# Problem-5 (Change in sales mix, break-even analysis and margin of safety)

Metro International manufactures two products – product X and product Y. Product X sells for \$800 and product Y for \$1200. Company sells its products through its own stores and outlets owned by various merchandising companies. Total fixed expenses of Metro International are \$132,000 per month. Variable expenses and monthly sales data are given below:

Variable expenses per unit:

• Product X: \$480
• Product Y: \$240

Monthly sales in units:

• Product X: 200 Units
• Product Y: 80 Units

Required:

1. Prepare a contribution margin income statement showing dollars and percent columns for the product X and Y and for the company as a whole.
2. Compute the break-even point in dollars and margin of safety using above information.
3. Metro International is considering to manufacture another product – product Z. The addition of new product will not affect the fixed cost of the company. The variable expenses to manufacture and sell a unit of product Z will be \$1,200. If the selling price of the new product is set at \$1,600 per unit, the company expect to sell 40 units per month.
(a). Prepare a new contribution margin income statement that includes product Z.
(b). Compute the new break-even point and margin of safety.
4. The president is unable to understand the increase in break-even sales because the new product has increased the sales revenue and contribution margin without any increase in fixed costs. Explain to the president the reason of increase in break-even sales.

## Solution:

### (2) Break-even point and margin of safety:

Break even point in dollars = Fixed expenses/CM ratio

\$132,000 / 0.55

\$240,000

Margin of safety in dollars = Actual sales – Break-even sales

= \$256,000 – \$240,000

= \$16,000

Margin of safety in percentage = Margin of safety/Actual sales

= \$16,000/\$256,000

= 6.25%

### (3). Addition of product Z:

a. New contribution margin income statement:

b. New break-even point and margin of safety:

Break-even point in dollars = Fixed expenses/CM ratio

= \$132,000/0.49

= \$269,388

Margin of safety in dollars = Actual sales – Break-even sales

= \$320,000 – \$269,388

= \$50,612

Margin of safety in percentage = Margin of safety/Actual sales

= \$50,612/\$320,000

= 15.82%

### (4). Explanation to the president:

The break-even point has increased from \$240,000 to \$269,388 because the new product (product Z) has decreased the overall or average contribution margin ratio of the company. Product Z has a contribution margin ratio of only 25% which has caused a drop in overall or average contribution margin ratio from 55% to 49%.

Even though the break-even point is higher, the addition of new product has increased the margin of safety from \$16,000 to \$50,612 or from 6.25% to 15.82% which tells that the company has shifted much further from its break-even point.