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.