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Color Rugs is holding a two-week carpet sale at Jerry’s Club, a local warehouse store. Color Rugsplans to sell carpets for $500 each. The company will purchase the carpets from a local distributorfor $350 each, with the privilege of returning any unsold units for a full refund. Jerry’s Club hasoffered Color Rugs two payment alternatives for the use of space.Option 1: A fixed payment of $5,000 for the Sale periodOption 2: 10% of total revenues earned during the Sale periodAssume Color Rugs will incur no other costs.Required1. Calculate the breakeven point in units for (a) option 1 and (b) option 2.2. At what level of revenues will Color Rugs earn the same operating income under eitheroption?a. For what range of unit sales will Color Rugs prefer option 1?b. For what range of unit sales will Color Rugs prefer option 2?3. Calculate the degree of operating leverage at sales of 100 units for the two rental options.4. Briefly explain and interpret your answer to requirement 3.

Question

Color Rugs is holding a two-week carpet sale at Jerry’s Club, a local warehouse store. Color Rugsplans to sell carpets for 500each.Thecompanywillpurchasethecarpetsfromalocaldistributorfor500 each. The company will purchase the carpets from a local distributorfor 350 each, with the privilege of returning any unsold units for a full refund. Jerry’s Club hasoffered Color Rugs two payment alternatives for the use of space.Option 1: A fixed payment of $5,000 for the Sale periodOption 2: 10% of total revenues earned during the Sale periodAssume Color Rugs will incur no other costs.Required1. Calculate the breakeven point in units for (a) option 1 and (b) option 2.2. At what level of revenues will Color Rugs earn the same operating income under eitheroption?a. For what range of unit sales will Color Rugs prefer option 1?b. For what range of unit sales will Color Rugs prefer option 2?3. Calculate the degree of operating leverage at sales of 100 units for the two rental options.4. Briefly explain and interpret your answer to requirement 3.

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Solution

  1. The breakeven point in units is calculated by dividing the fixed costs by the contribution margin per unit. The contribution margin per unit is the selling price per unit minus the variable cost per unit.

    a. Option 1: The fixed cost is 5,000andthecontributionmarginperunitis5,000 and the contribution margin per unit is 500 - 350=350 = 150. Therefore, the breakeven point is 5,000/5,000 / 150 = 33.33 units. Since we can't sell a fraction of a unit, we round up to 34 units.

    b. Option 2: The fixed cost is 10% of total revenues, or 50perunit(50 per unit (500 * 10%). The contribution margin per unit is now 500500 - 350 - 50=50 = 100. Therefore, the breakeven point is 5,000/5,000 / 100 = 50 units.

  2. The level of revenues at which Color Rugs will earn the same operating income under either option is when the total cost under both options is the same. This occurs when 5,000+5,000 + 150X = 50X+50X + 350X, where X is the number of units sold. Solving for X gives X = 50 units. Therefore, the level of revenues is 50 units * 500/unit=500/unit = 25,000.

    a. Color Rugs will prefer option 1 when the number of units sold is less than 50 units because the total cost under option 1 is less than under option 2 for these sales levels.

    b. Color Rugs will prefer option 2 when the number of units sold is more than 50 units because the total cost under option 2 is less than under option 1 for these sales levels.

  3. The degree of operating leverage is calculated as Contribution Margin / Operating Income. At sales of 100 units:

    a. Option 1: The contribution margin is 100 units * 150/unit=150/unit = 15,000. The operating income is 15,00015,000 - 5,000 = 10,000.Therefore,thedegreeofoperatingleverageis10,000. Therefore, the degree of operating leverage is 15,000 / $10,000 = 1.5.

    b. Option 2: The contribution margin is 100 units * 100/unit=100/unit = 10,000. The operating income is 10,00010,000 - 5,000 = 5,000.Therefore,thedegreeofoperatingleverageis5,000. Therefore, the degree of operating leverage is 10,000 / $5,000 = 2.

  4. The degree of operating leverage measures the sensitivity of operating income to changes in unit sales. A higher degree of operating leverage indicates a higher risk and higher potential return. In this case, option 2 has a higher degree of operating leverage, meaning it is riskier but could potentially bring in more income if sales are high.

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