# Discounted Payback Period

Last Updated :

21 Aug, 2024

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Dheeraj Vaidya

Table Of Contents

## What is the Discounted Payback Period?

Discounted payback period refers to the time period required to recover its initial cash outlay and it is calculated by discounting the cash flows that are to be generated in future and then totaling the present value of future cash flows where discounting is done by the weighted average cost of capital or internal rate of return.

##### Table of contents

### Discounted Payback Period Formula

**Discounted Payback Period = Year Before the Discounted Payback Period Occurs + (Cumulative Cash Flow in Year Before Recovery / Discounted Cash Flow in Year After Recovery)**

From a capital budgeting perspective, this method is a much better method than a simple payback period.

In this formula, there are two parts.

- The first part is “a year before the period occurs.” This is important because by taking the prior year, we can get the integer.
- The next part is the division between cumulative cash flow in the year before recovery and discounted cash flow in the year after recovery. The purpose of this part is to find out the proportion of how much is yet to be recovered.

### Explanation of Discounted Payback Period in Video

### Example

**Funny Inc. would like to invest $150,000 into a project as an initial investment. The firm expects to generate $70,000 in the first year, $60,000 in the second year, and $60,000 in the third year. The + " url="https://www.wallstreetmojo.com/weighted-average-cost-capital-wacc/"]weighted average cost of capital is 10%. Find out the discounted payback period of Funny Inc.**

We will go step by step.

First, we will find out the present value of the cash flow.

Let’s look at the calculations.

Please note the formula of present value - PV = FV / (1+i) ^n

- Year 0: - $150,000 / (1+0.10) ^0 = $150,000
- Year 1: $70,000 / (1+0.10) ^1 = $63,636.36
- Year 2: $60,000 / (1+0.10) ^2 = $49,586.78
- Year 3: $60,000 / (1+0.10) ^3 = $45,078.89

Now, we will calculate the cumulative discounted cash flows –

- Year 0: - $150,000
- Year 1: - 86,363.64
- Year 2: - 36,776.86
- Year 3: $8,302.03

Discounted Payback Period = Year before the discounted payback period occurs + (Cumulative cash flow in year before recovery / Discounted cash flow in year after recovery)

= 2 + ($36.776.86 / $45,078.89) = 2 + 0.82 = 2.82 years.

#### Example #2

A project is having a cash outflow of $ 30,000 with annual cash inflows of $ 6,000, so let us calculate the discounted payback period, in this case, assuming companies WACC is 15% and the life of the project is 10 years.

Year | Cash flow | Present value factor @ 15% | Present value of cash flows | Cumulative present value of cash flows |
---|---|---|---|---|

1 | $ 6,000 | 0.870 | $ 5,220 | $ 5,220 |

2 | $ 6,000 | 0.756 | $ 4,536 | $ 9,756 |

3 | $ 6,000 | 0.658 | $ 3,948 | $ 13,704 |

4 | $ 6,000 | 0.572 | $ 3,432 | $ 17,136 |

5 | $ 6,000 | 0.497 | $ 2,982 | $ 20,118 |

6 | $ 6,000 | 0.432 | $ 2,592 | $ 22,710 |

7 | $ 6,000 | 0.376 | $ 2,256 | $ 24,966 |

8 | $ 6,000 | 0.327 | $ 1,962 | $ 26,928 |

9 | $ 6,000 | 0.284 | $ 1,704 | $ 28,632 |

10 | $ 6,000 | 0.247 | $ 1,482 | $ 30,114 |

In this case, the cumulative cash flows are $ 30,114 in the 10^{th} year as, so the payback period is approx. 10 years

But, if you calculate the same in simple payback, the payback period is 5 years( $30,000/$6,000)

Please note that if the discount rate increases, the distortion between the simple rate of return and discounted payback period increases. Let me explain this further. **Let us take the 10% discount rate in the above example and calculate the discounted payback period.**

Year | Cash flow | Present value factor @ 10% | Present value of cash flows | The cumulative present value of cash flows |
---|---|---|---|---|

1 | $6,000 | 0.909 | $5,454 | $5,454 |

2 | $6,000 | 0.826 | $4,956 | $10,410 |

3 | $6,000 | 0.751 | $4,506 | $14,916 |

4 | $6,000 | 0.683 | $4,098 | $19,014 |

5 | $6,000 | 0.621 | $3,726 | $22,740 |

6 | $6,000 | 0.564 | $3,384 | $26,124 |

7 | $6,000 | 0.513 | $3,078 | $29,202 |

8 | $6,000 | 0.466 | $2,796 | $31,998 |

9 | $6,000 | 0.424 | $2,544 | $34,542 |

10 | $6,000 | 0.385 | $2,310 | $36,852 |

In this case, the discounting rate is 10% and the discounted payback period is around 8 years, whereas the discounted payback period is 10 years if the discount rate is 15%. But the simple payback period is 5 years in both cases. So, this means as the discount rate increases, the difference in payback periods of a discounted pay period and simple payback period increases.

Discount Rate | Simple Payback(a) | Discounted Payback(b) | The difference in payback period (b)- (a) |
---|---|---|---|

10% | 5 Years | 8 Years | 3 Years |

15% | 5 Years | 10 Years | 5 years |

I hope you guys got a reasonable understanding of what is payback period and discounted payback period. Let us take some more examples to understand the concept better.

#### Example #3

A company wants to replace its old semi-automatic machine with a new fully automatic machine. In the market, there are two models available in the market (Model A & Model B) at the cost of $ 5,00,000 each. The salvage value of an old machine is $ 1,00,000.The utilities of existing machinery that can be used are company purchases model A, and additional utilities to be bought are only $1,00,000. However, in case the company buys the model B, then all the existing utilities will have to be replaced, and new utilities cost$ 2,00,000, and a salvage value of old utilities is $20,000. The cash flows expected are as follows, and the discount rate is 15%

Year | A | B |
---|---|---|

1 | $ 1,00,000 | $ 2,00,000 |

2 | $ 1,50,000 | $ 2,10,000 |

3 | $ 1,80,000 | $ 1,80,000 |

4 | $ 2,00,000 | $ 1,70,000 |

5 | $ 1,70,000 | $ 40,000 |

Salvage value expected | $ 50,000 | $ 60,000 |

**Expenditure at Year of investment (Year Zero) **

Particulars | A | B |
---|---|---|

Cost of machine | $ 5,00,000 | $ 5,00,000 |

Cost of utilities | $ 1,00,000 | $ 2,00,000 |

Salvage of old machine | ($ 1,00,000) | ($ 1,00,000) |

Salvage of old machine | - | ($ 20,000) |

Total Exp | $ 5,00,000 | $ 5,80,000 |

Year | Present value factor @ 15% | Cash inflows (Machine A) | Present value of cash flows (Machine A) | Cumulative present value of cash flows (Machine A) | Cash inflows (Machine B) | Present value of cash flows (Machine B) | Cumulative present value of cash flows (Machine B) |
---|---|---|---|---|---|---|---|

0 (As calculated above) | 1.00 | $500,000 | $500,000 | $500,000 | $580,000 | $580,000 | $580,000 |

1 | 0.87 | $100,000 | $87,000 | $87,000 | $200,000 | $174,000 | $174,000 |

2 | 0.76 | $150,000 | $114,000 | $201,000 | $210,000 | $159,600 | $333,600 |

3 | 0.66 | $180,000 | $118,800 | $319,800 | $180,000 | $118,800 | $452,400 |

4 | 0.57 | $200,000 | $114,000 | $433,800 | $170,000 | $96,900 | $549,300 |

5(Including salvage value of $ 50,000 for Mach A and $ 60,000 for Mach B) | 0.50 | $ 170000+ $50,000 | $110,000 | $543,800 | $100,000 | $50,000 | $599,300 |

In this case, the discounted payback for Machine A is as follows…

Machine A is getting $ 4,33,800 at the end of year 4, and only $66,200($50000-$433800) has to get in year 5. So, payback here is …

4 years+ (66,200/1,10,000) = **4.6 Years**

Machine B is getting $ 5,49,300 at the end of year 4 and only $30,700 ($5,80,000- $5,49,300) has to get in year 5. So, payback here is …

4 years+ (30,700/50,000) = **4.6 Years**

**The discounted payback in both cases is the same.**

**Discounted Payback Period Calculation in Excel**

Let us now do the same example above in Excel.

This is very simple. You need to provide the two inputs of Cumulative cash flow in a year before recovery and Discounted cash flow in a year after recovery. You can easily calculate the period in the template provided.

### Use and Relevance

- The discounted payback period is a better option for calculating how much time a project would get back its initial investment; because, in a simple payback period, there’s no consideration for the time value of money.
- It can’t be called the best formula for finding out the payback period.
- But from the perspective of capital budgeting and accuracy, this method is far superior to a simple payback period; because in a simple payback period, there is no consideration for the time value of money and cost of capital.
- Many managers have been shifting their focus from a simple payback period to a discounted payback period to find a more accurate estimation of tenure for recouping the initial investments of their firms.

**Discounted Payback Period Calculator**

You can use the following Calculator

### Recommended Articles

This has been a guide to the discounted payback period and its meaning. Here we learn how to calculate a discounted period using its formula along with practical examples. Here we also provide you with a discounted payback period calculator with a downloadable excel template.

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