Financial Modeling Tutorials

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- Payback period Formula
- Discounted Payback Period Formula
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**Payback Period & Discounted Payback Period –**When a business makes capital investments like an investment on plant& machinery, buildings, land etc. it incurs a cash outlay in expectation of future benefits. The benefits generally extend beyond one year into the future. In this case, out of the different proposals available company has to choose a proposal that provides the best return and return equals to or more than that is expected by investors.

In order to maximize the returns of the shareholders of a company, it is very crucial that the best or most profitable investment projects are selected. This is because the investment decisions which went bad can be both financially and strategically devastating.

source: Lifehacker.com.au

The above article notes that Tesla’s Powerwall is not economically viable for most people. As per the assumptions used in this article, Powerwall’s payback ranged from 17 years to 26 years. Considering Tesla’s warranty is only limited to 10 years, payback period higher than 10 years is not ideal.

Like Payback Period, there are a number of other techniques available for appraisal of investment proposals like NPV, IRR, Profitability Index, Modified IRR etc. However, in this article, we look at **“Payback period”** and **“Discounted payback period” **in detail

The article is sequenced as per below

- Payback Period
- Advantages of Payback period method
- Disadvantages of Payback period method
- Payback Reciprocal
- Discounted payback period
- How to calculate Cash flows for Payback period or discounted payback period
- Calculating Payback cash flows

**Recommended Courses**

## Payback Period

The payback period of an investment is the length of the time period required for cumulative total net cash flows to total initial cash outlays.

In other words, at payback period the investor has recovered the money invested in the project.

**Steps to Calculate Payback Period:**

- The first step in calculating the payback period is determining the initial capital investment and
- The next step is calculating/estimating the annual expected after-tax net cash flows over the useful life of the investment.

#### Payback Period Calculation with Uniform cash flows

When cash flows are uniform over the useful life of the asset then the calculation of payback period is made through following formula.

Payback period Formula = Total initial capital investment /Expected annual after-tax cash inflow

Let us see an example of how to calculate pay back period when cash flows are uniform over using full life of the asset.

**Payback Period example:**

A project costs $2Mn and yields a profit of $30,000 after depreciation of 10% (straight line) but before tax of 30%. Lets us calculate the pay back period of the project.

Profit before tax $ 30,000

**Less: **Tax@30%(30000*30%) $ 9,000

Profit after tax $ 21,000

**Add: **Depreciation(2Mn*10%) $ 2,00,000

Total cash inflow $ 2,21000

While calculating cash inflow, generally depreciation is added back as it does not result into cash out flow.

Payback Period Formula = Total initial capital investment /Expected annual after-tax cash inflow

= $ 20,00,000/$2,21000 = **9 Years(Approx)**

#### Payback Period Calculation with Nonuniform cash flows

When cash flows are NOT uniform over the use full life of the asset then the cumulative cash flow from operations must be calculated for each year. In this case, the payback period shall be the corresponding period when cumulative cash flows is equal to the initial cash outlay.

In case, the sum does not match, then the period in which it lies should be identified. After that, we need to compute the fraction of the year that is needed to complete the payback.

**Payback Period example:**

Suppose ABC ltd is analyzing a project which requires investment of $2,00,000 and it is expected to generate cash flows as follows

Year |
Annual cash inflows |

1 | 80,000 |

2 | 60,000 |

3 | 60,000 |

4 | 20,000 |

In this cash pay back period can be computed as follows by calculating cumulative cashflows

Year |
Annual cash inflows |
Cumulative Annual cash inflows |
Payback period |

1 | 80,000 | 80,000 | |

2 | 60,000 | 1,40,000(80,000+60,000) | |

3 | 60,000 | 2,00,000(1,40,000+60,000) | In this Year 3 we got initial investment of $ 2,00,000 so this is the pay back year |

4 | 20,000 | 2,20,000(2,00,000+20,000) |

Suppose , in the above case, if the cash outlay is $2,05,000 then pa back period is

Year |
Annual cash inflows |
Cumulative Annual cash inflows |
Payback period |

1 | 80,000 | 80,000 | |

2 | 60,000 | 1,40,000(80,000+60,000) | |

3 | 60,000 | 2,00,000(1,40,000+60,000) | |

4 | 20,000 | 2,20,000(2,00,000+20,000) | Pay back period is between 3 and 4 years |

Since up to three years a sum of $2,00,000 is recovered, the balance amount of $ 5,000($2,05,000-$2,00,000) is recovered in fraction of year which is as follows.

Forgetting $20,000 additional cash flows the project is taking complete 12 months. So for getting additional of $ 5,000($2,05,000-$2,00,000) it will take (5,000/20,000) 1/4^{th} Year. i.e 3 months.

So, the project payback period is **3 years 3 months.**

## Advantages of Payback period method

- It is easy to calculate.
- It is easy to understand as it gives a quick estimate of the time needed for the company to get back the money it has invested in the project.
- The length of the project payback period helps in estimating the project risk. The longer the payback period, the riskier the project is. This is because the long-term predictions are less reliable.
- In the case of industries where there is a high obsolescence risk like software industry or mobile phone industry short payback periods often become determining a factor for investments.

## Disadvantages of Payback period method

- It ignores the time value of money
- It fails to consider the investment total profitability (I.e it considers cash flows from the initiation of the project till the payback period and fails to consider the cash flows after the payback period.
- It may cause company to place importance on projects which are short payback period thereby ignoring the need to invest in long-term projects
**( i.e A company cannot just determine a project feasibility only based on the number of years in which it is going to give your return back, there are number of other factors which it does not consider)** - It does not take into account the social or environmental benefits in the calculation.

## Payback Reciprocal

Payback reciprocal is the reverse of the payback period.This reciprocal of payback period is calculated by using following formula

Payback reciprocal = Annual average cash flow/Initial investment

For example, a project cost is $ 20,000 and annual cash flows are uniform at $4,000 per anum and life of asset acquire is 5 years then payback period reciprocal will be as follows.

$ 4,000/20,000 = **20%**

This 20% represents the rate of return the project or investment gives every year.

## Discounted payback period

Discounted payback period is next level of payback period where the cashflows are discounted before calculating the period of payback.

Some companies prefer to calculate the payback period as it considers the time value of money.

The discounting can be done using the WACC (Weighted average cost of capital) or IRR(Internal rate of return) or bank rate company got the lending or government risk-free bond rate.

The most appropriate rate to discount cash flows is WACC (Weighted average cost of capital) or IRR (Internal rate of return).

Let’s take an example for calculating the discounted payback period.

**Discounted Payback Period Example #1**

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 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 10^{th} year as, so 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 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 | 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 discounted payback period is around 8 years, whereas the discounted payback period is 10 years if the discount rate is 15%. But simple payback period is 5 years in both the cases. So, this means as the discount rate increases, the difference in payback periods of discounted pay period and simple payback period increases.

Discount Rate | Simple Payback(a) | Discounted Payback(b) | 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 example to understand the concept better.

**Discounted Payback Period Example #2**

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 a cost of $ 5,00,000 each. Salvage value of old machine is $ 1,00,000.The utilities of existing machinery can be used is company purchases model A and additional utilities to be bought is 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 salvage value of old utilities is $20,000 , The cash flows expected are as follows and 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% | Machine A |
Machine B |
||||

Cash in flows | Present value of cash flows | Cumulative present value of cash flows | Cash in flows | Present value of cash flows | Cumulative present value of cash flows | ||

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, pay back 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, pay back here is …

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

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

## How to calculate Cash flows for Payback period or discounted payback period

Generally, companies use one or more techniques for capital investment decisions. Some of them use different methods for different projects while others use multiple methods for each project.

For any technique, the calculation of projected cash flow is very important.

Since the timing of cash flows does not match with a period of profit, normally firms are more interested in cash flows. A firm may earn $ 100 Million profit but actual cash receipt may be lesser. This is because all sales and purchases and sales are not on a cash basis. Further depreciation is a noncash item and profit is calculated after considering depreciation.

## Calculating Payback cash flows

Various factors to keep in mind while arriving cash flows:

**Depreciation:**Since depreciation 1s a noncash item it does not affect the cash flow. However, the tax benefit from depreciation from depreciation affects cash flow.**Opportunity cost:**Opportunity cost is the income that would have been earned or cost that would have been incurred had the activity is done. For example, A company acquired a land at $ 10 Million 5 years ago and the cost of land, if sold now, is $ 25 Million. Assume that if the company uses this land now for the project, then its sale value if $ 25 Million forms part of initial cash outflow, The cost of acquisition of land 5 years ago at $ 10 million is irrelevant for decision making.**Sunk cost:**Sunk cost is the cost that is already spent and hence irrelevant for decision making. For example: If a company has paid $ 50,000 for consultancy charges for preparation of feasibility report whether to take a project or not. In this case, the charges of $ 50,000 paid are irrelevant as sum has already paid and shall not affect the decision whether the project should be undertaken or not.**Working capital:**Every project requires working capital to run the project. Therefore while calculating cash flows, the initial working capital requirement should be treated as cash outflows and at the end of the project, its release should be treated as a cash inflow. In case additional working capital is required during the life of a project, then the additional working capital required is treated as cash outflow at that period of time.**Allocated overheads:**Some overheads are allocated based on machine hours, labor hours etc, They may be allocated to the new project as well. Since those expenses are already incurred and are just allocated they should not be considered while calculating cash flows. However, sometimes the overhead costs increase due to acceptance of some project.Then, in that case, the incremental overhead costs should be considered as cash outflows while calculating cash flows**Additional Capex:**Generally entire CapEx is not incurred only during initial year, it may be incurred in subsequent years as well. In such as cases such cash outflows to be taken as outflows during those respective years.**Exclusion of Finance costs:**When cash flows relating to long term funds are being calculated, the financing costs of long-term funds should be excluded. Because the WACC used for discounting cash flows already takes into account the interest and dividend payments.**Post-tax cash flows:**The cash flows should be taken the net of tax. It is always better to avoid using pre-tax cash flows and pre-tax discounting rate

### Payback Period Video

### Related Articles –

- Bank Rate vs Repo Rate Differences
- Present Value Factor Formula Examples
- Internal Rate of Return in Excel
- Tax Shield
- Capital Lease vs Operating Lease
- Financing Acquisitions
- Convexity of a Bond

I hope you understand how to cash flows, and how to then derive the Payback and discounted payback period from those cash flows for capital projects.

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