Payback period

The payback period is the estimated time it will take to recoup the initial investment in a project. When comparing two projects based on payback periods, the project with a shorter payback period is more desirable than the project with a longer payback period. 

As an example (Table 6.1), if the initial investment in a project is 2,500 and the expectation is to receive 1,500 for the next 3 years, how long will it take to recoup the 2,500 initial investment At time zero t = 0), the initial outlay is 2,500. At year 1, 1,500 is received. The cumulative cash flow through year 1 is the initial outlay of 2,500 plus 1,500 (- 2,500 -E 1,500 = - 1,000). At year 2, the cumulative cash flow is the previous years cumulative cash flow plus year 2 cash inflow of another 1,500 (- 1,000 + 1,500 = 500). By year 2, the initial 2,500 has been recouped, along with an additional 500. If in the second year, the cash flows were evenly distributed throughout the year, the payback period can be determined from the following formula  

Payback period = Year before full recovery -e (Unrecovered cost at start of the year/Cash flow during the year) 

Some companies use another version of the payback period method. It is called the discounted payback period method, which considers the time value of money. The discount rate that is commonly used is the cost of capital for the company. Using the previous example from the NPV section, cash flows are discounted using a 10% discount rate (Table 6.2). 

The payback period is longer when cash flows are discounted. When ranking projects based on these two variants of the payback period method, there can be conflicting rankings. The payback period method is the same as breaking even. The regular payback period method shows when cash flows equal cash outlay. Contrastingly, the discounted payback period method shows when cash flows equal cash outlay plus debt and equity costs. 

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Payout time (PT), or payback period, is a measure of the time, usually in years, required to recover the investment in a scenario in which the time value of money is neglected. This can be represented by the general form... 

Payback Period Another traditional method of measuring profitability is the payback period or fixed-capital-return period. Actually, this is really a measure not of profitability but of the time it takes for cash flows to recoup the original fixed-capital expenditure. 

The payback-period method takes no account of cash flows or profits received after the breakeven point has been reached. The method is based on the premise that the earher the fixed capital is recovered, the better the project. However, this approach can Be misleading. 

Let us consider projects A and B, having net annual cash flows as listed in Table 9-2. Both projects have initial fixed-capital expenditures of 100,000. On the basis of payback period, project A is the more desirable since the fixed-capital expenditure is recovered in 3 years, compared with 5 years for projec t B. However, project B runs for 7 years with a cumulative net cash flow of 110,000. This is obviously more profitable than project A, which runs for only 4 years with a cumulative net cash flow of only 10,000. 

When considering future projects, top management will most likely require the discounted-cash-flow rate of return and the payback period. However, the estimators should also supply management with the following ... 

Relationship between (PBP) and (DCFRR) For the case of a single lump-sum capital expenditure Cpc which generates a constant annual cash flow Acf in each subsequent year, the payback period is given by the equation... 

Figure 9-13 is a plot of Eq. (9-61) in the form of the number of years n required to reach a certain discounted-cash-flow rate of return (DCFRR) for a given payback period (PBP). The figure is a modification of plots previously published by A. G. Bates [Hydrocarbon Process., 45, 181-186 (March 1966)], C. Estrup [Br Chem. Eng., 16, 171 (February-March 1971)], and F. A. Holland and F. A. Watson [Process Eng. Eeon., 1, 293-299 (December 1976)]. 

FIG. 9-13 Relationship between payback period and discounted-cash-flow rate of return. 

Inflation (DCFRR) and Payback Period More insight into the effect of inflation on (DCFRR) calculations can be gained dv considering the payback period (PBP), which is defined as the elapsed time necessary for the positive aftertax cash flows from the project to... 

The relationship set out in Eq. (9-115) can also be viewed via a different chain of causality with (DCFRR) as a given parameter, (PBP) as the independent variable, and n as the variable whose value is being sought. Such an approach is the basis for the lines in Fig. 9-31, each of which shows the number of years of projec t life required to achieve an effective interest rate or a (DCFRR) of 20 percent by projects having various payback periods. The three hues differ from each other with respec t to the matter of inflation. 

The magnitude of the effect comes through even more clearly in Fig. 9-32, a plot of the time needed to reach a nominal (DCFRR) of 20 percent against the inflation rate for various values of (PBP). This plot also shows that the longer the payback period, the greater the increase in apparent profitability of the project. 

The true rates of return L can be calculated from Eq. (9-116) to be 20, 9.09, 0, and —7.69 percent respec tively for generaf inflation rates of 0, 10, 20, and 30 percent. Thus, although the time required for a projec t with a payback period of 4 years to reach a nominal (DCFRR) of 20 percent is reduced from almost 9 years under conditions of no inflation to less than 3V2years for 30 percent inflation, the true rate of return that prevails for the latter condition is —7.69 percent, implying that the project loses money in real terms. 

It is interesting to note that, in order to reach a real (DCFRR) or of 20 percent within a reasonable project hfetime when the general inflation rate is 20 percent, it follows from Fig. 9-31 that the payback period for the project must not be much in excess of 2 years. 

FIG. 9-32 Adverse effect of inflation for higher payback periods. 

FIG. 9-33 Relationship between measured-survival function, number of payback periods, and contribution efBciency. 

Here, p is the number of payback periods that have elapsed since the project started to generate positive net annual cash flows Acp up to any given year n since project startup. It is given by... 

The relationship between the number of payback periods, the contribution efficiency, and the measiired-siii vival fiiucliou as set out in Eq. (9-117) is plotted in Fig. 9-33. 

Thus, (MSF) should in practice be regarded as a given or predetermined variable, and Eq. (9-117) accordingly becomes more useful if it is rearranged. For instance, the values of contribution efficiency for a given value of (MSF) are related to the number of elapsed payback periods by... 

It is also possible to combine (MSF) considerations with evaluation of the true discounted-cash-flow rate of return (DCFRR) by using Eq. (9-62). The relationship of Eq. (9-59) is independent of inflation if all money values are based on those prevailing in the startup year. For this case, Fig. 9-34 shows the true (DCFRR) reached in a given time, expressed as the number of elapsed payback periods for various values of the payback period. 

Let us consider a project having a contribution efficiency of 0.684 and a payback perioa of 3 years. Figure 9-33 shows that when two payback periods have elapsed, a measured-sui vival function of 0.9 has... 

The payback period in years for a heat-pump system is the additional feed-capital cost Cpc divided by the annual saving on heating costs. This can be written as... 

Equation (9-244) can be used to calculate the payback period when elec tricity oil, or gas, etc., is used to drive the compressor and also to provide the base heating. 

Equation (9-244) shows that, to have a low payback period (PBP), Cpc W and y should be small and y, (COP), and Cj large. Clearly as the unit cost of input energy Cj increases, the economics of heat pumps becomes more favorable. 

Equation (9-245) shows that in this particular case the fixed-capital cost per unit of input energy CpJW) must not exceed 160,000 (GJh" )" or 576 per kilowatt, to have a 1-year payback period if the heat pump is operational for 8000 h/year. For this case the corresponding value of y is about 0.12 for a heat pump with an operating life of 10 years purchased with money borrowed at a 10 percent rate of interest. 

The tables were based upon the cost of energy at the end of the first year, a 10 percent inflation rate on energy costs, a 15 percent interest cost, and a present-worth pretax profit of 40 percent per annum on the last increment of insulation thickness. Dual-layer insulation was used for 3l/2-in and greater thicknesses. The tables and a full explanation of their derivation appear in a paper by F. L. Rubin (op. cit.). Alternatively, the selected thicknesses have a payback period on the last nominal l/2-in increment of 1.44 years as presented in a later paper by Rubin [ Can You Justify More Piping Insiilation Hydrocarbon Process., 152-155 (July 1982)]. 

If an option proves to be technically ineffective or inappropriate, it is deleted from the list of potential alternatives. Either follo ving or concurrent with the technical evaluation, an economic study is performed, weighing standard measures of profitability such as payback period, investment returns, and net present value. Many of these costs (or, more appropriately, cost saving may be substantial yet are difficult to quantify. (Refer to Economic Considerations Associated with Pollution Prevention.)... 

High-efficiency expanders and their relatively short payback period made even smaller units economically attractive. These machines have demonstrated a high degree of reliability. Hundreds of units have been in continuous uninterrupted service for many years this has removed the need for backup equipment and has demonstrated that unattended operation is entirely feasible. 

As Figure 4-108 shows, increasingly large cash flows develop in later years of operation. These large cash flows are essentially ignored by a simple payback period calculation. 

Using the cash flows derived from the increasing utility rates, calculating the rate-of-return would show 33.8% for a one-stage unit and 35.5% for a two-stage unit. The corresponding payback periods are 3.7 years and 3.4 years. 

Applying two important tax credits would improve the early years cash flow and shorten the payback period. A 10% investment tax credit and a 10% energy tax credit applied to the incremental capital costs for the expanders yields nearly 1.0 million additional first-year cash... 

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