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Solve and document your solutions to the problems to be posted. Solutions must be detailed (documenting it in a word file explaining per cell in the excel file). 9-27. Refer to Example 9-4. By how much would the MARR have to change before the economic life decreases by one year? How about to increase the economic life by one year? (9.5) 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. EXAMPLE 9-4 TABLE 9-2 Determination of the Economic Life, N*, of a New Asset (Example 9-4) (6) (3) (5) Annual (1) (2) MV, End (4) Cost of Capital = 10% of Beginning of Year MV [= (3) + (4) + (5)] Total (Marginal) Cost for Year (7) EUACa Loss in Market Value (MV) during Year k End of through Year, k of Year k Expenses (Ek) (TCK) Year k 0 $30,000 1 22,500 $7,500 $3,000 $3,000 $13,500 2 16,875 5,625 2,250 4,500 12,375 3 12,750 4,125 1,688 7,000 12,813 4 9,750 3,000 1,275 10,000 14,275 5 7,125 2,625 975 13,000 16,600 EUACk = [C}_1 TC; (P/F, 10%,j)] (A/P, 10%,k) j=1 $13,500 12,964 12,918 N = 3 13,211 13,766 Solution by Hand The solution to this problem is obtained by completing columns 3, 4, 6 [Equation (9-2)], 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, MVk-1, and the end-of-year market value, MVk. 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 No. 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 = 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 = D5 / (1+ $B$1) A5 = PMT($B$1, A5,- ($B$4-B5)) + B5 * $B$1 = PMT($B$1, A5,- SUM($E$5:E5)) B C D E F G H A MARR 1 10% 2 End of Year MV Annual Expense PW of Annual Exp. EOY EUAC of Ann.Exp. Cumulative EUAC 3 CR Amount 4 0 5 1 6 2 $ 30,000 $ 22,500 $ 10,500 $ 3,000 $ $ 16,875 $ 9,250 $ 4,500 $ $ 12,750 $ 8,211 $ 7,000 $ $ 9,750 $ 7,363 $ 10,000 $ $ 13,000 $ 7 3 2,727 $3,000 $ 13,500 3,719 $ 3,714 $ 12,964 5,259 $ 4,707 $ 12,918