Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,500.00 to install, $5,117.00 to operate per year for 7 years at which time it will be sold for $6,875.00. The second, RayCool 8, costs $41,210.00 to install, $2,093.00 to operate per year for 5 years at which time it will be sold for $9,096.00. The firm’s cost of capital is 6.16%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

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

4

A firm is must choose to buy the GSU-3300 or the UGA-3000. Both machines make the firm’s production process more efficient which in turn increases incremental cash flows. The GSU-3300 produces incremental cash flows of $26,697.00 per year for 8 years and costs $103,885.00. The UGA-3000 produces incremental cash flows of $29,133.00 per year for 9 years and cost $123,906.00. The firm’s WACC is 8.63%. What is the equivalent annual annuity of the UGA-3000? Assume that there are no taxes.

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

Answer 1

1). Depreciation = Cost of the System / Useful life years = $41,210 / 5 = $8,242

OCF = [-Costs * (1 - t)] + [Depreciation * t]

= [-$2,093 * (1 - 0)] + [$8,242 * 0.0] = -$2,093 + $0 = -$2,093

After-tax salvage value at year 5 = Salvage Value * (1 - t) = $9,096 * (1 - 0) = $9,096

NPV = PV of Cash Inflows - PV of Cash Outflows

PV of Cash Outflows = Annual OCF * [{1 - (1 + r)^-n} / r] + Cost

= $2,093 * [{1 - (1 + 0.0616)^-5} / 0.0616] + $41,210

= $2,093 * [0.2584 / 0.0616] + $41,210

= [$2,093 * 4.1941] + $41,210 = $8,778.23 + $41,210 = $49,988.23

NPV = [$9,096 / (1 + 0.0616)⁵] - $49,988.23

= $6,745.99 - $49,988.23 = -$43,242.24

EAC = NPV / [{1 - (1 + r)^-n} / r]

= -$43,242.24 / [{1 - (1 + 0.0616)^-5} / 0.0616]

= -$43,242.24 / [0.2584 / 0.0616] = -$43,242.24 / 4.1941 = -$10,310.27

2). Depreciation = Cost of the System / Useful life years = $123,906 / 9 = $13,767.33

OCF = [-Costs * (1 - t)] + [Depreciation * t]

= [$29,133 * (1 - 0)] + [$13,767.33 * 0.0] = $29,133 + $0 = $29,133

NPV = PV of Cash Inflows - PV of Cash Outflows

PV of Cash Inflows = Annual Cash Inflows * [{1 - (1 + r)^-n} / r]

= $29,133 * [{1 - (1 + 0.0863)^-9} / 0.0863]

= $29,133 * [0.5253 / 0.0863]

= $29,133 * 6.0865 = $177,317.75

,NPV = $177,317.75 - $123,906 = $53,411.75

EAA = NPV / [{1 - (1 + r)^-n} / r]

= $53,411.75 / [{1 - (1 + 0.0863)^-9} / 0.0863]

= $53,411.75 / [0.5253 / 0.0863] = $53,411.75 / 6.0865 = $8,775.46