# Payback Period Vs Discounted Payback Period

Payback period is the time required to recover the cost of initial investment, it the time which the investment reaches its breakeven points. It calculates the number of years we need to generated the initial cost of investment. Its recovery depends on cash flow only, it not even consider the time value of money. This method completely ignores accrual basic and the time value of money.

The payback period will help the company to use their fund more effective, it recommends to invest in a project which has the shortest payback period. It will be less risky if we can receive money back faster.

## Payback Period Formula

\[Payback\ Period = { {Initial\ Investment} \over Net\ Annual\ Cash\ Inflow}\] |

## Example

Company A invests in a new machine which expects to increase the contribution of $100,000 per year for five years. There are no other expenses related to this additional machine. The cost of machine is $ 300,000. We assume all contributions equal to cash flow.

Payback period = $ 300,000 / $100,000 = 3 years

## Example 2

Company B is considering to invest in a new project. This project cost $ 300,000 expect to generate the cash flow as the following:

Year | Cash Inflow per year | Accumulate cash inflow |
---|---|---|

0 | (300,000) | (300,000) |

1 | 50,000 | (250,000) |

2 | 100,000 | (150,000) |

3 | 100,000 | (50,000) |

4 | 200,000 | 150,000 |

5 | 150,000 | 300,000 |

The payback period would be: 3 years + 50,000/200,000 = 3.25 years

## What are the Advantages of Payback Period?

Advantage of Payback Period | |
---|---|

Easy to understand | It is easy to understand for most people. The shorter the project takes to generate the initial investment, the less risk the company take and it expects to generate more profit. |

Easy to calculate | Payback period calculation is not complicated, it does not even involve the present value. |

Reliable forecast | The short term forecast will more reliable and less fluctuate compare to the long term budget. |

Improve liquidity | It only focuses on the short term profit, the company liquidity will look better. |

## What are the Disadvantages of Payback Period?

Disadvantages of Payback Period | |
---|---|

Ignore the whole project | Some projects may generate low cash flow at the beginning which lead to a longer payback period. However, it may have a huge cash inflow after that. Without analyzing the whole project, we may not be able to understand its full potential. |

Focus on Cash flow, not profit | The cash inflow is not the profit, it can be miss understanding. |

Ignore time value of money | This method completely ignores the time value of money. The future cash flow has less value in the present. |

## Discounted Payback Period

Discounted Payback period is the tool that uses present value of cash inflow to measure the time require to recover the initial investment. The concept is the same as the payback period except for the cash flow used in the calculation is the present value. It is the method that eliminates the weakness of the traditional payback period.

## Formula

\[Discounted\ Cash\ Inflow = { {Actual\ Cash\ inflow} \over (1+i)^n}\] |

**n**is the number of period, can be month or year**i**is the interest rate per period, it must be consistent with n above.

\[Discounted\ Payback\ Period = {A +}{ {B} \over C}\] |

**A**is the nth period which project generate accumulated negative cash flow.**B**is the negative number at the end of period A**C**is the cash inflow of period A + 1

## Example

Company A has selected a project which costs $ 350,000 and it expects to generate cash inflow $ 50,000 for ten years. The cost of capital is 10%.

Year | Cash Flow | DF | Present Value | Acc Cash Flow |

0 | (300,000) | 1.00 | (300,000) | (300,000) |

1 | 70,000 | 0.91 | 63,630 | (236,370) |

2 | 70,000 | 0.83 | 57,820 | (178,550) |

3 | 70,000 | 0.75 | 52,570 | (125,980) |

4 | 70,000 | 0.68 | 47,810 | (78,170) |

5 | 70,000 | 0.62 | 43,470 | (34,700) |

6 | 70,000 | 0.56 | 39,480 | 4,780 |

7 | 70,000 | 0.51 | 35,910 | 40,690 |

8 | 70,000 | 0.47 | 32,620 | 73,310 |

9 | 70,000 | 0.42 | 29,680 | 102,990 |

10 | 70,000 | 0.39 | 26,950 | 129,940 |

Discounted Payback period = 5 year + 34,700/39,480 = 5.87 years.

Advantages of discounted cash flow | |
---|---|

Easy to calculate | Discounted payback is straight forward, there no special software or system requires. |

Easy to understand | The method is easy to explain to others. The shorter the payback period, the less risk of the project. |

Suitable for the tech industry | This tool is very good for high tech software where the product’s life is very short, so the shorter the payback, the better the project. |

Fill the gap of the payback period | Payback period ignore the time value of money so this method have fixed this issue. |

## Limitation of Discounted Payback Period

Discounted Payback Period | |
---|---|

Ignore total project profitability | Similar to payback period, this method does not take into account the whole project profit. The project will be selected if it can payback in a short time. |

Focus on the early cash flow | In real practice, the early cash flow usually low. The project need sometime to generate significant cash flow. So such kind of projects will not be selected under discounted payback period. |

Ignore cash flow after payback period | This method completely ignore the cash flow generate after the payback period. The project may take long time to payback but the cash flow after that is huge. So by ignoring it, we may select the less profitable project. |

## Factor Effect Cash Inflow

The impact on Discounted Payback period | |
---|---|

Depreciation | Depreciation expense is not the cash flow, so it must be excluded from cash flow calculation. |

Sunk Cost | The sunk cost is the cost that already incurs, so it will not impact the decision. It needs to exclude from the calculation as it has no effect. |

Opportunity Cost | Opportunity Cost is the income that we give up in order to take any specific activities. |

Change in working capital | The change in working capital will impact the cash flow of the project. The increase of working capital means the company has pay money to acquire them and vice versa. |