Question

1. Compare the following alterntives given a market rate of 5.45% per year and an inflation rate of 3% per year. Use first the B/C method to determine feasibility and then the incremental B/C method to determine the oprimum level of investment.

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

Answer 1

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.