Question

Consider two alternative water resource projects, A and B.

•Project A will cost$2,533,000 and will return $1,000,000 at the end of 5 years and $4,000,000 at the end of10 years. Project A has a life of 10 years.

•Project B will cost $4,000,000 and will return $2,000,000 at the end of 5 and 15years, and another $3,000,000 at the end of 10 years. Project B has a life of 15 years.

Assuming an interest rate of 10%per year:

(a)Compute the net present value of each Project? Which Project is preferred?

(b)What is the annual net benefit for each Project?

(c)Would the preferred Project differ if the interest ratewas5%?

Answer 1

PROJECT A
YEAR	CASH INFLOWS(A)	PV FACTOR (B)	PRESENT VALUE (A*B)
1		0.909	-
2		0.826	-
3		0.751	-
4		0.683	-
5	10,00,000.00	0.621	6,20,921.32
6		0.564	-
7		0.513	-
8		0.467	-
9		0.424	-
10	40,00,000.00	0.386	15,42,173.16
	50,00,000.00	6.14	21,63,094.48
NPV	PRESENT VALUE - INITIAL COSTS	2533000-2163094.48	3,69,905.52

PROJECT B
YEAR	CASH INFLOWS(A)	PV FACTOR (B)	PRESENT VALUE (A*B)
1		0.91	-
2		0.83	-
3		0.75	-
4		0.68	-
5	20,00,000.00	0.62	12,41,842.65
6		0.56	-
7		0.51	-
8		0.47	-
9		0.42	-
10	30,00,000.00	0.39	11,56,629.87
11	-	0.35	-
12		0.32	-
13		0.29	-
14		0.26	-
15	20,00,000.00	0.24	4,78,784.10
	70,00,000.00	7.61	28,77,256.61
NPV	PRESENT VALUE - INITIAL COSTS	2877256.61-4000000	-11,22,743.39

A positive NPV means that the sum of the present value of future cash flow is greater than the cash flow.

This indicates that the project is profitable and therefore acceptable.

Negative NPV means that the sum of the future cash flow's present value is less than the cash flow.

SO IT IS ADVISED TO REJECT BOTH projects HAVING NEGATIVE NPV.

ANNUAL NET BENEFIT FOR EACH PROJECT
BC RATIO =	PV OF BENEFITS/ PV OF COSTS
PROJECT A	2163094.48 / 2533000	0.85
PROJECT B	2877256.61/4000000	0.72

C) PROJECT A
YEAR	CASH INFLOWS(A)	PV FACTOR AT 5%(B)	PRESENT VALUE (A*B)
1		0.952	-
2		0.907	-
3		0.864	-
4		0.823	-
5	10,00,000.00	0.784	7,83,526.17
6		0.746	-
7		0.711	-
8		0.677	-
9		0.645	-
10	40,00,000.00	0.614	24,55,653.01
			-
	50,00,000.00	6.14	32,39,179.18
NPV	PRESENT VALUE - INITIAL COSTS	3239179.18-2533000	7,06,179.18
PROJECT B
YEAR	CASH INFLOWS(A)	PV FACTOR AT 5%(B)	PRESENT VALUE (A*B)
1		0.952	-
2		0.907	-
3		0.864	-
4		0.823	-
5	20,00,000.00	0.784	15,67,052.33
6		0.746	-
7		0.711	-
8		0.677	-
9		0.645	-
10	30,00,000.00	0.614	18,41,739.76
11	-	0.585	-
12		0.557	-
13		0.530	-
14		0.505	-
15	20,00,000.00	0.481	9,62,034.20
			-
	70,00,000.00	10.38	43,70,826.29
NPV	PRESENT VALUE - INITIAL COSTS	2877256.61-4000000	3,70,826.29

A positive NPV means that the sum of the present value of future cash flow is greater than the cash flow.

This indicates that the project is profitable and therefore acceptable.

Negative NPV means that the sum of the future cash flow's present value is less than the cash flow.

SO IT IS ADVISED TO SELECT PROJECT A WHICH HAS HIGHER NPV $706179.18