Question

please show work for how to solve!

1. Consider the following three, mutually exclusive, projects. 1a. Using a benefit to cost ratio (BC) approach, choose the best project using a MARR of 9% and a project lifetime of each of 10 years. Your work must be shown for full credit. 40 points Initial Investment Annual Benefits (Income) Annual Cost (Maintenance) Salvage Value Project A $16,000 $3,500 $750 $2,930 Project B $13,000 $2,500 $400 $1,900 Project C $24,500 $4,500 $900 $1,780 Project D $20,000 $4,000 $1,200 $1,763 AE (1) AE (B) AE (C') Project A $2,300 $3,500 $750 3500/(2300+750) 1.15 Project B $1,900 $2,500 $400 2500/(1900+400) = 1.09 Project $3,700 $4,500 $900 4500/(3700+900) = 0.98 Eliminate C Project D $3,000 $4,000 $1,200 4000/(3000+1200) A-B $400 $1,000 $350 1000/750 =1.33 B/C 0.95 Eliminate D Choose A

Answer 1

ANSWER:

I = 9% AND N = 10 YEARS

1) PROJECT A:

aw of benefits = annual benefits + salvage value(a/f,i,n) = 3,500 + 2,930(a/f,9%,10) = 3,500 + 2,930 * 0.0658 = 3,500 + 192.794 = 3,692.794

aw of costs = annual cost + initial cost(a/p,i,n) = 750 + 16,000(a/p,9%,10) = 750 + 16,000 * 0.1558 = 750 + 2,492.8 = 3,242.8

b/c ratio = aw of benefits / aw of costs = 3,692.794 / 3,242.8 = 1.138

2) PROJECT B:

aw of benefits = annual benefits + salvage value(a/f,i,n) = 2,500 + 1,900(a/f,9%,10) = 2,500 + 1,900 * 0.0658 = 2,500 + 125.02 = 2,625.02

aw of costs = annual cost + initial cost(a/p,i,n) = 400 + 13,000(a/p,9%,10) = 400 + 13,000 * 0.1558 = 400 + 2,025.4 = 2,425.4

b/c ratio = aw of benefits / aw of costs = 2,625.02 / 2,425.4 = 1.082

3) PROJECT C:

aw of benefits = annual benefits + salvage value(a/f,i,n) = 4,500 + 1,780(a/f,9%,10) = 4,500 + 1,780 * 0.0658 = 4,500 + 117.124 = 4,617.124

aw of costs = annual cost + initial cost(a/p,i,n) = 900 + 24,500(a/p,9%,10) = 900 + 24,500 * 0.1558 = 900 + 3,817.1 = 4,717.1

b/c ratio = aw of benefits / aw of costs = 4,617.124 / 4,717.1 = 0.9788

4) PROJECT D:

aw of benefits = annual benefits + salvage value(a/f,i,n) = 4,000 + 1,763(a/f,9%,10) = 4,000 + 1,763 * 0.0658 = 4,000 + 116.0054 = 4,116.0054

aw of costs = annual cost + initial cost(a/p,i,n) = 1200 + 20,000(a/p,9%,10) = 1200 + 20,000 * 0.1558 = 1200 + 3,116 = 4,316

b/c ratio = aw of benefits / aw of costs = 4,116.0054 / 4,316 = 0.9536

since the b/c ratio of project a is the highest , so it will be selected.