# 2.17 “Question #2” – Continued

In doing AAA, we must compare Machine A to B in terms of its annual annuity equivalent. Initially, we do not assume that Machine A will be replicated at its term – after three years.

Machine A:

NPVA = (\$87,000) (2.3216) – \$190,000 = \$11,979

With replication: NPVA = \$11,979 + [(11,979 ÷ 1.143)] = \$20,065

AAAA = \$11,979 / 2.3216 = \$5,159.89

AAAA = \$20,065 / (3.8887) = \$5,159.89

Machine B:

NPVB = (\$98,300 (3.8887) – \$360,000 = \$22,259

AAAB = \$22,259 / 3.8887 = \$5,724.07

Conclusions:

• We assume that Machine A may be replicated at its term for another three years.  Since its annuity equivalent cash flow (AAA) is less than B’s, we choose the latter.
• The RCA also favors “B” since its NPV is greater than A’s. (This assumes that “A” is replicated.)
• Both approaches are, and should be, consistent with one another; the rankings or preferences are the same.
• The NPV and AAA methods are consistent with one another; they agree. Since the AAA uses the NPV as its present value, the AAA annuity will also be higher.