Question 10.3: The XYZ Company owns a Cyear-old pump that originally cost $......
The XYZ Company owns a Cyear-old pump that originally cost $3000. For the past four years the operating and maintenance costs of this pump have been:
\begin{matrix} \text{Year of Service, k} & \text{Operating and Maintenance Costs,} C_k \\ 1 & \$ 90 \\ 2 & 180 \\ 3 & 560 \\ 4 & 950 \end{matrix}
The company originally planned to keep this pump 8 years. If the pump is retained, the expected future operating and maintenance costs will be:
\begin{matrix} \text{Year of Service, k} & \text{Operating and Maintenance Costs,} C_k \\ 5 & \$1125 \\ 6 & 1500 \\ 7 & 1700 \\ 8 & 2000 \end{matrix}
The pump could be sold today as a used pump for SV_o = $1200. It is expected that the pump could be sold a year from now for $900; two years from now for $800; and afterwards for $500. A new, energy-saving pump, with expected service life of 8 years, has just become available for P = $4000. Its costs are as follows:
\begin{matrix}\text{Year of Service, j} & \text{Operating and Maintenance Costs,} C_j \\ 1 & \$\ 40 \\ 2 & 80 \\ 3 & 260 \\ 4 & 450 \\ 5 & 625 \\ 6 & 1000 \\ 7 & 1200 \\ 8 & 1500\end{matrix}
It is estimated that if this new pump is purchased it could be sold one year later for $3100, two years later for $2000, three years later for $1500, four years later for $1000, and thereafter for $900. Given a MARR of 15%, should the XYZ Company replace the old machine now, or at some later time?
In computing the EUAC curve of the old pump, the sunk costs of years 1 through 4 are disregarded. Thus, k = 5 becomes j = 1, and we have:
\operatorname{EUAC}(j)=\operatorname{CR}(j)+A(j) (j=1,\cdot\cdot\cdot,4) (1)
where
\text{CR}(j)=(\text{SV}_{0}-\text{SV}_{j})(\text{AIP},{159},j)+({0}.{15})\text{SV}_{j}
A(j)=[C_{1}(P/F,15\%,1)+\cdot\cdot\cdot+ C_{j}\left(P/F,15\%,j\right)]\left(\operatorname{AIP},15\%,j\right)
Similarly, for the new pump,
\mathrm{EUAC}(j)=\mathrm{CR}^{′}(j)+A^{′}(j)\qquad(j=1,\ldots,8) (2)
\mathrm{CR}^{\prime}(j)=(\mathrm{P-SV}^{'}_{j})\,(A/P,15\%,\,\mathbf{j})+(0.15)\mathrm{SV}_{j}^{\prime}
A^{\prime}(j)=[C_{1}^{\prime}(P/F,15\%,1)+\cdot\cdot\cdot+C_{j}^{\prime}(P/F,15\%,j)]\,(A/P,15\%,j)\,
Evaluating (1) for j = 1,. . . ,4 and (2) for j = 1, . . . ,8, we generate Table 10-2. It is seen that all the EUAC-values for the new pump are below the lowest EUAC-value for the old pump. Hence, the old pump should immediately be replaced by the new one. Even in the worst case, where the new pump is kept for only two years, its EUAC would still be lower than that for keeping the old pump for even one more year. The reader should note the oscillation of the EUAC curve for the new pump; the curve is not of the simple form shown in Fig. 10-1.
| Table 10-2 | ||
| Years From Now, j | EUAC(j) | EUAC'(j) |
| 1 | $1605.00 | $1540.00 |
| 2 | 1663.9 | 1588.84 |
| 3 | 1796.3 | 1436.55 |
| 4 | 1852.18 | 1384.18 |
| 5 | 1402.41 | |
| 6 | 1371.86 | |
| 7 | 1368.52 | |
| 8 | 1387.94 | |
