A city mayor decides to construct a new bridge over the majo

A city mayor decides to construct a new bridge over the major river in the town. The estimated life of such a structure will be 20 years. There is a 70% probability that the total initial costs (consulting fees and construction) will be $800,000 and a 30% probability that such costs would be $1 million. There is 100% probability that the maintenance costs would be $30,000 every 5 years. How much money should the city borrow now in order to carry out the entire project including maintenance? The interest rate is 5%.

Solution

Estimated life = 20 years

Initial cost can be 800,000 or 1,000,000

Prob                        0.7              0.3

cost*prob              560,000        300,000        =860000

Expected initial cost = 860000

Main costs              30,000 every 5 years

Maintenance costs will be 30000 after 5 years, again 30000 after 10 years ....4 times

Present value can be calculated for interest at 5% as

Hence total requirement at present value for maintenance = 67660.37

Initial cost expected                                                               860000

Amount to be borrowed                                                          927660.37

		Int rate	5%
Main costs	5 years	10 years	15 years	20 years
	30000	30000	30000	30000
Present value	23505.78	18417.4	14430.51	11306.68	67660.37