Question 8.8: The prospective maintenance expenses for a commercial heatin...
The prospective maintenance expenses for a commercial heating, ventilating, and air-conditioning (HVAC) system are estimated to be $12,200 per year in base-year dollars (assume that b = 0). The total price escalation rate is estimated to be 7.6% for the next three years (e_{1,2,3} = 7.6%), and for years four and five it is estimated to be 9.3% (e_{4.5} = 9.3%). The general price inflation rate (f) for this five-year period is estimated to be 4.7% per year. Develop the maintenance expense estimates for years one through five in actual dollars and in real dollars, using e_{j} and e′_{j} values, respectively .
| (1) End of Year, k | (2) A$ Adjustment (e_{j}) | (3) Maintenance Expenses, A$ | (4) R$ Adjustment (e′_{j}) | (5) Maintenance Expenses, R$ |
| 1 | $12,200(1.076)^{1} | $13,127 | $12,200(1.0277)^{1} | $12,538 |
| 2 | 12,200(1.076)^{2} | 14,125 | 12,200(1.0277)^{2} | 12,885 |
| 3 | 12,200(1.076)^{3} | 15,198 | 12,200(1.0277)^{3} | 13,242 |
| 4 | 12,200(1.076)^{3} (1.093)^{1} | 16,612 | 12,200(1.0277)^{3} (1.0439)^{1} | 13,823 |
| 5 | 12,200(1.076)^{3} (1.093)^{2} | 18,157 | 12,200(1.0277)^{3} (1.0439)^{2} | 14,430 |
The development of the annual maintenance expenses in actual dollars is shown in column 2 of Table 8-4. In this example, the general price inflation rate is not the best estimate of changes in future maintenance expenses. The five-year period is divided into two subperiods corresponding to the two different price escalation rates (e_{1,2,3} = 7.6%; e_{4,5} = 9.3%). These rates are then used with the estimated expenses in the base year; (A$)_{0} = (R$)_{0} = $12,200. The development of the maintenance expenses in real dollars is shown in column 4. This development is the same as for actual dollars, except that the e′_{j} values = [Equation (8-8 : e^{'}_{j}= \frac{e_{j}-f}{1+f})] are used instead of the e_{j} values. The e′_{j} values in this example are as follows:
e^{'}_{1,2,3}= \frac{0.076 − 0.047}{1.047} = 0.0277, or 2.77%;
e^{'}_{4,5}= \frac{0.093 − 0.047}{1.047} = 0.0439, or 4.39%.
This illustrates that differential inflation, or deflation, also results in market price changes in real dollars, as well as in actual dollars. An additional example of differential price changes is provided in Section 8.7 (case study).