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A city that is attempting to attract a professional football team is planning to build a new stadium costing $500 million. Annual upkeep is expected to amount to $1,000,000 per year. The artificial turf will have to be replaced every 20 years at a cost of $2,000,000. Painting every 5 years will cost $250,000. If the city expects to maintain the facility indefinitely, what will be its capitalized cost at an interest rate of 10% per year

Respuesta :

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

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