Answer:
Capitalized cost = - $510,758,686.20
Explanation:
Interest rate = r = 10%, or 0.10
Present value of base cost = $500 million = $500,000,000
Present value of annual upkeep = $1,000,000 / r = $1,000,000 / 0.10 = $10,000,000
Present value of the replacement cost of artificial turf every 20 years = ($2,000,000 * (r / (((1 + r)^20) - 1)) / r = ($2,000,000 * (0.10 / (((1 + 0.10)^20) - 1)) / 0.10 = $349,192.50
Present value of painting every 5 years = ($250,000 * (r / (((1 + r)^5) - 1)) / r = ($250,000 * (0.10 / (((1 + 0.10)^5) - 1)) / 0.10 = $409,493.70
Therefore, we have:
Capitalized cost = - Present value of base cost - Present value of annual upkeep - Present value of the replacement cost of artificial turf every 20 years - Present value of painting every 5 years = - $500,000,000 - $10,000,000 - $349,192.50 - $409,493.70 = - $510,758,686.20
