Question

The state of Pahang has decided to replace an old winding road. Planners agree that the old road must be replaced or repaired. Three alternatives are proposed. Alternative A is to repair and resurface the old road. Alternative B is to cut a new road following the terrain. Alternative C also involves a new highway to be built along a straight line. The initial cost, annual operation and maintenance cost, annual benefit and economic life of the three alternatives are summarized in Table 3, The interest rate is 9%, compounded annually. Evaluate the three alternatives based on Benefit Cost Ratio. i) 15 Marks) ij) Justify your opinion to select the best altcmative (4 Marks) Table 3 Alternative A Alternative BAlternative C Items Initial cost (RM)150,000,000 250,000,000 200,000,000 Annual operation and200,000 360,000 330,000 maintenace cost (RM) Annual benefit (RM)30,500,000 38,100,000 26,400,000 Economic life (Years) 10 12

Answer 1

ANSWER:

A)

1) Alternative a:

aw of benefits = annual benefit = 30,500,000

aw of costs = annual operation and maintenance cost + initial cost(a/p,i,n)

aw of costs = 200,000 + 150,000,000(a/p,9%,11)

aw of costs = 200,000 + 150,000,000 * 0.1469

aw of costs = 200,000 + 22,035,000

aw of costs = 22,235,000

b/c ratio = aw of benefits / aw of costs = 30,500,000 / 22,235,000 = 1.37

so the b/c ratio is 1.37

2) Alternative b:

aw of benefits = annual benefit = 38,100,000

aw of costs = annual operation and maintenance cost + initial cost(a/p,i,n)

aw of costs = 360,000 + 250,000,000(a/p,9%,10)

aw of costs = 360,000 + 250,000,000 * 0.1558

aw of costs = 360,000 + 38,950,000

aw of costs = 39,310,000

b/c ratio = aw of benefits / aw of costs = 38,100,000 / 39,310,000 = 0.97

so the b/c ratio is 0.97

3) Alternative c:

aw of benefits = annual benefit = 26,400,000

aw of costs = annual operation and maintenance cost + initial cost(a/p,i,n)

aw of costs = 330,000 + 200,000,000(a/p,9%,12)

aw of costs = 330,000 + 200,000,000 * 0.1397

aw of costs = 330,000 + 27,940,000

aw of costs = 28,270,000

b/c ratio = aw of benefits / aw of costs = 26,400,000 / 28,270,000 = 0.93

so the b/c ratio is 0.93

so the best alternative is alternative a as the best alternative has the b/c ratio more then 1.

B) Since alternative a has the lowest initial cost and lowest annual cost , it makes as the best alternative and supported by the fact that the b/c ratio of alternative is more then 1 as when we select any alternative a we look for lower costs and higher benefits and this alternative a has lowest costs out of the three alternatives.