Inflation DCFRR

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... 

In this equation, (DCFRR) can be viewed as the nominal discounted-cash-flow rate of return uncorrected for inflation and can be thought of as the true or real discounted-cash-flow rate of return. 

Instead of using Eq. (9-113), it is unfortunately common practice to try to obtain the true or effective rate of return by calculating the nominal (DCFRR), based on actual net annual cash flows uncorrected for inflation, and then subtracting the inflation rate from it as if... 

Equation (9-113) shows that Eq. (9-114) is only approximately true and should be used, if at all, solely for low interest rates. Let us consider the case of a nominal (DCFRR) of 5 percent and an inflation rate of 3 percent. Equation (9-14) yields an approximate effective return rate of 2 percent, compared with the real effective rate of 1.94 percent given by Eq. (9-113) i.e., there is an error of 3.1 percent. Now let us consider the case of a nominal (DCFRR) of 2.5 percent and an inflation rate of 23 percent. Equation (9-114) yields an approximate effective return rate of 2 percent, compared with 1.63 percent from Eq. (9-113) in this case, the error that results is 22.7 percent. 

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. 

If there is no inflation, then the middle hne pertains. Because there is no inflation, the nominal (DCFRR) is equal to or identical with the real discounted-cash-flow rate of return, as can be seen from the relationship expressed in Eq. (9-113). 

When inflation does exist, the relevant parameter is which is different from the nominal (DCFRR). Equation (9-113), manipulated into equivalent form,... 

Figure 9-31 shows that the elapsed time necessary to reach a nominal (DCFRR) for a given project decreases sharply with inflation. This figure, hke Fig. 9-29, shows that the effect of inflation is to make a projec t seem more profitable than it ac tuaUy is. 

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. 

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. 

If the fractional inflation rate is a fractional interest rate on a loan can be corrected to an effective rate of interest by Eq. (9-116) with ii substituted for (DCFRR). The effect of various amounts of loan, borrowed at various interest rates ii, on the net present value of a particular, fairly simple project is shown in Fig. 9-37. Thus, if 25,000 were borrowed at an interest rate of 15 percent for the project, the (NPV) would be about 43,000 at a zero inflation rate. But if the inflation for goods and services i, is 10 percent, the effective interest rate for that loan can be calculated from Eq. (9-116) to be only 4.55 percent. It is seen from Fig. 9-37 that this increases the (NPV) of the project to 48,000. This confirms the economic advantage of borrowing at a fixed interest rate in a time of general inflation. 

Effect of Inflation on (DCFRR) A net annual cash flow Acf will have a cash value of Acf(1 + i) 1 year later if invested at a fractional interest rate i. If there is inflation at an annual rate then an effective rate of return or interest rate % can be defined by the equation... 

Intuitively, DCFRR might be seen equivalent with the maximum interest rate of money borrowed to finance the project under the condition that the net cumulative cash flow over the project lifetime would be just sufficient to pay all principal and accumulated interests. In order to obtain consistent comparison, it is recommended to use after-tax values corrected for inflation. Hence, DCFRR is a synthetic measure of process profitability. 

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