37: a firm must decide which of 3 alternatives to adopt to expand its capacity. the firm wishes a minimum annual profit of 20% of the initial cost of each separable increment of investment. any money not invested in capacity expansion can be invested elsewhere for an annual yield of 20% of initial cost. your reasoning must include the ∆irr for each challenger-defender comparison.

As the firm requires a 20% profit on each increment of investment, we should examine the B- A increment of $200,000. (With only a 16% profit rate, C is unacceptable.)

Alt. Initial Cost   Annual Profit   Change in Cost     Change in Profit   Change in Profit Rate

A    $100,000         $30,000

B    $300,000         $66,000              $200,000            $36,000               18%

C   $500,000          $80,000

With the alternative A it produces a 30% profit rate. The $200,000 increment of investment of B rather than A, that is, B- A, yield an 18% profit rate and is not acceptable. Thus it means Alternative B with an overall 22% profit rate can be considered as made up of Alternative A plus the B- A increment. Because the B-A increment is not acceptable, Alternative B should not be adopted.

Therefore the best investment of $300,000, for instance, would be Alternative A (annual profit = $30,000) plus $200,000 elsewhere (which is yielding 20% or $40,000 annually). At this combination firm yields a $70,000 profit, which is better than Alternative B profit of $66,000.