Asked by Mariah Donnally on May 25, 2024
Verified
Bill Braddock is considering opening a Fast 'n Clean Car Service Center. He estimates that the following costs will be incurred during his first year of operations: Rent $9200 Depreciation on equipment $7000 Wages $16400 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 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 Costs 4,000$6,0006,000$7,3009,000$9,60012,000$12,60014,000$15,000\begin{array} { c c } \text { Number of Oil Changes } & \text { Utility Costs } \\\hline 4,000 & \$ 6,000 \\6,000 & \$ 7,300 \\9,000 & \$ 9,600 \\12,000 & \$ 12,600 \\14,000 & \$ 15,000\end{array} Number of Oil Changes 4,0006,0009,00012,00014,000 Utility Costs $6,000$7,300$9,600$12,600$15,000 Bill Braddock anticipates that he can provide the oil change service with a filter at $25 each.
Instructions
(a) Using the high-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 parts (a) and (b) determine the oil changes required to earn net income of $20000 assuming fixed costs are $32000 and the contribution margin per unit is $8.
High-Low Method
A technique used in managerial accounting to estimate fixed and variable costs associated with production.
Break-Even Point
The financial calculation where total revenues equal total expenses, resulting in no profit or loss.
Variable Costs
Costs that vary in total directly and proportionately with changes in the activity level or volume, such as materials and labor.
- Assess the break-even points and buffer margins in numerical counts and currency amounts.
- Harness the high-low method for scrutinizing variable and fixed cost elements from designated data.
- Investigate the influence of shifts in expenditure framework and sales magnitudes on a business's financial gain.
Verified Answer
AA
Ashley Ann EdmundMay 30, 2024
Final Answer :
(a) Separation of mixed costs:
Change in cost/Change in quantity: ($15,000−$6,000)(14,000−4,000)=$9,00010,000=$.90\frac { ( \$ 15,000 - \$ 6,000 ) } { ( 14,000 - 4,000 ) } = \frac { \$ 9,000 } { 10,000 } = \$ .90(14,000−4,000)($15,000−$6,000)=10,000$9,000=$.90 per oil change
Variable costs: Fixed costs: Oil (5 quarts ×$2.00)$10.00 Rent $9,200 Filter 3.00 Depreciation 7,000 Franchise fee 1.10 Wages 16.400 Utility costs (variable) .90‾ Utility costs 2.400∗ Total variable $15.00‾ Total $3500‾‾\begin{array} { l r l r } \text { Variable costs: } & \text { Fixed costs: } \\ \text { Oil } ( 5 \text { quarts } \times \$ 2.00 ) & \$ 10.00 & \text { Rent } & \$ 9,200 \\ \text { Filter } & 3.00 & \text { Depreciation } & 7,000 \\ \text { Franchise fee } & 1.10 & \text { Wages } & 16.400 \\ \text { Utility costs (variable) } & \underline { .90 } & \text { Utility costs } & 2.400 ^ { * } \\ \quad \text { Total variable } & \underline { \$ 15.00 } & \text { Total } & \underline { \underline { \$ 3500 } } \end{array} Variable costs: Oil (5 quarts ×$2.00) Filter Franchise fee Utility costs (variable) Total variable Fixed costs: $10.003.001.10.90$15.00 Rent Depreciation Wages Utility costs Total $9,2007,00016.4002.400∗$3500
$$6,000−(4,000×.90)=$2,400\$ \$ 6,000 - ( 4,000 \times .90 ) = \$ 2,400$$6,000−(4,000×.90)=$2,400 (b) (1) Break-even oil changes in units:
Fixed costs Unit contribution margin =$35,000$10.00∗=3,500 oil changes \frac{\text { Fixed costs }}{\text { Unit contribution margin }}=\frac{\$ 35,000}{\$ 10.00^{*}}=3,500 \text { oil changes } Unit contribution margin Fixed costs =$10.00∗$35,000=3,500 oil changes
(2) Break-even sales in dollars:
Fixed costs Contribution margin ratio =$35,000.40=$87,500\frac { \text { Fixed costs } } { \text { Contribution margin ratio } } = \frac { \$ 35,000 } { .40 } = \$ 87,500 Contribution margin ratio Fixed costs =.40$35,000=$87,500
*Selling price per unit (a) $25 Variable cost per unit $5‾ Unit contribution margin (b) $10%‾ Contribution margin ratio (b) ÷ (a) 40%‾\begin{array} { l r } \text { *Selling price per unit (a) } & \$ 25 \\ \text { Variable cost per unit } & \underline { \$ 5 } \\ \text { Unit contribution margin (b) } & \underline { \$ 10 \% } \\ \text { Contribution margin ratio (b) } \div \text { (a) } & \underline { 40 \% } \end{array} *Selling price per unit (a) Variable cost per unit Unit contribution margin (b) Contribution margin ratio (b) ÷ (a) $25$5$10%40%
(c) Fixed costs + Net income Unit contribution margin =$32,000+$20,000$8=6,500\frac { \text { Fixed costs + Net income } } { \text { Unit contribution margin } } = \frac { \$ 32,000 + \$ 20,000 } { \$ 8 } = 6,500 Unit contribution margin Fixed costs + Net income =$8$32,000+$20,000=6,500 oil changes
Change in cost/Change in quantity: ($15,000−$6,000)(14,000−4,000)=$9,00010,000=$.90\frac { ( \$ 15,000 - \$ 6,000 ) } { ( 14,000 - 4,000 ) } = \frac { \$ 9,000 } { 10,000 } = \$ .90(14,000−4,000)($15,000−$6,000)=10,000$9,000=$.90 per oil change
Variable costs: Fixed costs: Oil (5 quarts ×$2.00)$10.00 Rent $9,200 Filter 3.00 Depreciation 7,000 Franchise fee 1.10 Wages 16.400 Utility costs (variable) .90‾ Utility costs 2.400∗ Total variable $15.00‾ Total $3500‾‾\begin{array} { l r l r } \text { Variable costs: } & \text { Fixed costs: } \\ \text { Oil } ( 5 \text { quarts } \times \$ 2.00 ) & \$ 10.00 & \text { Rent } & \$ 9,200 \\ \text { Filter } & 3.00 & \text { Depreciation } & 7,000 \\ \text { Franchise fee } & 1.10 & \text { Wages } & 16.400 \\ \text { Utility costs (variable) } & \underline { .90 } & \text { Utility costs } & 2.400 ^ { * } \\ \quad \text { Total variable } & \underline { \$ 15.00 } & \text { Total } & \underline { \underline { \$ 3500 } } \end{array} Variable costs: Oil (5 quarts ×$2.00) Filter Franchise fee Utility costs (variable) Total variable Fixed costs: $10.003.001.10.90$15.00 Rent Depreciation Wages Utility costs Total $9,2007,00016.4002.400∗$3500
$$6,000−(4,000×.90)=$2,400\$ \$ 6,000 - ( 4,000 \times .90 ) = \$ 2,400$$6,000−(4,000×.90)=$2,400 (b) (1) Break-even oil changes in units:
Fixed costs Unit contribution margin =$35,000$10.00∗=3,500 oil changes \frac{\text { Fixed costs }}{\text { Unit contribution margin }}=\frac{\$ 35,000}{\$ 10.00^{*}}=3,500 \text { oil changes } Unit contribution margin Fixed costs =$10.00∗$35,000=3,500 oil changes
(2) Break-even sales in dollars:
Fixed costs Contribution margin ratio =$35,000.40=$87,500\frac { \text { Fixed costs } } { \text { Contribution margin ratio } } = \frac { \$ 35,000 } { .40 } = \$ 87,500 Contribution margin ratio Fixed costs =.40$35,000=$87,500
*Selling price per unit (a) $25 Variable cost per unit $5‾ Unit contribution margin (b) $10%‾ Contribution margin ratio (b) ÷ (a) 40%‾\begin{array} { l r } \text { *Selling price per unit (a) } & \$ 25 \\ \text { Variable cost per unit } & \underline { \$ 5 } \\ \text { Unit contribution margin (b) } & \underline { \$ 10 \% } \\ \text { Contribution margin ratio (b) } \div \text { (a) } & \underline { 40 \% } \end{array} *Selling price per unit (a) Variable cost per unit Unit contribution margin (b) Contribution margin ratio (b) ÷ (a) $25$5$10%40%
(c) Fixed costs + Net income Unit contribution margin =$32,000+$20,000$8=6,500\frac { \text { Fixed costs + Net income } } { \text { Unit contribution margin } } = \frac { \$ 32,000 + \$ 20,000 } { \$ 8 } = 6,500 Unit contribution margin Fixed costs + Net income =$8$32,000+$20,000=6,500 oil changes
Learning Objectives
- Assess the break-even points and buffer margins in numerical counts and currency amounts.
- Harness the high-low method for scrutinizing variable and fixed cost elements from designated data.
- Investigate the influence of shifts in expenditure framework and sales magnitudes on a business's financial gain.
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