Question

Riyadh City is planning a public recreational facility with an initial cost of SR 7.2 Million and a maintenance cost of 800,000/year. Number of people expected to visit the facility is 90,000 person/year. 40% of visitors will receive a benefit of SR 12/visit, 45% will receive SR 18/visit, and 15% will receive SR 28/visit. For a 30-year planning horizon and 12% interest rate, the B/C ratio of the investment is closest to:

a) 0.909

b) 0.984

c) 1.069

d) 1.163

Answer 1

Initial Investment of the facility = SR 7,200,000

Annual Maintenance cost = 800,000/year

Number of people expected to the visit the facility = 90,000 person/year

Out of the 90,000 person/per year

40% visitors receive benefit of 12/visit – 40% of 90,000 = 36,000

45% visitors receive benefit of 18/visit – 45% of 90,000 = 40,500

15% visitors receive benefit of 28/visit – 15% of 90,000 = 13,500

Annual Benefit will be = (36,000 * 12) + (40,500 * 18) + (13,500 * 28) = 1,539,000

Planning horizon = 30 years

Interest Rate = 8%

Calculating the B/C Ratio using the Present Worth Method

B/C Ratio = PW of Benefits ÷ PW of Costs

PW of Benefits = 1,539,000 (P/A, 8%, 30)

PW of Benefits = 1,539,000 (11.25778) = 17325723

PW Cost = 7,200,000 + 800,000 (P/A, 8%, 30)

PW Cost = 7,200,000 + 800,000 (11.25778) = 16206224

B/C Ratio = 17325723.42 ÷ 16206224

B/C Ratio = 1.069

Answer – c) 1.069