Asked by Willis Sands on Jun 24, 2024
Verified
A firm produces three products in a repetitive process facility. Product A sells for $60; its variable costs are $20. Product B sells for $200; its variable costs are $80. Product C sells for $25; its variable costs are $15. The firm has annual fixed costs of $320,000. Last year, the firm sold 1000 units of A, 2000 units of B, and 10,000 units of C. Calculate the break-even point of the firm. The firm has some idle capacity at these volumes, and chooses to cut the selling price of A from $60 to $45, believing that its sales volume will rise from 1000 units to 2500 units. What is the revised break-even point?
Break-Even Point
The level of production or sales at which total revenues equal total costs, resulting in no net loss or gain.
Variable Costs
Costs that vary directly with the level of production or volume of output.
- Comprehend the idea of breakeven analysis and its utilization in making business-related decisions.
- Calculate and interpret break-even points for various business models and scenarios.
Verified Answer
SG
sumielizabath georgeJun 26, 2024
Final Answer :
Calculations for the original version of this problem are:
Selling Variable Percent of Weighted Product price P cost V V/P1−V/P Sales sales contrib A$60$20.333.667$60,000.0845.0564B$200$80400.600$400,000.5634.3380C$25$15.600400$250,000.35211408$710,0001.00000.5352\begin{array}{|l|r|r|r|r|r|r|r|}\hline&\text { Selling } & \text { Variable }&&&& \text { Percent of } &\text { Weighted }\\\text { Product }&\text { price P } & \text { cost V } &\mathrm{V} / \mathrm{P} & 1-\mathrm{V} / \mathrm{P} & \text { Sales }&\text { sales }&\text { contrib }\\\hline \mathrm{A} & \$ 60 & \$ 20 & .333 & .667 & \$ 60,000 & .0845 & .0564 \\\hline \mathrm{B} & \$ 200 & \$ 80 & 400 & .600 & \$ 400,000 & .5634 & .3380 \\\hline \mathrm{C} & \$ 25 & \$ 15 & .600 & 400 & \$ 250,000 & .3521 & 1408 \\\hline & & & && \$ 710,000 & 1.0000 & 0.5352 \\\hline\end{array} Product ABC Selling price P $60$200$25 Variable cost V $20$80$15V/P.333400.6001−V/P.667.600400 Sales $60,000$400,000$250,000$710,000 Percent of sales .0845.5634.35211.0000 Weighted contrib .0564.338014080.5352 The original break-even for this firm was $320,000 / .5352 = $597,907. This is a calculator-based result; Excel reports $597,895.
When the price of A is reduced, the revised calculations are:
Selling Variable Percent of Weighted Product price P cost V V/P1−V/P Sales sales contrib A$45$20444556$112,500.1475.0820B$200$80400.600$400,000.5246.3149C$25$15.600400$250,000.3279131$762,5001.00000.5280\begin{array}{|l|r|r|r|r|r|r|r|}\hline&\text { Selling } & \text { Variable }&&&& \text { Percent of } &\text { Weighted }\\\text { Product }&\text { price P } & \text { cost V } &\mathrm{V} / \mathrm{P} & 1-\mathrm{V} / \mathrm{P} & \text { Sales }&\text { sales }&\text { contrib }\\\hline \mathrm{A} & \$ 45 & \$ 20 & 444 & 556 & \$ 112,500 & .1475 & .0820 \\\hline \mathrm{B} & \$ 200 & \$ 80 & 400 & .600 & \$ 400,000 & .5246 & .3149 \\\hline \mathrm{C} & \$ 25 & \$ 15 & .600 & 400 & \$ 250,000 & .3279 & 131 \\\hline & & & & & \$ 762,500 & 1.0000 & 0.5280 \\\hline\end{array} Product ABC Selling price P $45$200$25 Variable cost V $20$80$15V/P444400.6001−V/P556.600400 Sales $112,500$400,000$250,000$762,500 Percent of sales .1475.5246.32791.0000 Weighted contrib .0820.31491310.5280 The firm's breakeven point has increased to $320,000 / .5280 = $606,061. (Calculator-based; Excel reports $606,211).
Selling Variable Percent of Weighted Product price P cost V V/P1−V/P Sales sales contrib A$60$20.333.667$60,000.0845.0564B$200$80400.600$400,000.5634.3380C$25$15.600400$250,000.35211408$710,0001.00000.5352\begin{array}{|l|r|r|r|r|r|r|r|}\hline&\text { Selling } & \text { Variable }&&&& \text { Percent of } &\text { Weighted }\\\text { Product }&\text { price P } & \text { cost V } &\mathrm{V} / \mathrm{P} & 1-\mathrm{V} / \mathrm{P} & \text { Sales }&\text { sales }&\text { contrib }\\\hline \mathrm{A} & \$ 60 & \$ 20 & .333 & .667 & \$ 60,000 & .0845 & .0564 \\\hline \mathrm{B} & \$ 200 & \$ 80 & 400 & .600 & \$ 400,000 & .5634 & .3380 \\\hline \mathrm{C} & \$ 25 & \$ 15 & .600 & 400 & \$ 250,000 & .3521 & 1408 \\\hline & & & && \$ 710,000 & 1.0000 & 0.5352 \\\hline\end{array} Product ABC Selling price P $60$200$25 Variable cost V $20$80$15V/P.333400.6001−V/P.667.600400 Sales $60,000$400,000$250,000$710,000 Percent of sales .0845.5634.35211.0000 Weighted contrib .0564.338014080.5352 The original break-even for this firm was $320,000 / .5352 = $597,907. This is a calculator-based result; Excel reports $597,895.
When the price of A is reduced, the revised calculations are:
Selling Variable Percent of Weighted Product price P cost V V/P1−V/P Sales sales contrib A$45$20444556$112,500.1475.0820B$200$80400.600$400,000.5246.3149C$25$15.600400$250,000.3279131$762,5001.00000.5280\begin{array}{|l|r|r|r|r|r|r|r|}\hline&\text { Selling } & \text { Variable }&&&& \text { Percent of } &\text { Weighted }\\\text { Product }&\text { price P } & \text { cost V } &\mathrm{V} / \mathrm{P} & 1-\mathrm{V} / \mathrm{P} & \text { Sales }&\text { sales }&\text { contrib }\\\hline \mathrm{A} & \$ 45 & \$ 20 & 444 & 556 & \$ 112,500 & .1475 & .0820 \\\hline \mathrm{B} & \$ 200 & \$ 80 & 400 & .600 & \$ 400,000 & .5246 & .3149 \\\hline \mathrm{C} & \$ 25 & \$ 15 & .600 & 400 & \$ 250,000 & .3279 & 131 \\\hline & & & & & \$ 762,500 & 1.0000 & 0.5280 \\\hline\end{array} Product ABC Selling price P $45$200$25 Variable cost V $20$80$15V/P444400.6001−V/P556.600400 Sales $112,500$400,000$250,000$762,500 Percent of sales .1475.5246.32791.0000 Weighted contrib .0820.31491310.5280 The firm's breakeven point has increased to $320,000 / .5280 = $606,061. (Calculator-based; Excel reports $606,211).
Learning Objectives
- Comprehend the idea of breakeven analysis and its utilization in making business-related decisions.
- Calculate and interpret break-even points for various business models and scenarios.
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