In: Accounting
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
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 |
PV of Annual Disbenefits | 483 | 483 |
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