Question

Air conditioning for a college dormitory will cost $3 million to install and $125,000 per year to operate at current prices. The system should last 14 years. The real cost of capital is 10%, and the college pays no taxes. What is the equivalent annual cost?

Answer 1

The EAC will be as follows:

= Present value of installation and operation / Present value annuity factor of 10% of 14 years

Present value of installation and operation is computed as follows:

= Installation cost + Annual cost of operation x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 3,000,000 + $ 125,000 x [ (1 - 1 / (1 + 0.10)¹⁴ ) 0.10 ]

= $ 3,000,000 + $ 125,000 x 7.366687457

= $ 3,920,835.932

Present value annuity factor of 10% of 14 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= [ (1 - 1 / (1 + 0.10)¹⁴ ) / 0.10 ]

=  7.366687457

So, the cost will be as follows:

= $ 3,920,835.932 / 7.366687457

= $ 532,238.67

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