For the data in Problem 16-2 (problem 2 on this homework) calculate the expected

Question

For the data in Problem 16-2 (problem 2 on this homework) calculate the expected value of the equivalent uniform annual construction cost per mile. Problem 2 is as follows:

A road between Fairbanks and Nome, Alaska will have a most likely construction cost of $4 million per mile. Doubling this cost is considered to have a probability of 30%, and cutting the cost by 25% is considered to have a probability of 10%. The state's interest rate is 8% and the road should last 40 years. What is the probability distribution of the equivalent uniform annual construction cost per mile?

Explanation / Answer

Let us first find Expected value of construction cost

Thus expected construction cost = 5.1 million per mile

Expected value of the equivalent uniform annual construction cost per mile = Cost/PVIFA(8%,40years)

=5.1/11.9246

= $0.4277 million per mile

Particulars Construction cost
(1) Probability
(2) Expected value
(1*2) Most likely 4 60% 2.4 Doubling the cost 8 30% 2.4 Reducing co by 25% 3 10% 0.3 5.1

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