205 |

5 | 150,000 | 0.621 | 93,150 | 153,365 |

Discounted Payback Period:

= (A - 1) + | Cost - Cumulative Present Value of Cash Flow^{( A - 1)} |

Present Value of Cash Flow^{A} |

= 4 + | 100,000 - 60,205 |

93,150 | |

= 4.43 years or 4 years and 157* days |

* 0.43 x 365 = 157

## Advantages

- Discounted Payback Period incorporates the principle of time value of money into the payback period calculation which provides a more relevant measure of the risk of non-recoverability of investments.

## Limitations

Discounted Payback Period suffers most of the drawbacks of simple payback period summarized below:

- Does not take into account the post-payback period cash flows of investments.
- Its calculation can be problematic where multiple negative cash flows are incurred during the investment period. This problem can be solved however by applying the modified payback period approach.
- Involves the use of judgment in its interpretation as it does not present a definitive decision rule unlike other investment appraisal methods such as NPV (e.g. all positive NPV investment should be accepted).