Question 9.4: Economic Life of a Challenger (New Asset) A new forklift tru...
Economic Life of a Challenger (New Asset)
A new forklift truck will require an investment of $30,000 and is expected to have year-end MVs and annual expenses as shown in columns 2 and 5, respectively, of Table 9-2. If the before-tax MARR is 10% per year, how long should the asset be retained in service? Solve by hand and by spreadsheet.
TABLE 9-2 Determination of the Economic Life, N^{\ast }, of a New Asset (Example 9-4)
| (1) End of Year, k | (2) MV, End of Year k | (3) Loss in Market Value (MV) during Year k | (4) Cost of Capital = 10% of Beginning of Year MV | (5) Annual Expenses (E_{k}) | (6) [= (3) + (4) + (5)] Total (Marginal) Cost for Year (TC_{k}) | (7) EUAC^{a} through Year k |
| 0 | $30,000 | |||||
| 1 | 22,500 | $7,500 | $3,000 | $3,000 | $13,500 | $13,500 |
| 2 | 16,875 | 5,625 | 2,250 | 4,500 | 12,375 | 12,964 |
| 3 | 12,750 | 4,125 | 1,688 | 7,000 | 12,813 | 12,918 N^{\ast}_{c}= 3 |
| 4 | 9,750 | 3,000 | 1,275 | 10,000 | 14,275 | 13,211 |
| 5 | 7,125 | 2,625 | 975 | 13,000 | 16,600 | 13,766 |
^{\ast} EUAC_k =\left[\sum_{j=1}^{k} TC_j(P/F,10\%,j)\right] (A/P,10\%,k)
The solution to this problem is obtained by completing columns 3, 4, 6 [Equation (9-2 : TC_{k}(i%) = MV_{k-1} − MV_{k}+ iMV _{k-1} + E_{k})], and 7 of Table 9-2. In the solution, the customary year-end occurrence of all cash flows is assumed. The loss in MV during year k is simply the difference between the beginning-of-year market value, MV_{k-1}, and the end-of-year market value, MV_{k}. The opportunity cost of capital in year k is 10% of the capital unrecovered (invested in the asset) at the beginning of each year. The values in column 7 are the EUACs that would be incurred each year (1 to k) if the asset were retained in service through year k and then replaced (or retired) at the end of the year. The minimum EUAC occurs at the end of year N^{\ast}_{c}. It is apparent from the values shown in column 7 that the new forklift truck will have a minimum EUAC if it is kept in service for only three years(i.e., N^{\ast}_{c} = 3).
Spreadsheet Solution
Figure 9-1 illustrates the use of a spreadsheet to solve for the economic life of the asset described in Example 9-4. The capital recovery formula in column C uses absolute addressing for the original capital investment and relative addressing to obtain the current year market value. Column E calculates the PW of the annual expense values in column D. Column F determines the EUAC of the annual expenses. The cumulative EUAC column (G) is the sum of columns C and F. The IF function in column H places a label that identifies the minimum EUAC value, which corresponds to the economic life of the asset.
