Question

4. The Indiana Highway Department wants to construct a new rural highway. The engineering team is considering two designs:

a. Design A calls for a concrete pavement costing $90/ft. with a 20-year life, two paved ditches each costing $3/ft., three box culverts each costing $9,000/mile, annual maintenance costs of $1,800/mile, culvert cleaning costs of $450/mile every five years. Design A has a 20-year life.

b. Design B calls for a bituminous pavement costing $45/ft. with a 10-year life, two sodded ditches each costing $1.50/ft., three pipe culverts each costing $2,250/mile with a 10-year life, replacement culverts will cost $2,400 each, annual maintenance costs of $2,700/mile, culvert cleaning cost of $225/mile every year, and annual ditch maintenance costs of $3/ft.

Compare the two designs on the basis of equivalent worth per mile for a 20-year period. The interest rate is 6%.

Answer 1

Since the number of cash flows in this problem is large, it is recommended to solve it in a spreadsheet program like excel. Let's start with design A.

The approach to design A:

1) In this case, we calculate the per mile cost for all years from 0 to 20. So, for example 90$ per ft becomes 90 x 5280 = 475200$ per mile.

2) After we get the year by year costs for everything, we discount each cost to the present value by using the Present value (PV) formula.

PV = FV x (1+i)^-n

where FV = future value of the cash flow;

i = interest rate = 6% = 0.06

n = number of years

Following is the calculation I made in excel for design A

So, you can clearly see that the present value of future costs for design A is 555,441.48 $.

Let's move on to design B. This gets a little tricky because the life is only 10 years. This means that the road will have to be built once again after 10 years and the relevant costs will have to be considered.

The calculation method for design B is same as design A. Only the costs are different. Refer the following spreadsheet for design B:

So, you can see, in this case, the design B road costs 611,992.47$ per mile.

Bottom line is; for 20 years, design A is cheaper than design B by 56,550.99$ per mile