# 2.20 NPV and AAA One Last Problem (“Question #8”)

-You are given two competing projects, “A” and “B.”

-Project A costs \$1,000 and produces a \$250 annuity for twelve years.

-Project B costs \$150 and produces a \$100 annuity for four years. Analysts imagine that the project can be replicated at least three times with no change in the -projected data.

-K = 10%, annual

1.       NPVA = 250 (PVAF 0.10; 12) – 1,000

= 250 (6.8137) – 1,000

= \$703.425

2.       NPVB = (100) (PVAF 0.10; 4

= (100) (3.1699) – 150

= \$166.99

= \$166.99 ÷ (1.10)0 = 166.99

+ \$166.99 ÷ (1.10)4 =  114.05

+ \$166.99 ÷ (1.10)8 =   77.90

NPVB  = \$358.94

Alternate Solution:      \$166.99 ÷ 3.1699 = 52.68 (This is the AAA)

52.68 (6.8137)                     = \$358.94

Another Solution:      \$100 (6.8137) – 150 – 150 (0.6830) – 150 (0.4665)

= \$358.94

3.       AAAA =

703.425 = (x) (6.8137)

X = \$103.24

4.      AAAB =

One way:      \$358.94 = (x) (6.8137) = \$52.68

Another:       \$166.99 = (x) (3.1699) = \$52.68

5. We choose Project A

 NPV AAA A \$703.425 \$103.24 B \$358.94 \$52.68

Remember: AAA does not require replication, assuming no change in projected data for subsequent periods.