Question

The Santa Clara Valley Water District (SCVWD) wants to explore the possibility of constructing a flood protection project. The cost of constructing the project is 20 million dollars. The life of the project is 60 years. The salvage value is six million dollars. The operating cost is five million dollars per year the first year and linearly increases by 10 percent per year thereafter. The project will benefit 600 thousand customers. Assuming an annual interest rate of seven percent, Answer the following questions:

How much money should the SCWD charge Cost) each costumer who benefits from the project such that the customers cover both the cost of investment and maintenance over the life of the project?

Answer 1

Answer: $1214.98

Explanation:

Given that;

Construction Cost C = $ 20,000,000

Life n = 60 years

Salvage value S = $ 6,000,000

Operating cost for first year R = $ 5,000,000

Increase in operating costs every year g = 10%  = 0.1

Annual interest rate i = 7% = 0.07

Now Present value of growing annual cost can be calculated as follows;

p = R/(i - g) [1 - ((1+g)/(1+i))^n]

Where R is Annual costs in first year , i is Rate of interest , g is Rate of growth , n is time (in years) .

So present value of maintenance cost,

p = 5,000,000/(0.07 - 0.1) [1 - ((1+0.1)/(1+0.07))^60]

= $709,089,487.69

Present value of salvage value can be calculated by below formula:

P = S/(1 + i)^n

Where S is Salvage value , i is Rate of interest , n is time (in years)

Now present value of salvage value,

P2  = 6,000,000 / (1 + 0.07)^60

= $103,543.92

Net Present Value of the project (P) = C + P1 - P2

= 20,000,000 + 709,089,487.69 - 103,543.92

= $728,985,943.77

Now we calculate required revenue from the customers:

Given that;

Number of customers benefitted = 600,000

REVENUE required from each customer  =  Net Present Value of the project / number of customers

= 728,985,943.77 / 600,000

= $1214.98