Alt |
Construction Cost $ |
Annual Benefits $/yr |
Life yrs |
A |
105,000 |
40,000 |
5 |
B |
230,000 |
52,000 |
6 |
C |
350,000 |
64,000 |
7 |
D |
600,000 |
100,000 |
8 |
For the purpose of computing benefits from the projects, the real discount rate is used assuming that cashflows of these alternatives are not inflated.
Particulars | A | B | C | D |
Annual Benefit | 40,000 | 52,000 | 64,000 | 100,000 |
Life | 5 | 6 | 7 | 8 |
PVAF (2.45%,life) | 4.6525 | 5.5173 | 6.3615 | 7.1854 |
PVCI (Annual ben*PVAF) | 186,100 | 286,900 | 407,136 | 718,540 |
Construction cost | 105,000 | 230,000 | 350,000 | 600,000 |
benefit-to-cost ratio | 1.7724 | 1.2474 | 1.1632 | 1.1976 |
Since b/c ratio > 1 in each of the alternatives, therefore, each of the alternatives is justified.
But for finding optimum investment level would be as follows;
Computing Incremental b/c:
Incremental Analysis for Alternative B | |
Particulars | Amount |
Incremental Cashinflows for 5 years | 12,000 |
Pvaf (2.45%,5years) | 4.6525 |
PVCI (a) | 55,830 |
Incremental Cashinflows for 6th year | 52,000 |
pvf(2.45%,6th year) | 0.8648 |
PVCI (b) | 44,970 |
Total PVCI | 1,00,800 |
Incremental Construction cost | 1,25,000 |
Increment b/c | 0.80640 |
Since the incremental b/c <1, hence alternative B shouldn’t opt. |
Incremental Analysis for Alternative C | |
Particulars | Amount |
Incremental Cash inflows for 5 years | 24,000 |
Pvaf (2.45%,5years) | 4.6525 |
PVCI (a) | 1,11,660 |
Incremental Cash inflows for 6th & 7th yr | 64,000 |
pvf(2.45%,6th year and 7th year) | 1.7089 |
PVCI (b) | 1,09,370 |
Total PVCI | 2,21,030 |
Incremental Construction cost | 2,45,000 |
Increment b/c | 0.90216 |
Since the incremental b/c <1, hence alternative C shouldn’t opt. |
Incremental Analysis for Alternative D | |
Particulars | Amount |
Incremental Cashinflows for 5 years | 60,000 |
Pvaf (2.45%,5years) | 4.6525 |
PVCI (a) | 2,79,150 |
Incremental Cashinflows for 6-8 yrs | 1,00,000 |
pvf(2.45%,6-8 yrs) | 2.5329 |
PVCI (b) | 2,53,290 |
Total PVCI | 5,32,440 |
Incremental Construction cost | 4,95,000 |
Increment b/c | 1.07564 |
Since the incremental b/c >1, hence alternative D should opt. |
Hence the Optimum investment level would be at Alternative D.
Compare the following alterntives given a market rate of 5.45% per year and an inflation rate...
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