# 1.6 The Payback and Discounted Payback Methods

The analyst’s job is to assess the financial merits of a potential capital project based on Free Cash Flow projections, and to make a recommendation to either “accept” or “reject” it accordingly. Presented below are two basic analytic approaches, presented as a starting point for project investment analysis, i.e., Capital Budgeting.

Code:

PVF: Present Value Factor

PVCF: Present (discounted) Value of the Cash Flow

 Analyst’s Pro-forma Payback Method Discounted Payback Method Period Free Cash Flow Cumulative Cash Flow PVF (r =.10) PVCF Cumulative PVCF 0 (\$10,000) (\$10,000) 1.0000 (\$10,000) (\$10,000) 1 1,000 (9,000) 0.9091 910 (9,090) 2 2,000 (7,000) 0.8264 1,653 (7,437) 3 3,000 (4,000) 0.7513 2,254 (5,183) 4 4,000 000 0.68308 2,732 (2,451) 5 4,000 4,000 0.6209 2,484 33 6 4,000 0.5654 2,262 2,295 7 4,000 0.5132 2,053 8 4,000 n 4,000

You will note above that in “year 0,” the firm invested \$10,000 in the project. In the first year, the project is expected to produce \$1,000 in free cash flow, so that the firm will then be “behind” by only \$9,000. This goes on until the project recovers its initial cost, and thereafter produces “profits,” in some sense.

The discounted payback adjusts the cash inflows for the time value of money. This adjustment reduces the nominal values to their respective present values, and therefore, extends the length of the payback. We have used a discount rate of 10% above.

The decision rule for the payback identifies a preference for the project, among competing alternatives, with the shorter (discounted) payback – here only one project is presented, but you may imagine another with a different payback. The simple payback method does not account for the time value of money, and hence is analytically deficient. In our example, the proposed project’s payback is four years, and the discounted payback is just over fourTake note that Payback is expressed in terms of years. Should another competing project have a shorter (discounted) payback, the analyst would prefer that.

The discounted payback indeed accounts for TVM, but is deficient in that it ignores any cash flows after the payback period. Imagine you have two competing, mutually-exclusive projects and you choose the one with the shorter discounted payback. The rejected project however, may have substantial, and vastly superior, cash inflows to be received after its payback. The method (but perhaps not you!) ignores these later cash flows, which may contribute substantially to the firm’s financial position and profits.

The payback methods do not provide any rule of thumb in the matter of the evaluation of a single, independent, non-competing project. What does it mean – financially – when we may say that a project’s payback is “four” years? Shall we accept it? On what objective basis shall we do so?

Question:

What if the sequence of the first four cash inflows were reversed? Under each method, what would the Paybacks be?

1. There would be no change in the case of the simple Payback.
2. In the case of the Discounted Payback, the greater cash flows would come in sooner and the payback would be shorter, due to TVM!

Assumptions for “Ranking Criteria”:

Earlier, we used the word “Preference.” In other words, we could rank-order our project preferences using the relative Payback (or Discounted Payback) periods of competing projects. Projects with shorter paybacks would be preferred, but not necessarily accepted. These methods provide no “Rule of Thumb” which informs us explicitly whether to accept (“green light”) or reject (“red light”) the project.

We are also assuming a known Discount Rate. The discount rate used would be the corporation’s “Cost of Capital.” You will recall that the Free Cash Flow projections excluded the cost of (Debt and Equity) Capital. We now bring that cost back in – in the form of the discount rate. In a later chapter, we will discuss the meaning of, and formula for, calculating the Cost of Capital. For now, it will be a “given.”