# Discounted Payback Period

The discounted payback period is a projection of the time it will take to receive a full recovery on an investment that has an accompanying discount rate.

To better understand this concept, let’s look at the individual parts. A regular payback period is an estimate of the length of time that it will take for an investment to generate enough cash flow to pay back the full amount of the cash invested. This is assuming that the investment would make regular payments to repay the money.

In other words, let’s say a company invests cash in a project that will earn money. If they require the project to make annual payments, the payback period will tell them how many years it will take to repay the amount.

However, the ordinary payback period does not factor in the time value of money. The discounted payback period does. Therefore, the discounted payback period is more accurate. If you were to take the money you’re investing in a project and put it in an account with an interest rate, what would be the value of that amount?

As the project’s money is not earning interest, you look at its cash flow after the amount of money it would have earned from interest. The company should have an ideal payback period in mind as well.

## Discounted Payback Period Formula

In order to calculate the discounted payback period, you first need to calculate the discounted cash flow for each period of the investment.

Here is the formula for the discounted cash flow:

$DCF = \dfrac{C}{(1 + r)^{n}}$
• C = actual cash flow
• r = discount rate
• n = period of the individual cash flow

The easiest way to accomplish this is to create a small table that lays out the investment for each period. Here is a sample table:

Note that period 0 doesn’t need to be discounted because that is the initial investment. Now, we can take the results from this equation and move on to the next step.

Here is the formula for the discounted payback period:

$DPP = W + \dfrac{B}{F}$
• W = Last period where the whole discounted cash flow goes to investment recovery
• B = Remaining balance of the initial investment to be recovered
• F = Total amount of discounted cash flow of the final period

To calculate variable B—the investment’s remaining balance—you would take the total amount invested and subtract the sum total of each period up to and including variable W.

These formulas account for irregular payments, which are likely to occur. They will work for both even and uneven payments.

## Discounted Payback Period Example

Mr Smith is considering investing $200,000 in a promising new startup. However, he wants to see his money back within 5 years. The startup is projected to generate a cash flow of$50,000 per year. Calculate the discounted payback period of this project if Mr Smith is using a discount rate of 10%.

Let’s break it down in a table using our formula: DCF = C / (1 + r)n

(Discounted cash flow amounts have been rounded to the nearest whole number)

Now we can identify the meaning and value of the different variables needed to find the discounted payback period.

• The discounted payback period (DPP): Unknown
• Last period where the whole discounted cash flow goes to recovery (W): 5
• Remaining balance after variable W (B): $10,463 • The total amount of discounted cash flow of the final period (F):$28,223

We can apply the values to our variables and calculate the discounted payback period for the investment.

$DPP = 5 + \dfrac{10463}{28223} = 5.37$

In this case, the startup would be able to make the money back in 5.37 years. If they invest, they would not be making their money back until 0.37 years after their deadline. As a result, the startup would not be a financially sound investment for the company.

Because of these formulas, Mr Smith can be sure about his decision. At the end of the day, it doesn’t matter how “promising” the start-up or project is. If it is not financially viable enough to repay the initial investment within the time frame, then it is likely not a good investment.

## Discounted Payback Period Analysis

When trying to estimate whether or not a new investment is financially viable, you should have a discount rate in mind.

If a company is using the discounted payback period but they are not sure of their discount rate, they can use the Weighted Average Cost of Capital (WACC). This takes into account the company’s debt to equity ratio as well as their rate of risk.

You can see by the examples above the benefit that knowing the discounted payback period would have on evaluating the potential of a new project or investment. A business would accept projects if the discounted cash flows pay for the initial investment in a set amount of time.

## Discounted Payback Period Conclusion

• The discounted payback period is the time it will take to receive a full recovery on an investment that has a discount rate.
• To find the discounted payback period, two formulas are required: discounted cash flow and discounted payback period.
• The discounted cash flow requires 3 variables: actual cash flow, discount rate, and period of the individual cash flow.
• The discounted payback period requires 3 variables: the last period where the whole discounted cash flow goes to recovery, the remaining balance, and the total amount of discounted cash flow of the final period.