Payback Period Formula. To find exactly when this occurs, the following formula can be used: Applying the formula to the example, we take the initial investment at its absolute value. The opening and closing period cumulative cash flows are $900,000 and $1,200,000, respectively.
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 FlowA |
Where:
A | = | Year in which the cumulative cash flows from investment exceed the initial cost. |
A - 1 | = | The year prior to A. |
Cash FlowA | = | 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 FlowA | ||
= 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 FlowA |
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 FlowA | = | 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. |
![Payback Period Formula Payback Period Formula](/uploads/1/2/4/9/124958433/343563389.jpg)
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 FlowA | ||
= 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.
Related Topics
Please enable JavaScript to view the comments powered by Disqus.comments powered by DisqusPayback period is the time in which the initial outlay of an investment is expected to be recovered through the cash inflows generated by the investment. It is one of the simplest investment appraisal techniques.
Since cash flow estimates are quite accurate for periods in the near future and relatively inaccurate for periods in distant future due to economic and operational uncertainties, payback period is an indicator of risk inherent in a project because it takes initial inflows into account and ignores the cash flows after the point at which the initial investment is recovered.
Projects having larger cash inflows in the earlier periods are generally ranked higher when appraised with payback period, compared to similar projects having larger cash inflows in the later periods.
Formula
The formula to calculate the payback period of an investment depends on whether the periodic cash inflows from the project are even or uneven.
If the cash inflows are even (such as for investments in annuities), the formula to calculate payback period is:
Payback Period = | Initial Investment |
Net Cash Flow per Period |
When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula:
Payback Period = | A + | B |
C |
Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A
Cumulative net cash flow is the sum of inflows to date, minus the initial outflow.
Both of the above situations are explained through examples given below.
Examples
Example 1: Even Cash Flows
Company C is planning to undertake a project requiring initial investment of $105 million. The project is expected to generate $25 million per year in net cash flows for 7 years. Calculate the payback period of the project.
Solution
Payback Period
= Initial Investment ÷ Annual Cash Flow
= $105M ÷ $25M
= 4.2 years
= Initial Investment ÷ Annual Cash Flow
= $105M ÷ $25M
= 4.2 years
Example 2: Uneven Cash Flows
Company C is planning to undertake another project requiring initial investment of $50 million and is expected to generate $10 million net cash flow in Year 1, $13 million in Year 2, $16 million in year 3, $19 million in Year 4 and $22 million in Year 5. Calculate the payback value of the project.
Solution
![Payback Period Formula Payback Period Formula](/uploads/1/2/4/9/124958433/428451337.gif)
Year | (cash flows in millions) | |
---|---|---|
Annual Cash Flow | Cumulative Cash Flow | |
0 | (50) | (50) |
1 | 10 | (40) |
2 | 13 | (27) |
3 | 16 | (11) |
4 | 19 | 8 |
5 | 22 | 30 |
Payback Period = 3 + 11/19 = 3 + 0.58 ≈ 3.6 years
Decision Rule
The longer the payback period of a project, the higher the risk. Between mutually exclusive projects having similar return, the decision should be to invest in the project having the shortest payback period.
When deciding whether to invest in a project or when comparing projects having different returns, a decision based on payback period is relatively complex. The decision whether to accept or reject a project based on its payback period depends upon the risk appetite of the management.
Management will set an acceptable payback period for individual investments based on whether the management is risk averse or risk taking. This target may be different for different projects because higher risk corresponds with higher return thus longer payback period being acceptable for profitable projects. For lower return projects, management will only accept the project if the risk is low which means payback period must be short.
Advantages and Disadvantages
Advantages of payback period are:
- Payback period is very simple to calculate.
- It can be a measure of risk inherent in a project. Since cash flows that occur later in a project's life are considered more uncertain, payback period provides an indication of how certain the project cash inflows are.
- For companies facing liquidity problems, it provides a good ranking of projects that would return money early.
Disadvantages of payback period are:
- Payback period does not take into account the time value of money which is a serious drawback since it can lead to wrong decisions. A variation of payback method that attempts to address this drawback is called discounted payback period method.
- It does not take into account, the cash flows that occur after the payback period. This means that a project having very good cash inflows but beyond its payback period may be ignored.
Written by Irfanullah Jan and last modified on