Bill Braddock is considering opening a fast %u2018n Clean car Service Center. He

Question

Bill Braddock is considering opening a fast %u2018n Clean car Service Center. He estimates that the following costs will be incurred during his first year of operations: Rent $9,200, Depreciation on equipment $7,000, Wages $16,400, Motor oil $2.00 per quart. He estimates that each oil change will require 5 quarts of oil. Oil filters will cost $3.00 each. He must also pay the Fast n%u2019 Clean Corporation a franchise fee of $1.10 per oil change, since he will operate the business as a franchise. In addition, utility costs are expected to behave in relation to the number of oil changes as follows:

Number of oil changes                             Utility cost               

4,000                                                           $ 6,000

6,000                                                           $ 7,300

9,000                                                          $ 9,600

12,000                                                         $ 12,600

14,000                                                         $ 15,000

Bill Braddock anticipates that he can provide the oil change service with a filter at $ 25 each.

(A)   Using the high and low method, determine variable costs per unit and total fixed costs.

(B)   Determine the break-even point in number of oil changes and sales dollars.

    (C) Without regard to your answers in part A and B, determine the oil changes required to earn net income of $20,000, assuming fixed costs are $32,000 and the contribution margin per unit is $8.

please show all working.

Explanation / Answer

Hi,

Please find the answer as follows:

Part A:

Variable Cost Per Unit (Utility) = (15000 - 6000)/(14000 - 4000) = .9 per unit

Total Variable Cost =5*2(Oil) + 3(Filter) + 1.10(Franchise Fee) + .90(Utility Cost) = $15 per Unit

Fixed Cost(Utility) = 15000 - 14000*.9 = 2400

Total Fixed Cost = 9200(Rent) + 7000(Depreciation) + 16400(Wages) + 2400(Utility) = 35000

Part B

Break Even Point in Units = Fixed Cost/(Contribution Per Unit) = 35000/(25-15) = 3500 Oil Changes.

Break Even Point in Dollars = 3500*25 = $87500

Part C:

Total Oil Changes Required = Fixed Cost+Desired Income/Contribution = (32000 + 20000)/8 = 6500 Oil Changes

Thanks.

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