# Discounted Payback Period: How to Calculate & Examples

## What is a Discounted Payback Period?

The discounted payback period is a capital budgeting procedure which is frequently used to determine the profitability of a project. It is an extension of the payback period method of capital budgeting, which does not account for the time value of money.

It takes into account the time value of money by discounting the cash inflows of the project to their present values and then computing the time it will take for the sum of the present values of these cash inflows to equal the initial investment made in the project. The time value of money is the concept that a dollar today is worth more than a dollar in the future, because money can earn interest or returns if invested.

This method of capital budgeting helps businesses in making decisions about whether a particular project is worth investing in or not, based on how quickly they can recover their initial investment taking into account the time value of money. The shorter the payback period, the more attractive the investment is considered.

Unlike the regular payback period, the discounted payback period accounts for the risks and uncertainties that might be associated with future cash flows, and thus provides a more accurate and realistic assessment of the project’s profitability.

##### Key Points

- The discounted payback period is a financial metric that helps evaluate the time it takes for an investment to generate enough cash flows to recover the initial investment, considering the time value of money.
- It addresses one of the limitations of the regular payback period by incorporating the concept of discounting future cash flows.
- The discounted payback period considers the present value of cash flows by applying a discount rate to account for the time value of money.

## Understanding the Discounted Payback Period

The Discounted Payback Period is a capital budgeting method used to determine the length of time it takes to break even on an investment in terms of its discounted cash flows. Unlike the simple payback period, which doesn’t account for the time value of money, the Discounted Payback Period takes this into consideration.

The time value of money is a fundamental concept in finance that suggests that a dollar in hand today is worth more than a dollar promised in the future. This is because money available today can be invested and earn a return, hence growing over time. In other words, the purchasing power of money decreases over time due to factors such as inflation or interest rates.

When evaluating investments or projects with long-term horizons, the Discounted Payback Period becomes particularly important. It adjusts future cash flows to reflect their reduced value, providing a more realistic view of when an investment or project will break even.

To understand it, one should be familiar with two key concepts:

**Cash Flows**These are the inflows and outflows of cash that will occur as a result of the investment or project. Inflows are the returns or revenues generated, while outflows represent the costs or expenses.**Discount Rate**This is the rate of return required from the investment. It represents the investment’s opportunity cost, i.e., the return foregone by choosing this investment over the next best alternative.

The Discounted Payback Period calculation takes these cash flows and discount rate into account, providing a more nuanced understanding of the return period of an investment.

## Calculating the Discounted Payback Period

The calculation of the discounted payback period can be more complex than the standard payback period because it involves discounting the future cash flows of the investment.

Here’s a step-by-step process on how to calculate it:

**Identify Cash Flows**The first step is to determine the projected cash flows of the investment for each period (typically yearly). These can include revenues, savings, etc.**Determine the Discount Rate**The discount rate is often the required rate of return for the investment, or it could be the cost of capital. It represents the rate at which future cash flows will be discounted back to their present value.**Calculate Discounted Cash Flows**Next, you calculate the present value of each cash flow. This is done by dividing the cash flow by (1 + discount rate) raised to the power of the period number.

The formula is:

Discounted Cash Flow = Cash Flow / (1 + r) ^ t

Where:

r = Discount Rate,

t = Time (in periods).**Cumulatively Add Discounted Cash Flows**Add the discounted cash flows cumulatively until the sum equals or exceeds the initial investment. The period in which this happens is the discounted payback period.

Remember, the discounted payback period provides the time in which the initial investment will be recovered in terms of discounted or present value cash flows. Unlike the simple payback period, it provides a more realistic timeframe, factoring in the time value of money.

## Interpreting the Discounted Payback Period

**Shorter Payback Periods**A shorter discounted payback period is typically preferable as it indicates that the investment will pay back its initial outlay sooner when considering the time value of money. This can be particularly important for businesses or investors with tight cash flow constraints or high capital costs.**Comparison to Other Investments**Comparing investment opportunities can involve considering their respective durations for recovering the initial investment. Generally, investments with shorter payback periods may appear more appealing, given similar levels of risk and potential return.**Comparison to Non-discounted Payback Period**If the discounted payback period is significantly longer than the non-discounted payback period, this can indicate that the later cash flows in the project’s life are significant. This could be a warning sign if those cash flows are risky or uncertain.**Recovery of Capital**By providing a timeframe in which the investment recovers its initial outlay in present value terms, the discounted payback period helps measure the risk of an investment. The faster the capital is recovered, the less risk the investment carries.

However, like all financial metrics, it shouldn’t be used in isolation. It’s important to consider other financial metrics and factors specific to the investment before making a decision.

## Advantages of the Discounted Payback Period

**Time Value of Money**Unlike the regular payback period, the discounted payback period takes into account the time value of money, providing a more accurate reflection of the investment’s profitability over time.**Risk Assessment**It helps to evaluate the risk of an investment by providing the time frame in which an investment is expected to break even. The shorter the payback period, the less risk the investment carries.**Cash Flow Management**This method is useful for cash flow management, as it indicates when the invested funds will be recovered, allowing for better planning and allocation of resources.**Comparative Tool**It can be used to compare different investment opportunities. An investment with a shorter discounted payback period may be considered more attractive, assuming other factors like risk and potential returns are equal.**Simplicity**Despite accounting for discounting, it remains a relatively simple and straightforward financial metric to calculate and interpret, making it accessible to investors of all levels.**Flexibility**The discounted payback period allows the discount rate to be adjusted according to the risk profile of the cash flows, thereby providing a more tailored analysis of an investment’s break-even point.

## Limitations of the Discounted Payback Period

**Ignores Cash Flows Beyond Payback Period**The primary limitation of the discounted payback period is that it does not take into account the cash flows that occur after the payback period. This could lead to potentially profitable long-term investments being overlooked.**Subjectivity in Discount Rate**The discount rate used in the calculation is often subjective and can significantly impact the results. Small changes in the discount rate can lead to large changes in the payback period, making comparisons between investments difficult.**No Profit Measure**Unlike other investment appraisal methods, such as net present value (NPV) or internal rate of return (IRR), the discounted payback period does not give any indication of the profitability of an investment. It merely provides the time taken to recover the initial investment.**Neglects Risk Variations Over Time**The discounted payback period applies a constant discount rate over the entire investment period, which may not accurately reflect the changing risk profile of an investment over time.**Arbitrary Cut-off Point**The use of the payback period as a decision criterion involves an arbitrary cut-off point. There is no logical reason why cash flows received one period after the payback period should be regarded as less important.

Despite these limitations, it is still a useful tool for initial investment screening and can provide valuable insights when used in conjunction with other financial metrics.

## Examples of Discounted Payback Period

### Example 1: Individual Investment

Let’s assume that you are an investor who has invested $10,000 in a project, expecting cash inflows of $3,000 per year for the next five years. If we consider the discount rate to be 10%, the discounted payback period can be calculated as follows:

Year | Discounted Cash Flow | Cumulative Discounted Cash Flow |
---|---|---|

1 | $2,727.27 | $2,727.27 |

2 | $2,479.34 | $5,206.61 |

3 | $2,253.94 | $7,460.55 |

4 | $2,048.12 | $9,508.67 |

5 | $1,862.84 | $11,371.51 |

By the end of Year 5, the total discounted cash inflow is $11,371.51, which is more than the initial investment of $10,000. So, the discounted payback period would be somewhere in the 5th year. To be more precise, it would be 4 years plus the fraction of the 5th year needed to reach a total of $10,000, which can be calculated as: 4 + ($10,000 – $9,508.67) / $1,862.84 ≈ 4.26 years.

### Example 2: Business Investment

A business invests $50,000 in a new machine that is expected to generate cash inflows of $15,000 for the next 5 years. If the company uses a discount rate of 8%, the discounted payback period can be calculated using the same method as shown in Example 1. The company would use this calculation to decide if the investment in the new machine is worth the cost based on when they would recover the initial investment considering the time value of money.

### Example 3: Real Estate Investment

Let’s say a real estate investor decides to invest $200,000 in a rental property. The expected cash inflows from the rental income are $45,000 per year for the next six years. The investor uses a discount rate of 6% to account for the time value of money. Here is how it would be calculated:

Year | Discounted Cash Flow | Cumulative Discounted Cash Flow |
---|---|---|

1 | $42,452.83 | $42,452.83 |

2 | $40,050.78 | $82,503.61 |

3 | $37,783.96 | $120,287.57 |

4 | $35,645.82 | $155,933.39 |

5 | $33,631.34 | $189,564.73 |

6 | $31,731.64 | $221,296.37 |

By the end of Year 6, the total discounted cash inflow is $221,296.37, which is more than the initial investment of $200,000. So, the discounted payback period would be somewhere in the 6th year. To be more precise, it would be 5 years plus the fraction of the 6th year needed to reach a total of $200,000, which can be calculated as: 5 + ($200,000 – $189,564.73) / $31,731.64 ≈ 5.33 years.

### Example 4: Technology Investment

A technology firm decides to invest $2 million in the development of a new software product. The firm expects cash inflows of $700,000 per year for the next four years from the sale of this software. The firm uses a discount rate of 5% to account for the time value of money. The discounted payback period would be calculated using the same method as shown in the above examples. The firm would use this calculation to decide if the investment in the new software development project is financially viable based on when they would recover the initial investment considering the time value of money.

## FAQs

**What is the discounted payback period?**

The discounted payback period is a financial metric that measures the time it takes for an investment to recover its initial cost, taking into account the time value of money.

**How is the discounted payback period different from the regular payback period?**

The discounted payback period considers the present value of future cash flows by applying a discount rate, while the regular payback period does not account for the time value of money.

**Why is the discounted payback period important?**

It helps assess the risk and profitability of an investment by considering the timing and value of cash flows, providing a more accurate picture of its financial feasibility.

**What is the decision criteria for the discounted payback period?**

The decision criteria can vary depending on the organization’s goals, but it often involves comparing the calculated discounted payback period to a predetermined payback period or target set by the company.

### About Paul

Paul Boyce is an economics editor with over 10 years experience in the industry. Currently working as a consultant within the financial services sector, Paul is the CEO and chief editor of BoyceWire. He has written publications for FEE, the Mises Institute, and many others.