# A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an...

## Question:

## Fixed Costs vs Variable costs

When doing a break-even analysis, it is useful to understand the difference between fixed and variable costs. A company's fixed costs are those that remain the same no matter how much or how little it sells. An example could be the monthly lease on a factory, which would be a constant amount regardless of the company's monthly sales. On the other hand, a variable cost is one that would change in line with increases or decreases in sales. A good example would be a manufacturing company's raw materials costs, which would naturally vary according to the level of the company's sales.

## Answer and Explanation: 1

**a.** When variable costs are directly proportional to sales, the simple break-even formula can be used to calculate break-even quantity.

The formula is: {eq}Q = F/(p-v)
{/eq}, where *Q* = break-even quantity, *F* = total fixed costs, *p* = price (or revenue) per unit, and *v* = variable costs per unit.

Thus, here are the break-even quantities for each of the 3 alternatives:

- Alternative A:

- Alternative B:

- Alternative C:

ANSWER: The alternative with the lowest break-even quantity is **A**.

**b.** For the second question, use the formula: {eq}Profit = Q(p-v) - F
{/eq}

Substitute 10,000 for *Q* and the same values for *F*, *p*, and *v* as in question a.

- Alternative A profits: 10,000(50-22) - 100,000 =
**$180,000** - Alternative B profits: 10,000(50-20) - 120,000 =
**$180,000** - Alternative C profits: 10,000(50-30) - 80,000 =
**$120,000**

ANSWER: The alternative with the highest profits for annual output of 10,000 units is **A or B**.

**c.** Use the same formula as in b. above, but substitute $50,000 for *Profit* and solve for *Q*. Thus, {eq}Q = (50,000+F)/(P-v)
{/eq} Notice this is the same equation as question a., except that $50,000 has been added to the numerator.

Here are the volumes (rounded to the nearest unit) needed to generate an annual profit of $50,000 :

- Alternative A: {eq}(50,000+100,000)/(50-22) = 150,000/28 = 5,357 {/eq}

- Alternative B: {eq}(50,000+120,000)/(50-20) = 170,000/30 = 5,667 {/eq}

- Alternative C: {eq}(50,000+80,000)/(50-30) = 130,000/20 = 6,500 {/eq}

ANSWER: The alternative with the lowest volume of output to generate a $50,000 annual profit is **A**.

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Chapter 4 / Lesson 3A break-even analysis utilizes a price calculation formula to determine how much product a business must sell and at what price in order to make a profit. Learn how to apply this analysis through examples with fixed and variable costs, and discover the importance of a margin of safety.