Question 8.2: Real-Dollar Equivalent of Actual After-Tax Cash Flow An engi...
Real-Dollar Equivalent of Actual After-Tax Cash Flow
An engineering project team is analyzing the potential expansion of an existing production facility. Different design alternatives are being considered. The estimated after-tax cash flow (ATCF)in actual dollars for one alternative is shown in column 2 of Table 8-1. If the general price inflation rate (f) is estimated to be 5.2% per year during the eight-year analysis period, what is the real-dollar ATCF that is equivalent to the actual-dollar ATCF? The base time period is year zero (b = 0).
TABLE 8-1 ATCFs for Example 8-2
| (1) End of Year, k | (2) ATCF (A$) | (3) (P/F,f%, k − b) = [1/(1.052)^{k-0}] | (4) ATCF (R$), b = 0 |
| 0 | −172,400 | 1 | −172,400 |
| 1 | −21,000 | 0.9506 | −19,963 |
| 2 | 51,600 | 0.9036 | 46,626 |
| 3 | 53,000 | 0.8589 | 45,522 |
| 4 | 58,200 | 0.8165 | 47,520 |
| 5 | 58,200 | 0.7761 | 45,169 |
| 6 | 58,200 | 0.7377 | 42,934 |
| 7 | 58,200 | 0.7013 | 40,816 |
| 8 | 58,200 | 0.6666 | 38,796 |
The application of Equation (8-1 : (R\$ )_{k}= (A\$ )_{k}\left(\frac{1}{1+f} \right) ^{k-b}= (A$)_{k}(P/F, f%, k − b)) is shown in column 3 of Table 8-1. The ATCF in real dollars shown in column 4 has purchasing power in each year equivalent to the original ATCF in actual dollars (column 2) .