The Discounted Payback Period Calculator is a financial tool used to determine the time it takes for an investment to recover its initial cost through discounted cash flows. Unlike the simple payback period, which does not consider the time value of money, the discounted payback period accounts for the present value of future cash inflows.
This makes the Discounted Payback Period (DPP) a more accurate and reliable metric when assessing the profitability and risk of investments, as it provides insight into how long it will take to break even, considering the time value of money. The calculator is often used in capital budgeting, project evaluation, and investment analysis to help companies make informed financial decisions.
Formula
Discounted Payback Period (DPP)
The Discounted Payback Period (DPP) is the time it takes for the initial investment to be recovered using discounted cash flows. To calculate this, follow these steps:
- Calculate the Present Value (PV) of each cash inflow: PV = Cash Inflow / (1 + r)^t Where:
- Cash Inflow = the expected cash flow in each period (e.g., yearly, quarterly)
- r = the discount rate (expressed as a decimal, e.g., 10% = 0.10)
- t = the period number (e.g., year 1, year 2, etc.)
- Calculate the cumulative discounted cash flow for each period: Cumulative PV = Sum of (Cash Inflow_i / (1 + r)^t) This will give you the cumulative present value over multiple periods.
- Find the period when the cumulative discounted cash flow equals or exceeds the initial investment: The discounted payback period is the time when the cumulative present value of cash inflows equals or exceeds the initial investment.
Key Points to Remember:
- The discount rate accounts for the opportunity cost of capital, inflation, and investment risk.
- The DPP will always be longer than the simple payback period because it considers the time value of money.
- A shorter DPP indicates a quicker return on investment and a less risky project.
General Terms for Discounted Payback Period Calculation
The following table provides some general terms and units related to the Discounted Payback Period Calculator, helping users better understand the essential components involved in the calculation:
| Term | Description |
|---|---|
| Cash Inflow | The expected cash flow generated from an investment or project over time. |
| Discount Rate (r) | The rate used to discount future cash inflows to present value, reflecting the risk or opportunity cost of the investment. |
| Time Period (t) | The specific time interval (e.g., year, quarter, etc.) at which the cash flow occurs. |
| Present Value (PV) | The current value of future cash flows, adjusted for the discount rate. |
| Cumulative PV | The total of the present values of all cash inflows up to a given period. |
| Initial Investment | The amount of money initially invested in the project or asset. |
| Discounted Payback Period (DPP) | The period it takes for the discounted cash inflows to recover the initial investment. |
This table will be helpful when working with the discounted payback period formula and understanding the various components involved in the calculation.
Example
Let’s go through an example to demonstrate how to use the Discounted Payback Period Calculator.
Example 1: Calculate the Discounted Payback Period
Imagine you are evaluating an investment with the following details:
- Initial Investment = $100,000
- Discount Rate (r) = 10% or 0.10
- Annual Cash Inflows = $40,000 for the next 4 years
We will calculate the present value (PV) for each year and determine the cumulative discounted cash flow.
Step 1: Calculate the Present Value of Cash Inflows for Each Year
For Year 1:
PV = 40,000 / (1 + 0.10)^1 = 40,000 / 1.10 = 36,363.64
For Year 2:
PV = 40,000 / (1 + 0.10)^2 = 40,000 / 1.21 = 33,057.85
For Year 3:
PV = 40,000 / (1 + 0.10)^3 = 40,000 / 1.331 = 30,060.66
For Year 4:
PV = 40,000 / (1 + 0.10)^4 = 40,000 / 1.4641 = 27,321.66
Step 2: Calculate the Cumulative Present Value
- Year 1: 36,363.64
- Year 2: 36,363.64 + 33,057.85 = 69,421.49
- Year 3: 69,421.49 + 30,060.66 = 99,482.15
- Year 4: 99,482.15 + 27,321.66 = 126,803.81
Step 3: Find the Year When Cumulative PV Equals or Exceeds the Initial Investment
The cumulative discounted cash flow exceeds the initial investment of $100,000 in Year 4. Therefore, the Discounted Payback Period (DPP) is approximately 4 years.
Most Common FAQs
The key difference is that the simple payback period ignores the time value of money, while the discounted payback period adjusts for the time value of money by considering the present value of future cash inflows. The DPP gives a more accurate assessment of how long it takes to recover an investment, as it factors in the discount rate.
The discount rate is typically based on the opportunity cost of capital, the expected rate of return, or the risk level of the investment. It reflects the return that could be earned on an alternative investment with a similar risk profile.
Yes, the discounted payback period can be used for any investment or project where cash inflows are expected over time. However, it is most useful for investments with regular, predictable cash flows, such as real estate, infrastructure, or capital projects.