# Discounted Payback Period

Some firms use a variant of the regular payback, the discounted payback period, which is similar to the regular payback period except that the expected cash flows are discounted by the project's cost of capital. Thus, the discounted payback period is defined as the number of years required to recover the investment from discounted net cash flows. Figure 7-3 contains the discounted net cash flows for Projects S and L,

 Project S: Net cash flow 0 1 2 3 4 -1,000 500 400 300 100 Cumulative NCF -1,000 -500 -100 200 300 PaybackS = 2.33 years. Project L: Net cash flow 0 1 2 3 4 -1,000 100 300 400 600 Cumulative NCF -1,000 -900 -600 -200 400 PaybackL = 3.33 years.

FIGURE 7-3 Projects S and L: Discounted Payback Period

Project S: Net cash flow Discounted NCF (at 10%) Cumulative discounted NCF Paybacks = 2.95 years.

Project L: Net cash flow Discounted NCF (at 10%) Cumulative discounted NCF PaybackL = 3.88 years.

 0 1 2 3 4 1,000 500 400 300 100 1,000 455 331 225 68 1,000 -545 -214 11 79
 0 1 2 3 4 1,000 100 300 400 600 1,000 91 248 301 410 1,000 -909 -661 -360 50

assuming both projects have a cost of capital of 10 percent. To construct Figure 7-3, each cash inflow is divided by (1 + r)t = (1.10)t, where t is the year in which the cash flow occurs and r is the project's cost of capital. After three years, Project S will have generated \$1,011 in discounted cash inflows. Because the cost is \$1,000, the discounted payback is just under three years, or, to be precise, 2 + (\$214/\$225) = 2.95 years. Project L's discounted payback is 3.88 years:

Discounted paybacks = 2.0 + \$214/\$225 = 2.95 years.

Discounted paybackL = 3.0 + \$360/\$410 = 3.88 years.

For Projects S and L, the rankings are the same regardless of which payback method is used; that is, Project S is preferred to Project L, and Project S would still be selected if the firm were to require a discounted payback of three years or less. Often, however, the regular and the discounted paybacks produce conflicting rankings.

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### Responses

• jayden
What are the project’s payback and discounted payback periods?
8 years ago