Question

A flood control project with a life of 13 years will require an investment of ​$55000 and annual maintenance costs of ​$5500. The project will provide no benefits for the first three years but will save ​$28000 per year in flood damage starting in the fourth year. The appropriate MARR is 12​% per year. What is the modified​ B-C ratio for the flood control​ project?

a. 1.25

b.5.72

c. 1.41

d. 2.05

e. 1.86

Answer 1

Initial Cost=I=$55000

Annual maintenance cost=C=$5500

Useful life=n=13 years

MARR=i=12%

Annual benefit =R=$28000 starting in 4th year

PW of maintenance costs=PW(M)=C*(P/A,12%,13)

PW of maintenance costs=PW(M)=5500*6.423548 =$35,329.51

Let us now calculate the PW of benefits which is given by

PWB=R*(P/F,12%,3)*(P/A,12%,10)

(P/F,0.12,3)=1/(1+0.12)^3=0.711780

PWB=28000*0.711780*5.650223 =$112608.04

Modified B-C ratio=(PWB-PWC)/I=(112608.04-35329.51)/55000=1.405

Correct option is

c) 1.41