13.3
349
Payback Analysis
The payback period np is an estimated time for the revenues, savings, and any other monetary benefits to completely recover the initial investment plus a stated rate of return i. There are two types of payback analysis as determined by the required return. No return; i50%: Also called simple payback, this is the recovery of only the initial investment. Discounted payback; i . 0%: The time value of money is considered in that some return, for example, 10% per year, must be realized in addition to recovering the initial investment. An example application of payback may be a corporate senior manager who insists that every proposal return the initial cost and some stated return within 3 years. Using payback as an initial screening tool, no proposal with np . 3 years can become a viable alternative. The payback period should be determined using a required i . 0%. Unfortunately in practice, no-return payback is used too often to make economic decisions. After the formulas are presented, a couple of cautions about payback usage are provided. The equations used to determine np differ for each type of analysis. For both types, the terminology is P for the initial investment in the asset, project, contract, etc., and NCF for the estimated annual net cash flow. Using Equation [1.5], annual NCF is NCF 5 cash inflows 2 cash outflows To calculate the payback period for i 5 0% or i . 0%, determine the pattern of the NCF series. Note that np is usually not an integer. For t 5 1, 2, . . . , np, t5n p
No return, i 5 0%; NCFt varies annually:
0 5 2P 1
No return, i 5 0%; annual uniform NCF:
P NCF np 5 ———
o NCF
t
[13.6]
t51
[13.7] t5n p
Discounted, i . 0%; NCFt varies annually:
0 5 2P 1
NCFt(PyF, i, t) [13.8] t51
Discounted, i . 0%; annual uniform NCF:
0 5 2 P 1 NCF(PyA, i, np)
[13.9]
After n p years, the cash flows will recover the investment in year 0 plus the required return of i%. If the alternative is used more than n p years, with the same or similar cash flows, a larger return results. If the estimated life is less than n p years, there is not enough time to recover the investment and i% return. It is important to understand that payback analysis neglects all cash flows after the payback period of np years. Consequently, it is preferable to use payback as an initial screening method or supplemental tool rather than as the primary means to select an alternative. The reasons for this caution are that No-return payback neglects the time value of money, since no return on an investment is required. Either type of payback disregards all cash flows occurring after the payback period . These cash flows may increase the return on the initial investment. Payback analysis utilizes a signifi cantly different approach to alternative evaluation than the primary methods of PW, AW, ROR, and ByC. It is possible for payback analysis to select a different alternative than these techniques. However, the information obtained from discounted payback analysis performed at an appropriate i . 0% can be very useful in that a sense of the risk involved in undertaking an alternative is provided. For example, if a company plans to utilize a machine for only 3 years and payback is 6 years, indication is that the equipment should not be obtained. Even here, the 6-year payback is considered supplemental information and does not replace a complete economic analysis.
EXAMPLE 13.4
Payback period