Question 9.4: The KLN Company is attempting to determine the economically ......
The KLN Company is attempting to determine the economically best size of processor machine for their facilities. The six alternative machine sizes which are feasible are as given in Table 9-3. Each machine has a life of 100 years and no salvage value, so that i* = R/I, as in Example 9.3. The company has a total capital budget of $350 000 and a MARR of 15%. Which machine should they buy?
| Table 9-3 | |||
| Size of
Machine |
Annual Revenue,
R |
Investment,
I |
i* |
| Economy | $7 200 | $60000 | 12% |
|
Regular Super Delux Bulk |
25 000
36 000 45 000 50 000 |
100 000 200 000 220 000 300000 |
25%
18% 20.45% 16.67% |
| Extended | 52 000 | 385000 | 20.5% |
The Extended machine is unacceptable according to step 1 of the selection algorithm, and the Economy machine is unacceptable according to step 3. The application of steps 5 and 6 to the four surviving candidates is shown in Table 9-4; step 7 gives Delux as the winner.
Let us examine the logic of the selection algorithm, on the assumption that the company can realize 15% (the MARR) by implementing the do-nothing alternative. Consider the first comparison in Table 9-4. Super costs AI = $100 000 more than Regular, and yields AR = $11 000 more per year. If the company chose Super, it would, in effect, be making $11 000 a year on a $100000 investment; that is, it would be investing at rate Ai* = 11%, whereas it could be earning MARR = 15%. Choosing Super would thus entail an opportunity loss of
(15% – 11%)($100 000) = $4000 per year
Or, looked at in a slightly different way, if the Regular machine is purchased, at a saving of $100 000, the company will earn $25 000 a year on the machine, plus 15% × $100 000 = $15 000 a year on the do-nothing alternative. This is a total annual return of $40 000 on a total investment of $200 000. The same total investment in the Super machine will earn only $36 000 a year.
In this first comparison, it so happens that the economically superior machine has the larger i*-value. Note however, that the eventual winner, Delux, has a smaller i*-value than Regular. As we have seen, when purchase prices differ, a mere comparison of i*-values is not decisive; one must also consider what will be done with any funds left over from the purchase of the cheaper machine.
| Table 9-4 | ||
| Comparisons | i* | Steps 5 and 6 |
|
Regular vs. Super |
25% vs. 185 |
\left. \begin{matrix} \text{Standard \#1} \\ \text{vs.} \\ \text{Challenger \#1} \end{matrix} \right\} \to \Delta i^*\ =\ \frac{A\ R}{\Delta\ I}\ =\ \frac{\$36\ 000\ -\ \$25\ 000}{\$200\ 000\ -\ \$100\ 000} = \frac{\$11\ 000}{\$100\ 000} = 11\% < \text{MARR}
Decision: reject challenger #1 and repeat step 5 |
|
Regular vs. Delux |
25% vs. 20.455 |
\left. \begin{matrix} \text{Standard \#1} \\ \text{vs.} \\ \text{Challenger \#2} \end{matrix} \right\} \to \Delta i^*\ =\ \frac{\$20\ 000}{\$120\ 000}\ =\ 16.7\%\ >\ \text{MARR}
Decision: replace standard #1 (Regular) with challenger #2 (Delux) and repeat step 5 |
| Delux
vs. Bulk |
20.45%
vs. 16.67% |
\left. \begin{matrix} \text{Standard \#2} \\ \text{vs.} \\ \text{Challenger \#3} \end{matrix} \right\} \to \Delta i^*\ =\ \frac{\$5\ 000}{\$80\ 000}\ =\ 6.25\% < \text{MARR}
Decision: reject challenger #3 |