# Calculating Discounted Cash Flows in Payback Period

The payback period is a quick and simple capital budgeting method that many financial managers and business owners use to determine how quickly their initial investment in a capital project will be recovered from the project's cash flows. Capital projects are those that last more than one year. The discounted payback period calculation differs only in that it uses discounted cash flows.

## Disadvantages of Discounted Payback Period

The discounted payback period calculation is still widely used by managers who want to know when they will recoup their initial investment, but it has three major flaws:

First, the time value of money is not considered when you calculate the payback period. In other words, no matter for which year you receive a cash flow, it is given the same weight as the first year. This flaw overstates the time to recover the initial investment.

A second flaw is the lack of consideration of cash flows beyond the payback period. If the capital project lasts longer than the payback period, the cash flows the project generates after the initial investment is recovered are not considered at all in the payback period calculation.

The third, and perhaps most important, a flaw is that calculating the discounted payback period does not really give the financial manager or business owner the information needed to make the best investment decision. In addition to the first two flaws, the business owner also has to guess at the interest rate or cost of capital. Consequently, it is not the best method to use when choosing an investment project. That said, this third flaw of the discounted payback period can be dismissed if the weighted average cost of capital is used as the rate at which to discount the cash flows.

Although not entirely satisfactory, the calculation of the discounted payback period is comparatively better than a calculation using an undiscounted payback period as a capital budgeting decision criterion. That said, an even better calculation to use in many instances is the net present value calculation.

## Calculation

The calculation for discounted payback period is a bit different than the calculation for regular payback period because the cash flows used in the calculation are discounted by the weighted average cost of capital used as the interest rate and the year in which the cash flow is received. Here is an example of a discounted cash flow:

Imagine that the first year's cash flow from a project is \$400 and the weighted average cost of capital is 8%. Here is the formula:

Discounted Cash Flow Year 1 = \$400/(1+i)^1, where i = 8% and the year = 1

The calculation of the discounted payback period using this example is the following. Imagine that a company wants to invest in a project costing \$10,000 and expects to generate cash flows of \$5,000 in year 1, \$4,000 in year 2, and \$3,000 in year 3. The weighted average cost of capital is 10%. Here are the steps you use to calculate the discounted payback period:

### 1. Discount the cash flows back to the present or to their present value:

Here are the calculations:

• Year 0: -\$10,000/(1+.10)^0 = \$10,000
• Year 1: \$5000/(1+.10)^1= \$4,545.45
• Year 2: \$4000/(1+.10)^2= \$3,305.79
• Year 3: \$3000/(1+.10)^3= \$2,253.94

### 2. Calculate the cumulative discounted cash flows:

• Year 0: - \$10,000
• Year 1: - \$5,454.55
• Year 2: - 4\$2,148.76
• Year 3: \$105.18

Discounted payback period (DPP) occurs when the negative cumulative discounted cash flows turn into positive cash flows which, in this case, is between the second and third year.

The formula to find the exact discounted payback period follows:

DPP = Year Before DPP Occurs + Cumulative Cash Flow in Year Before Recovery ÷ Discounted Cash Flow in Year After Recovery

Using our example above, the precise discounted payback period (DPP) would equal 2 + \$2,148.76/\$2,253.94 or 2.95 years. In the example, the investment recovers its outlays in a little under three years.

## Using a Financial Calculator

You can determine the payback period with a minimum of actual calculation by using one of the many recommended financial calculators available at most office supply stores. Alternatively, go to one of several financial online financial calculator sites.