APY NRG Energy plans to construct a giant solar plant in San

APY? NRG Energy plans to construct a giant solar plant in Santa Teresa, New Mexico, to supply electricity to West Texas Electric. The plant will have 390,000 heliostats to concentrate sunlight onto 32 water towers to generate steam. It will provide enough power for 30,000 homes. If the company spends $35 million per month for 10 years in constructing the plant, how much will the company have to make each year in years 3 through 10 (that is, 8 years) to recover its investment plus 18% per year, compounded monthly? 4.

Solution

4.

Monthly spending = $35 million

Time n = 120 months

Monthly interest rate R = 18%/12 = 1.5%

Present value of the investment = 35*(1-1/(1+1.5%)^120)/.015

Present value of the investment = $1942.45 Million

Now,

Effective annual interest rate (K) = (1+18%/12)^12 - 1 = 19.56%

Let, X is the amount to be collected every year from year 3 to year 10 to recover investment and effective 19.56% return.

For this purpose,

1942.45 = X*(1/1.1956^3 + 1/1.1956^4 + 1/1.1956^5 + 1/1.1956^6 + 1/1.1956^7 + 1/1.1956^8 + 1/1.1956^9 + 1/1.1956^10)

1942.45 = X*2.72

X = 1942.45/2.72

X = $714.136 Million (approx. due to the approximation of the interest rate up to 2 decimal units)