A City is planning to build a bridge over a riverthat has been experiencing incr
ID: 2586712 • Letter: A
Question
A City is planning to build a bridge over a riverthat has been experiencing increasing flood levels in recent decades. The city is considering three different bridge designs. There are concerns that climate change and the consequent rise in flood levels would raise the maintenance and repair costs of the bridge. The city has analyzed the net present value of the bridge benefits in terms of economic development and the bridge construction and maintenance expenses under three conditions evolving during the next 100 years(based on the opinions of climate change experts): (i) no change in flood levels (with probability of 30%); (ii) moderate rise in flood levels (with probability of 60%); and (iii) extreme rise in flood levels (with probability of 10%). The net present values over 100 years associated with the three designs and these three flood levels are as follows:
DETERMINE the preferred design for each of the following decsion criteria:
A)expected value
B) Most probable value
C) Long shot value
D) expected loss
E) most probably lost
F) Long shot loss
Design No flood level change (30% probability) moderate rise in flood level (60% probability) extreme rise in flood level (10%probability) 1 $120 Million $60 Million $20 Million 2 $150 Million $ - 90 Million $ -120 Million 3 $90 Million $80 Million $60 MillionExplanation / Answer
A. Expected Value - Calculate the total probable benefits from each design
Design 1 = $120 x 30% + $60 x 60% + $20 x 10% = $74 Million
Design 2 = 150 x 30% + (-$90 x 60%) + (-120 x 10%) = -21 Million
Design 3 = $90 x 30% + $80 x 60% + $60 x 10% = $81 Million
Since the expected benefits are highest in design 3, it should be preferred.
B. Most Probable Value - Design with highest benefits in 60% probability condition should be accepted under most probable value. Since the designs are being selected on the basis of highest probability.
Design 3 should be preferred as it has highest benefits of $80 million under 60% probability.
C. Long shot Value - Under long shot value project should be chosen on the basis of most extreme climate conditions i.e. Extreme rise in floods. Since project 3 is having highest benefits of $60 Million in that category, it is most preferred under long shot value.
D. Expected Loss - Under expected loss, project with the least expected losses should be selected.
Design 1 = $120 x 30% + $60 x 60% + $20 x 10% = $74 Million
Design 2 = 150 x 30% + (-$90 x 60%) + (-120 x 10%) = -21 Million
Design 3 = $90 x 30% + $80 x 60% + $60 x 10% = $81 Million
Since design 2 is having negative benefits, it means it should not be accepted as having highest expected losses. Design is most preferred out of the reamaning two as it is having maximum benefits and least losses.
E. Most Probable Lost - Preferred design should be the one which is having most losses. In the given case, preferred design is 2 as it is having losses.
F. Long shot loss - Design two should be selected as it is having losses.
Dear Student, kindly comment if any answer is wrong or needs clarification.
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