Question

An automobile leasing company has a contract with a new car dealer to do major repairs for $720 per car. The leasing company estimates that for $400,000, it could buy equipment to service their own cars at a cost of $300 per car.

Required:

a) If the equipment will have a salvage value of 10% of its first cost after 15 years, the minimum number of cars that must require major servicing each year to justify the equipment at a MARR of 10% per year is closest to _________.

Answer 1

a) 123 cars will breakeven the project.

Step-by-step explanation:

We need to solve for the equivalent annual cost of the equipment and then, solve for the car to achieve a finnancial break-even:

Salvage value present value

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity $40,000.00

time 15.00

rate 0.10000

`(40000)/((1 + 0.1)^(15) ) = PV`

PV 9,575.6820

Present value of the Equipment

400,000 - 9,576 = 390,424

Equivalent annual cost:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 390,424.00

time 15

rate 0.1

`390424 / (1-(1+0.1)^(-15) )/(0.1) = C\\`

C $ 51,330.518

Each car generates 720 of reveneu with a cost of 300 dollar the contribution is 420 per car

51,330 equivalent annual equipment cost

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420 contribution margin per car

break even = 122.12 = 123 cars