A city mayor decides to construct a new bridge over the major river in the town.

Question

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%.

Explanation / Answer

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

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