Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,161.00 to install, $5,148.00 to operate per year for 7 years at which time it will be sold for $6,874.00. The second, RayCool 8, costs $41,347.00 to install, $2,073.00 to operate per year for 5 years at which time it will be sold for $9,004.00. The firm’s cost of capital is 6.50%. What is the equivalent annual cost of the AC360? Assume that there are no taxes.

Answer format: Currency: Round to: 2 decimal places.

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,409.00 to install, $5,143.00 to operate per year for 7 years at which time it will be sold for $6,929.00. The second, RayCool 8, costs $41,079.00 to install, $2,125.00 to operate per year for 5 years at which time it will be sold for $9,006.00. The firm’s cost of capital is 6.50%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

Answer format: Currency: Round to: 2 decimal places.

Could really use the help!!! Please show all steps (not excel) for better understanding!! :D Thank You.

Answer 1

Sol: The values provided in the question for AC360 are as follows:

Cost to install for AC360 = $26161

Cost to operate AC360 per year = $5148

Years AC360 is operated = 7

Selling price of AC360 = $6874

Cost of capital = 6.5%

The formula to calculate Equivalent annual cost is as follows:   

Equivalent annual cost for AC360 = (Net Present Value for AC360 * Cost of capital) / (1 - (1 + Cost of capital) ^ (- Years operated))

The formula to calculate Net Present Value (NPV) for using AC360 is as follows:

NPV = - Cost to install - (Operating cost / (1 + cost of capital)) - (Operating cost / ((1 + cost of capital) ^ 2)) - (Operating cost / ((1 + cost of capital) ^ 3)) - (Operating cost / ((1 + cost of capital) ^ 4)) - (Operating cost / ((1 + cost of \ capital) ^ 5)) - (Operating cost / ((1 + cost of capital) ^ 6)) - (Operating cost / ((1 + cost of capital) ^ 7)) + (Selling price / ((1 + cost of capital) ^ 7))

Using values provided in question to calculate NPV:

NPV = - 26161 - (5148 / (1 + 0.065)) - (5148 / ((1 + 0.065) ^ 2)) - (5148 / ((1 + 0.065) ^ 3)) - (5148 / ((1 + 0.065) ^ 4)) - \ (5148 / ((1 + 0.065) ^ 5)) - (5148 / ((1 + 0.065) ^ 6)) - (5148 / ((1 + 0.065) ^ 7)) + (6874 / ((1 + 0.065) ^ 7))

= - 26161 - (5148 / 1.065) - (5148 / 1.134) - (5148 / 1.208) - (5148 / 1.286) - (5148 / 1.37) - (5148 / 1.459) - (5148 / 1.554) + (6874 / 1.554) (rounding decimals to 3 places)

= - 26161 - 4833.803 - 4539.683 - 4261.589 - 4003.11 - 3757.664 - 3528.444 - 3312.741 + 4423.423 (rounding decimals to 3 places)

= - 49974.611

Using NPV values in Equivalent annual cost formula

Equivalent annual cost = (- 49974.611 * 0.065) / (1 - ((1 + 0.065) ^ (- 7)))

= - 3248.35 / (1 - (1.065 ^ (- 7)))

= - 3248.35 / (1 - 0.644)

= - 3248.35 / 0.356

= - 9124.58 (rounded to 2 decimals)

The values provided in the question for RayCool8 are as follows:

Cost to install for RayCool8 = $41079

Cost to operate RayCool8 per year = $2125

Years RayCool8 is operated = 5

Selling price of RayCool8 = $9006

Cost of capital = 6.5%

The formula to calculate Equivalent annual cost is as follows:   

Equivalent annual cost for RayCool8 = (Net Present Value for RayCool8 * Cost of capital) / (1 - (1 + Cost of capital) ^ (- Years operated))

The formula to calculate Net Present Value (NPV) for using RayCool8 is as follows:

NPV = - Cost to install - (Operating cost / (1 + cost of capital)) - (Operating cost / ((1 + cost of capital) ^ 2)) - (Operating cost / ((1 + cost of capital) ^ 3)) - (Operating cost / ((1 + cost of capital) ^ 4)) - (Operating cost / ((1 + cost of \ capital) ^ 5)) + (Selling price / ((1 + cost of capital) ^ 5))

Using values provided in question to calculate NPV:

NPV = - 41079 - (2125 / (1 + 0.065)) - (2125 / ((1 + 0.065) ^ 2)) - (2125 / ((1 + 0.065) ^ 3)) - (2125 / ((1 + 0.065) ^ 4)) - \ (2125 / ((1 + 0.065) ^ 5)) + (9006 / ((1 + 0.065) ^ 5))

= - 41079 - (2125 / 1.065) - (2125 / 1.134) - (2125 / 1.208) - (2125 / 1.286) - (2125 / 1.37) + (9006 / 1.37) (rounding decimals to 3 places)

= - 41079 - 1995.305 - 1873.898 - 1759.106 - 1652.401 - 1551.095 + 6573.723 (rounding decimals to 3 places)

= - 43337.082

Using NPV values in Equivalent annual cost formula

Equivalent annual cost = (- 43337.082 * 0.065) / (1 - ((1 + 0.065) ^ (- 5)))

= - 2816.91 / (1 - (1.065 ^ (- 5)))

= - 2816.91 / (1 - 0.73)

= - 2816.91 / 0.27

= - 10433 (rounded to 2 decimals)