2.19 Solution for “Questions #6 & #7”
Question #6
| NPV Calculation | Machine A | |
| Cost = | $100,000 | ($100,000) |
| PV of CF | ||
| (Stage 1) | $30,000 x 3.4331= | 102,993 |
| PV of Cost (Stage 2) | $105,000 x 0.5194= | (54,537) |
| PV of CF (Stage 2) | $102,993 x 0.5194= | 53,495 |
| NPV= | $1,951 | |
AAA
1,951 / 5.2161= AAA = $373.32
Notes:
- Can you think of a slightly shorter way in which to calculate the NPV for “A”? Hint: We have a $30 million annuity for ten years.
- There really is no point in calculating the AAA. Because the machine’s anticipated replacement cost has been changed, the AAA for Stage 1 and the combined AAA for both stages will be different. In comparing the two machines’ respective AAAs (see below), the PVAF denominator is the same in each calculation therefore, of course A will be preferred, as its NPV/numerator is greater.
| NPV Calculation | Machine B | |
| Cost = | $132,000 | ($132,000) |
| PV of CF | $25,000 X 5.2161 | 130,403 |
| NPV= | ($1,597) |
AAA
(1,597) / 5.2161 = AAA= ($306.87)
Recommendation: While Machine A is not terribly attractive, we would prefer it over B. The corporation may choose not to replace it after the first five years, because the second five years are projected at a loss.
Question #7
A: -$10,000 + 4,000 (3.1699) – 12,000 (0.6830) + 4,200 (3.1699) (0.6830) = $3,576
B: -15,000 + 3,500 (5.3349) = $3,672
Recommendation: Choose B.
Note: In this case, both the machine’s anticipated replacement cost and the cash flows were changed, not “replicated.”
