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

Question

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[latex]^{\ast }[/latex], 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[latex]_{k}[/latex])	(6) [= (3) + (4) + (5)] Total (Marginal) Cost for Year (TC[latex]_{k}[/latex])	(7) EUAC[latex]^{a}[/latex] 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[latex]^{\ast}_{c}[/latex]= 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

[latex]^{\ast}[/latex][latex] EUAC_k =\left[\sum_{j=1}^{k} TC_j(P/F,10\%,j)\right] (A/P,10\%,k) [/latex]

Accepted Answer

The solution to this problem is obtained by completing columns 3, 4, 6 [Equation (9-2 : TC[latex]_{k}[/latex](i%) = MV[latex]_{k-1}[/latex] − MV[latex]_{k}[/latex]+ iMV [latex]_{k-1}[/latex] + E[latex]_{k}[/latex])], 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[latex]_{k-1}[/latex], and the end-of-year market value, MV[latex]_{k}[/latex]. 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[latex]^{\ast}_{c}[/latex]. 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[latex]^{\ast}_{c}[/latex] = 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.

Question 9.4: Economic Life of a Challenger (New Asset) A new forklift tru...

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