Question

1.       A project has the following cash flow.

Year	Costs	Benefits
0	$10,000	0
1	0	$5,000
2	$1,000	$5,000
3	0	$3,000

Assuming a discount rate of 10%, estimate the following:

a)      Net Present Value (NPV)

b)     Discounted Benefit-Cost Ratio

c)      Net discounted Benefit-Cost Ratio

d)     Is the project feasible? Explain your answer

Answer 1

(a) Annual net benefit = Annual benefit - Annual cost

NPV is sum of all annual net benefit discounted at 10%, computed as follows.

Year	Cost ($)	Benefit ($)	Net Benefit ($)	PV Factor @10%	Discounted Net Benefit ($)
	(A)	(B)	(C)=(B)-(A)	(D)	(C)x(D)
0	10,000	0	-10,000	1.0000	-10,000
1	0	5,000	5,000	0.9091	4,545
2	1,000	5,000	4,000	0.8264	3,306
3	0	3,000	3,000	0.7513	2,254
				NPV ($) =	105

(b)

Present Value (PV) of Costs and Benefits are computed as follows.

Year	Cost ($)	PV Factor @10%	Discounted Cost ($)
	(A)	(B)	(A) x (B)
0	10,000	1.0000	10,000
1	0	0.9091	0
2	1,000	0.8264	826
3	0	0.7513	0
		PV of Costs ($) =	10,826
Year	Benefit($)	PV Factor @10%	Discounted Benefit ($)
	(A)	(B)	(A) x (B)
0	0	1.0000	0
1	5,000	0.9091	4,545
2	5,000	0.8264	4,132
3	3,000	0.7513	2,254
		PV of Benefit ($) =	10,932

Discounted Benefit-Cost ratio (BCR) = PV of benefits / PV of costs

= $10,932 / $10,826

= 1.01

Note that Discounted BCR and Net Discounted BCR are the same terms.

(c) Since NPV is positive and (Net) Discounted Benefit-Cost ratio is higher than 1, the project is feasible.