# Discounted Payback Period: Method & Example

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• 0:35 Definition
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Lesson Transcript
Instructor: Ian Lord

Ian is a real estate investor, MBA, former health professions educator, and Air Force veteran.

In this lesson we will review how a business investor can use the discounted payback period to determine the break-even point for a particular investment while accounting for the time value of the money tied up in that business activity.

## Discounted Payback Period

Rick is considering purchasing a second car wash using the money he's made from the one he already owns and operates. As part of his capital budgeting process he will want to determine how profitable a second location could be before he commits to making the purchase. He needs to know how long it will take to make up the costs of buying the second location. Let's look at how to apply the discounted payback period formula to determine the break-even point and how it offers an advantage over using an ordinary payback measurement.

## Definition

The discounted payback period gives Rick the amount of time it takes in years to break even after buying the second car wash. The formula accounts for the time value of money by recognizing that a dollar earned today is more valuable than a dollar earned years in the future. This is accomplished by applying a discount rate, or percentage reduction to the business's cash flow. The discount rate is the amount of return Rick could get by using that money elsewhere. If he could expect to return 10% in the stock market, for example, instead of purchasing the second location he would use a 10% discount rate.

Let's say that Rick will spend \$140,000 to buy the second location and expects to have cash flows of \$45,000 per year. First, prepare a chart showing the cash flow for each year along with an adjustment for the discount rate. In order to find the discounted cash flow amount he must find out the present value factor which considers the diminished value of cash flows in future years.

## Calculating Present Value Factor

The present value factor is calculated as:

Present Value of \$1 = 1 / (1 + interest rate)^year of cash flow being adjusted

Since the discount interest rate is assumed to be 10%, the present value factor for the first year's cash flow is 1 / (1+.10)1 or 0.9090. The second year would be 1 / (1+.1)2, and so on for each additional year in the table. Rick will continue to fill out a new row for each year until the cumulative discounted cash flow reaches a positive number.

Year Cash Flow Present Value Factor Discounted Cash Flow Total Discounted Cash Flow
0 -\$140,000 1.0 -\$140,000 -\$140,000
1 \$45,000 0.9090 \$40,905 -\$99,095
2 \$45,000 0.8264 \$37,188 -\$61,907
3 \$45,000 0.7513 \$33,808.50 -\$28,098.5
4 \$45,000 0.6830 \$30,735 \$2,636.5

## Computing Discounted Payback Period

The formula for calculating the discounted payback period is:

Discounted payback period = A + (B / C) where

A = Last period with a negative discounted total cash flow
B = Absolute value of discounted total cash flow at the end of A
C = Discounted cash flow during the period after A

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