Question

10) Make a benefit/cost analysis by evaluating B/C for the following:

a) a project with initial cost = $7,254 , annual cost= $868, annual benefits= $ 1,867, disbenefits having a present worth PW value of $1,613, interest rate= 9% and life = 5 years

b) a project with initial cost = $2,126 , annual cost= $1,806, annual benefits= $ 1,434, annual disbenefits= $408, interest rate= 3% and life = 9 years.

c) a project with total annual cost= $7,744, annual benefits= $ 9,376, annual disbenefits= $614.

d)for a project with a total PW of cost of $6,439, annual benefits of $ 1,444, annual disbenefits of $482,interest rate of 7% and life of 7 years

Answer 1

Solution:

a).

Particulars/Year	1	2	3	4	5	Total
Annual Cost (B)	868	868	868	868	868	4,340
Annual Benefit (C)	1,867	1,867	1,867	1,867	1,867	9,335
PVF @ 9%	0.92	0.84	0.77	0.71	0.65
PV of Annual Cost	796	731	670	615	564	3,376
PV of Annual Benefits	1,713	1,571	1,442	1,323	1,213	7,262
Total Cost = Initial Cost + PV of annual cost
= 7,254 + 3,376 = 10,630
Total Benefits = PV of Annual Benefits - Disbenefits
= 7,262 - 1,613 = 5,649
Benefit/Cost Ratio = 5,649/10,630
= 0.53

b).

Particulars/Year	1	2	3	4	5	6	7	8	9	Total
Annual Cost (B)	1,806	1,806	1,806	1,806	1,806	1,806	1,806	1,806	1,806	16,254
Annual Benefit (C)	1,434	1,434	1,434	1,434	1,434	1,434	1,434	1,434	1,434	12,906
Annual Disbenefits	408	408	408	408	408	408	408	408	408	3,672
PVF @ 3%	0.97	0.94	0.92	0.89	0.86	0.84	0.81	0.79	0.77
PV of Annual Cost	1,753	1,702	1,653	1,605	1,558	1,512	1,468	1,426	1,384	14,062
PV of Annual Benefits	1,392	1,352	1,312	1,274	1,237	1,201	1,166	1,132	1,099	11,165
PV of Annual Disbenefits	409	409	409	409	409	409	409	409	409	3,680
Total Cost = Initial Cost + PV of annual cost
= 2,126 + 14,062 = 16,188
Total Benefits = PV of Annual Benefits - PV of Disbenefits
= 11,165 - 3,680 = 7,485
Benefit/Cost Ratio = 7,485/16,188
= 0.46

c).

Assuming life is 1 year

Total Cost = 7,744

Total Benefits = Annual Benefits - Disbenefits

= 9,376 - 614 = 8,762

Benefit/Cost Ratio = 8,762/7,744

= 1.13

d).

Particulars/Year	1	2	3	4	5	6	7	Total
Annual Benefit (C)	1,444	1,444	1,444	1,444	1,444	1,444	1,444	10,108
Annual Disbenefits	482	482	482	482	482	482	482	3,374
PVF @ 7%	0.93	0.87	0.82	0.76	0.71	0.67	0.62
PV of Annual Benefits	1,350	1,261	1,179	1,102	1,030	962	899	7,782
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