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.
