In this article, we will cover how to calculate discounted payback period. This will include the overview, key definition, example calculation, advantages and limitation of discounted payback period that you should know.
Overview
When businesses evaluate and appraise projects or investments, they consider two-factor evaluations. The rate of return on the investment and the time it will take to recover the project costs. Cash flows help improve the liquidity of a business, hence often play a critical role in final investment appraisals.
A simple payback period with an investment or a project is a time of recovery of the initial investment. The projected cash flows are combined on a cumulative basis to calculate the payback period. However, the simple payback period ignores the time value of money.
What is Discounted Payback Period?
Discounted payback period is the time required to recover the project’s initial investment/costs with the discounted cash flows arising from the project. It is sometimes called adjusted payback period or modified payback period. The discounted payback period is one of the capital budgeting techniques in valuating the investment appraisal. The discounted payback period method takes the time value of money into consideration. Only project relevant costs and revenue streams should be included in the discounted payback period analysis. The discounted payback period method considers the company cost of capital as a discounting factor. That makes the investment cost-benefit analysis simpler to compare for the company management. It gives greater weight-age to early cash inflows from the project, which improves the project payback period.
How to Calculate Discounted Payback Period?
There are two components of discounted payback period analysis as follow:
- cost of capital and
- Relevant cash flows.
The cash flows are discounted at the company cost of capital or the weighted average cost of capital precisely. Only the project relevant cash flows should be identified and included in the evaluation.
Discounted Payback Period Formula:
The discounted payback period can be calculated by using the simplified formula as below:
Discounted Payback Period = A +B/ (B+C)
Where:
A = Last year of negative cumulative cash flow or net present value
B = Last negative cumulative cash flow
C= First positive cumulative cash flow
Working Example and Calculation:
Suppose a company has a weighted average cost of capital of 7%. It evaluates an investment option for a project with the following relevant cash flow details. The project total lifespan is 5 years.
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| ($ 80,000) | $ 23,000 | $ 35,000 | $ 30,000 | $ 25,000 | $ 20,000 |
Required: Calculate the discounted payback period.
Solution:
The discounted payback period can be calculated by first discounting the cash flows with the cost of capital of 7%. The discounted cash flows are then added to calculate the cumulative discounted cash flows.
| Year | Cash flow $ | Discount factor at 7% | Discounted Cash flow | Cumulative Cash flow $ |
| from NPV Table | CF × DF at 7% | |||
| 0 | -80,000 | 1.00 | -80,000 | -80,000 |
| 1 | 23,000 | 0.935 | 21,505 | -58,495 |
| 2 | 35,000 | 0.873 | 30,555 | -27,940 |
| 3 | 30,000 | 0.816 | 24,480 | -3,460 |
| 4 | 25,000 | 0.763 | 19,075 | 15,615 |
| 5 | 20,000 | 0.713 | 14,260 | 29,875 |
The discounted payback period is the time when the cash inflows break-even the total initial investment. In other words, the time when the negative cumulative cash flow turn to positive.
From our table above, it should be after 3 years and in the 4th year.
Discounted Payback Period = 3 years + [3460/ (3,460+15,615)] = 3 + 0.181
Hence, Discounted Payback Period = 3.181 years
Therefore, it takes 3.181 years in order to recover from the investment.
Payback Period vs Discount Payback Period
Both project appraisal methods offer simple calculations for the initial costs associated with the project. The important differentiating factor between the two methods is the time value of the money. For example, if we ignore the discounting factor at WACC, our cash flows will remain the same. It will change the project period like:
| Year | Cash flow US$ | Cumulative Cash flow US$ |
| 0 | -80,000 | -80,000 |
| 1 | 23,000 | -57,000 |
| 2 | 35,000 | -22,000 |
| 3 | 30,000 | 8,000 |
| 4 | 25,000 | 33,000 |
| 5 | 20,000 | 53,000 |
Payback Period = 2 + [22,000/ (22,000 +8,000)] = 2.733 years
In large project appraisals, it may not present a true picture or the forecast that may affect the resource allocation and project appraisal decisions.
Advantages of Discounted Payback Period
Discounted payback period analyses can play an important role in project ranking and appraisal decisions. The business may then evaluate the projects with higher NPV and shorter payback period over other options. Other advantages of using the discounted payback period as investment appraisal include:
- It does not ignore the time value of money like the simple payback period method
- It is a simple and easy to understand method with a readily available method to calculate the results
- Discounted cash flows offer a clear indication of net increase/decrease for the company and shareholders’ wealth
- Discounted payback period takes into account more of projects’ cash flows. This is because it takes the time value of money into consideration. Thus, it produces longer payback period than simple payback period or non-discounted payback period.
- It offers in absolute terms a simple measure of comparison to rank multiple investment options. Thus, it gives a clear accept or reject criterion for investment appraisal.
Limitations of the Discounted Payback Period Method
The discounted payback period method offers a great starting point for investment appraisals. With all its usefulness, it also offers some limitations:
- It ignores the total project profitability which is the prime criteria for undertaking any investment for any business.
- Similar to the simple payback period, it also ignores the cash flows arising after the project completion
- It uses the company weighted average cost of capital (unadjusted cost of capital), which may not be the correct option for project appraisals. A more precise analysis is to use the adjusted to reflect project risk and uncertainty. Net Present Value (NPV) takes into account of this adjusted rate.
- Both payback period methods emphasis on early cash inflows
Conclusion
The discounted payback period method provides a useful investment appraisal method. It offers simple and easy to understand analysis. It can be best utilized in conjunction with other investment appraisal methods. However, a project with a shorter payback period with discounted cash flows should be taken on a priority basis.
