Question

"The military is considering purchasing a new transport helicopter. It is believed the helicopter will be needed for 12 years. Helicopter 1 has an immediate purchase cost of $112,000; the annual maintenance is $5,000; it can be salvaged for $19,000 at the end of its service life of 2 years. Helicopter 2 has an immediate acquisition cost of $164,000; the annual maintenance is $8,000, and it can be salvaged for $18,000 at the end of its service life of 6 years. Assume both helicopters can be purchased and operated repeatedly at the same costs. What is the annual equivalent cost of the helicopter that the military should purchase if the interest rate is 8.1%?"

Answer 1

Equivalent Annual Cost = Asset Price x [Discount Rate/1 - (1 + Discount Rate)^-Periods] + Annual Maintenance Cost

For Helicopter 1:

Purchase cost = $ 112,000

Salvage value = $ 19,000

PV of salvage value = $ 19,000/ (1+0.081)²

                                = $ 19,000/ (1.081)²

                                = $ 19,000/1.168561

                                = $ 16,259.31

Asset price = Purchase cost – PV of Salvage value = $ 112,000 - $ 16,259.31 = $ 95,740.69

Discount Rate = 8.1 % = 0.081

Periods = 2

Annual maintenance = $ 5,000

Equivalent Annual Cost = $ 95,740.69 x [0.081/1-(1+0.081)^-2] + $ 5,000

                                      = $ 95,740.69 x [0.081/1-(1.081)^-2] + $ 5,000

                                       = $ 95,740.69 x [0.081/1- 0.855753] + $ 5,000

                                       = $ 95,740.69 x [0.081/0.144247] + $ 5,000

                                      = ($ 95,740.69 x 0.561538) + $ 5,000

                                      = $ 53,762.05 + $ 5,000

                                      = $ 58,762.05

For Helicopter 2:

Purchase cost = $ 164,000

Salvage value = $ 18,000

PV of salvage value = $ 18,000/ (1+0.081)⁶

                                 = $ 19,000/ (1.081)⁶

                                 = $ 19,000/ 1.595711

                               = $ 11,280.24

Asset price = Purchase cost – PV of Salvage value = $ 164,000 - $ 11,280.24 = $ 152,719.76

Discount Rate = 8.1 % = 0.081

Periods = 6

Annual maintenance = $ 8,000

Equivalent Annual Cost = $ 152,719.76 x [0.081/1-(1+0.081)^-6] + $ 8,000

                                      = $ 152,719.76 x [0.081/1-(1.081)^-6] + $ 8,000

                                      = $ 152,719.76 x [0.081/1- 0.62668] + $ 8,000

                                    = $ 152,719.76 x [0.081/0.37332] + $ 8,000

                                      = ($152,719.76 x 0.216972) + $ 8,000

                                    = $ 33,135.92 + $ 8,000

                                    = $ 41,135.92

The military should purchase helicopter 2 having annual equivalent cost of $ 41,135.92