Question 15.9: PW with Two Inflation Rates In Examples 15.7 and 15.8, the P...
PW with Two Inflation Rates
In Examples 15.7 and 15.8, the PW of the cost of accounting services was calculated using differential inflation rates. Calculate the PW using the 6% inflation rate for the services ( f_{a}) and the 4% inflation rate for the economy ( f ).
First, the year-1 dollars of CF_{1} are chosen as the constant-value unit. The next step is to apply Equation 15.1 to calculate the nominal-dollar cash flows shown in column B of Exhibit 15.6. These are calculated at the 6% inflation rate ( f_{a}) for accounting services. Then, Equation 15.4 and f, the economy’s inflation rate of 4%, are used to calculate the real, or constant-value, cash flows shown in column C. Column B can be calculated recursively; that is:
F_{T+t} = F_{T} (1 + f )^{t} (15.1)
Real CF_{t} = Nominal CF_{t} /(1 + f )^{t−1} (15.4)
Nominal CF_{t} = Nominal CF_{t−1}(1 + f_{a}).
However, column C cannot be computed recursively; it must use Equation 15.4.
Those column C values are simply multiplied by the (P/F,8%,t) values in column D. The result is shown and then summed in column E. If an EAW were needed, then the PW would be
multiplied by (A/P,8%,5). As in the previous examples, columns D and E could be replaced by NPV(A5,C9:C13) function.
This approach is identical mathematically to that used in Example 15.8. As before, the
| E | D | C | B | A | |
| CF year 1 | -$20,000 | 1 | |||
| f = CPI | 4% | 2 | |||
| f(a) = inflation rate for accounting | 6% | 3 | |||
| f(delta-a) = exact differential rate for accounting | 1.92% | 4 | |||
| real interest rate | 8% | 5 | |||
| market interest rate | 12.32% | 6 | |||
| 7 | |||||
| PW of CF(t) | PW factor | Constant $ Cash Flow | Nominal $ Cash Flow | Year | 8 |
| -18,519 | .9259 | -20,000 | -20,000 | 1 | 9 |
| -17,477 | .8573 | -20,385 | -21,200 | 2 | 10 |
| -16,493 | .7938 | -20,777 | -22,472 | 3 | 11 |
| -15,565 | .7350 | -21,176 | -23,820 | 4 | 12 |
| -14,689 | .6806 | -21,583 | -25,250 | 5 | 13 |
| Total – $82,743 | -$82,743 | 14 | |||
| =NPV (A6,B9:B13)*(1+A2) | 15 | ||||
constant-value dollar cash flows and the PW are measured in year-1 dollars. Amarket interest rate computed using Equation 15.2 can be used to compute the PW from the nominal cash flows. The NPV function computes the PW in year-0 dollars. Thus, the formula in B14 includes (1 +A2) or (1 + f ) to convert to year-1 dollars.
(1 + Market rate) = (1 + i )(1 + f ) (15.2)