Question

A hydroelectric dam would cost $50,000,000 to build, and annual maintenance cost of $1,000,000 need to be made per year. In addition to that, every 5 years, a major overhaul cost of $4,000,000 needs to be made. Assume applicable interest rate of 10% per year, and the dam is expected to last indefinitely. a. What would be the capitalized cost (present worth) of the dam?

Answer 1

The capitalized cost or present worth of the hydroelectric dam is $75,614,046.

Step-by-step explanation:

To calculate the capitalized cost or present worth of the dam, we need to determine the total cost of the dam over its lifetime. The annual maintenance cost of $1,000,000 per year can be viewed as a perpetuity, which means a constant annual payment forever. Using the formula for the present value of a perpetuity, the present worth of the annual maintenance cost is $1,000,000 / 0.10 = $10,000,000.

The major overhaul cost of $4,000,000 every 5 years can be treated as an annuity. The present value of an annuity can be calculated using the formula for the present value of an annuity. The present worth of the major overhaul cost is $4,000,000 * (1 - (1 + 0.10)-5) / 0.10 = $15,614,046.

Finally, we can calculate the present worth of the dam by summing up the initial cost of $50,000,000, the present worth of the annual maintenance cost of $10,000,000, and the present worth of the major overhaul cost of $15,614,046. The capitalized cost or present worth of the dam is $50,000,000 + $10,000,000 + $15,614,046 = $75,614,046.