A road between Yellowknife, NWT and Uranium City, Saskatchewan will have a most likely construction cost of $5 million per mile. Doubling this cost is considered to have a probability of 30%, and cutting it by 25% to have a probability of 10%. The government uses an interest rate of 8% for these types of projects, and the road should last 40 years. Calculate the expected value of the equivalent annual construction cost per mile

Given that the construction cost is $ 5 million per mile, doubling cost probability is 30%, cutting cost 25% probability is 10%, interest rates is 8% and the number of years is 40.

We can calculate the expected value of construction cost as follows.

IN most likely to get the expected value = Construction cost x Double probability

= 5 x 60% = 3

Doubling the cost, the expected value = (2 x construction cost) x probability

= (2 x 5) x 30% = 3

Reducing the cost by 25, the expected value = (75% of construction cost) x the probability

= (75% x 5) x 10% = 0.375

The total expected value will be as follows;

3 + 3 + 0.375 = 6.375

Therefore, the expected construction cost per mile is 6.375 per mile.

Calculating the Annuity PV factor

Construction cost is $ 5million, number of years is 40, r is 8%, the pv is as follows;

Annuity pv value = {1- (1+ r) ^-n}/ r

Annuity pv value = {1- (1+ 0.08) ^-25}/ 0.08

=[1 - (1.08)^-40]/0.8

=[1 - 0.0460]/ 0.08

=0.954/0.08

=11.92

 Expected value of the equivalent annual construction cost per mile = Expected construction cost/ PV factor

6.375/11.92

$0.5348 million per mile