Question

Two plans have been put forward for the construction of a new bridge in Sunbury in Victoria. The costs and benefits for Plan I and Plan II are given in the following table. What should be the annual benefit for Plan I to have the same benefit-cost ratio as Plan II. It is anticipated that the operation life of both plans will be 80 years. The annual interest rate is set at 9%. Please provide only two numbers in the available box: (1) benefit-cost ratio for Plan II; (2) Annual Benefit for Plan I. (7 points to calculate benefit-cost ratio for Plan II and 10 points to calculate annual benefit for Plan I) Construction material cost Installation Cost Annual Costs Annual Benefit Plan I $65,000,000 $15,000,000 $545,000 X Plan II $35,000,000 $5,000,000 $150,000 $3,200,000

Answer 1

(1)

B-C Ratio, Plan II = PW of annual benefits / (Material cost + Installation cost + PW of annual benefit)

= [3,200,000 x P/A(9%, 80)] / [35,000,000 + 5,000,000 + 150,000 x P/A(9%, 80)]

= [3,200,000 x 11.0998**] / [35,000,000 + 5,000,000 + 150,000 x 11.0998**]

= 35,519,360 / (40,000,000 + 1,664,970)

= 35,529,360 / 41,664,970

= 0.85

(2)

Let annual benefit for Plan I be B. Then

B-C Ratio, Plan I = B-C Ratio, Plan II

0.85 = [B x P/A(9%, 80)] / [65,000,000 + 15,000,000 + 545,000 x P/A(9%, 80)]

0.85 = [B x 11.0998**] / [80,000,000 + 545,000 x 11.0998**]

0.85 = [B x 11.0998**] / [80,000,000 + 6,049,391]

0.85 = [B x 11.0998**] / 86,049,391

B x 11.0998** = 73,141,982.35

B = $6,589,486.51

**From P/A factor table