Question 8.7: After-Tax Analysis: A Mixture of Fixed and Responsive Cash F...
After-Tax Analysis: A Mixture of Fixed and Responsive Cash Flows The cost of a new and more efficient electrical circuit switching equipment is $180,000. It is estimated (in base year dollars, b = 0) that the equipment will reduce current net operating expenses by $36,000 per year (for 10 years) and will have a $30,000 market value at the end of the 10th year. For simplicity, these cash flows are estimated to increase at the general price inflation rate (f = 8% per year). Due to new computer control features on the equipment, it will be necessary to contract for some maintenance support during the first three years. The maintenance contract will cost $2,800 per year. This equipment will be depreciated under the MACRS (GDS) method, and it is in the five-year property class. The effective income tax rate (t) is 38%; the selected analysis period is 10 years; and the MARR_{m} (after taxes) is i_{m}= 15% per year.
(a) Based on an actual-dollar after-tax analysis, is this capital investment justified?
(b) Develop the ATCF in real dollars .
(a) The actual-dollar after-tax economic analysis of the new equipment is shown in Table 8-3 (columns 1–7). The capital investment, savings in operating expenses, and market value (in the 10th year) are estimated in actual dollars (column 1), using the general price inflation rate and Equation (8-1). The maintenance contract amounts for the first three years (column 2) are already in actual dollars. (They are unresponsive to further price changes.) The algebraic sum of columns 1 and 2 equals the before tax cash flow (BTCF) in actual dollars (column 3). In columns 4, 5, and 6, the depreciation and income-tax calculations are shown. The depreciation deductions in column 4 are based on the MACRS (GDS) method and, of course, are in actual dollars. The entries in columns 5 and 6 are calculated as discussed in Chapter 7. The effective income tax rate (t) is 38% as given. The entries in column 6 are equal to the entries in column 5 multiplied by −t. The algebraic sum of columns 3 and 6 equals the ATCF in actual dollars (column 7). The PW of the actual-dollar ATCF, using im = 15% per year, is
PW(15%) = −$180,000 + $36,050(P/F, 15%, 1)
+···+ $40,156(P/F, 15%, 10) = $33,790.
Therefore, the project is economically justified.
(b) Next, Equation (8-1) is used to calculate the ATCF in real dollars from the entries in column 7. The real-dollar ATCF (column 9) shows the estimated economic consequences of the new equipment in dollars that have the constant purchasing power of the base year. The actual-dollar ATCF (column 7) is in dollars that have the purchasing power of the year in which the cost or saving occurs. The comparative information provided by the ATCF in both actual dollars and real dollars is helpful in interpreting the results of an economic analysis. Also, as illustrated in this example, the conversion between actual dollars and real dollars can easily be done. The PW of the real-dollar ATCF (column 9), using ir = (im − f)/(1 + f) = (0.15 − 0.08)/1.08 = 0.06481, or 6.48%, is PW(6.48%) = −$180,000 + $33,379(P/F, 6.48%, 1)
+ · · ·+ $18,600(P/F, 6.48%, 10)
= $33,790.
Thus, the PW (equivalent worth in the base year with b = 0) of the real-dollar ATCF is the same as the PW calculated previously for the actual-dollar ATCF.
TABLE 8-3 Example 8-7 When the General Price Inflation Rate Is 8% per Year
| End of Year, k | (1) A$ Cash Flows | Contract (A$) | Depreciation (A$) | Taxable Income | Income Taxes (t = 0.38) | ATCF | R$ Adjustment [1/(1 + f)]^{k−b} |
| 0 | −$180,000 | −$180,000 | −$180,000 | 1.0000 | |||
| 1 | 38,880^a | −$2,800 | 36,080 | $36,000 | −$30 | 46.186 | 0.9259 |
| 2 | 41,990 | −2,800 | 39,190 | 57,600 | 6,996 | 39.513 | 0.8573 |
| 3 | 45,349 | −2,800 | 42,549 | 34,560 | −3,036 | 38.246 | 0.7938 |
| 4 | 48,978 | 48.978 | 20,736 | −10,732 | 40.675 | 0.7350 | |
| 5 | 52,895 | 52.895 | 20,736 | −10,732 | 39.359 | 0.6806 | |
| 6 | 57,128 | 57.128 | 10,368 | −10,732 | 38.252 | 0.6302 | |
| 7 | 61,697 | 66.697 | −10,732 | 41.312 | 0.5835 | ||
| 8 | 66,632 | 71.964 | −10,732 | 44.618 | 0.5403 | ||
| 9 | 71,964 | 77.720 | −10,732 | 48.186 | 0.5003 | ||
| 10 | 64,767^b | 64.767 | −24,611 | 40.156 | 0.4632 |