Question

16. Use incremental analysis to select the best alternatives using Benefit - Cost ration Cost Pw(benefits) 4000 2000 6000 1000 9000 10000 7330 47000 8730 1340 9000 9600 Useful life is 20years Interest 6%

Answer 1

	A	B	C	D	E	F
Cost (C)	4,000	2,000	6,000	1,000	9,000	10,000
Pw (benefits) (B)	7,330	47,000	8,730	1,340	9,000	9,500
Useful life is 20 years
Interest 6%
BCR (Benefit/Cost)	1.83	23.50	1.46	1.34	1.00	0.95
PVIFA (n=20, i=6%)	11.470	11.470	11.470	11.470	11.470	11.470
PV (Cost) (A)	45,880.00	22,940.00	68,820.00	11,470.00	103,230.00
PV (Benefits) (B)	84,075.10	539,090.00	100,133.10	15,369.80	103,230.00
B-C Ratio (B/A)	1.83	23.50	1.46	1.34	1.00	0.95

Steps :

First of all we will reject the alternative with BCR less than 1. Hence, F is straightaway rejected as its BCR is 0.95 i.e. cost is more than benefit.

The order of the alternatives with respect to their costs are D, B, A, C, E

Then we will find the present value of costs and benefits of all the optimal alternatives considering n = 20 and i = 6% and will then calculate the Benefit Cost (B-C) Ratio as Present value of Benefits / Present Value of Costs. We can see that the ratio is same when we calculate considering the present value of all the cash flows or by considering only the absolute values since the cost and benefits both are recurring in nature.

Incremental Cost-Benefit Analysis :

Alternative D requires the least investment and its B-C Ratio is 1.34 (as calculated above) and is acceptable.

Now the incremental B-C ratio if we compare Alternative D with

1. Alternative B =

(539,090.00 - 15,369.80)/(22,940.00 - 11,470.00) = 45.66

2. Alternative A=

(84,075.10 - 15,369.80)/(45,880.00 - 11,470.00) = 2

3. Alternative C =

(100,133.10 - 15,369.80)/(68,820.00 - 11,470.00) = 1.48

4. Alternative E =

(103,230.00 - 15,369.80)/(1,03,230.00 - 11,470.00) = 0.96

Therefore based on the above, Alternative B is selected as final alternative as the incremental B-C ratio is highest in its case.