The following information relates to Clyde Corporation,which produced and sold 50,000 units last month.
There were no beginning or ending inventories.Production and sales next month are expected to be 40,000 units.In the next month,what should the company's unit contribution margin be?

Question

The following information relates to Clyde Corporation,which produced and sold 50,000 units last month. 
There were no beginning or ending inventories.Production and sales next month are expected to be 40,000 units.In the next month,what should the company's unit contribution margin be?

Quizplus · Accepted Answer

The unit contribution margin is calculated as follows:

Unit Sales Price - Unit Variable Costs = Unit Contribution Margin

Since there were no beginning or ending inventories, we can assume that the company sold all of the 50,000 units that it produced.

To calculate the unit contribution margin, we need to know the total sales revenue and the total variable costs for the month. We are not given this information directly, but we can use the information provided to calculate these amounts.

Since the company produced 50,000 units and sold them all, we know that total revenue is equal to the sales price per unit multiplied by the number of units sold. We are not given the sales price directly, but we can use the contribution margin ratio to calculate it.

The contribution margin ratio is equal to the unit contribution margin divided by the unit sales price. We are not given the contribution margin ratio directly, but we can calculate it using the information provided.

Since there were no beginning or ending inventories, we know that the total variable costs for the month are equal to the variable costs per unit multiplied by the number of units produced. We are not given the variable costs per unit directly, but we can use the contribution margin ratio to calculate it.

Using this approach, we can calculate the unit contribution margin as follows:

Contribution Margin Ratio = Unit Contribution Margin / Unit Sales Price

Contribution Margin Ratio = Total Contribution Margin / Total Sales Revenue

Total Sales Revenue = 50,000 x Unit Sales Price

Total Variable Costs = 50,000 x Unit Variable Costs

Contribution Margin Ratio = (Total Sales Revenue - Total Variable Costs) / Total Sales Revenue

0.3 = (Unit Contribution Margin / Unit Sales Price)

0.3 = (Total Contribution Margin / Total Sales Revenue)

Unit Sales Price - Unit Variable Costs = Unit Contribution Margin

Unit Sales Price - (Unit Sales Price x 0.7) = (Unit Sales Price x 0.3)

0.3Unit Sales Price = 0.7Unit Variable Costs

Unit Sales Price = (0.7 / 0.3) x Unit Variable Costs

Unit Sales Price = 2.33 x Unit Variable Costs

Since we are told that production and sales next month are expected to be 40,000 units, we can use this sales volume to calculate the unit contribution margin:

Unit Sales Price = 2.33 x Unit Variable Costs

Unit Contribution Margin = Unit Sales Price - Unit Variable Costs

Unit Contribution Margin = (2.33 x Unit Variable Costs) - Unit Variable Costs

Unit Contribution Margin = 1.33 x Unit Variable Costs

We are not given the unit variable costs directly, but we can use the information provided to calculate them.

Total Costs = Total Fixed Costs + Total Variable Costs

Total Fixed Costs = Fixed Cost per Unit x Number of Units Produced

Total Fixed Costs = 800,000 / 50,000

Total Fixed Costs = $16

Total Costs = Total Fixed Costs + Total Variable Costs

Total Variable Costs = Total Costs - Total Fixed Costs

Total Variable Costs = $2,680,000 - $16 = $2,679,984

Unit Variable Costs = Total Variable Costs / Number of Units Produced

Unit Variable Costs = $2,679,984 / 50,000

Unit Variable Costs = $53.60

Unit Contribution Margin = 1.33 x $53.60 = $71.17

Therefore, the company's unit contribution margin should be $71.17 next month. The correct answer is D.

The Following Information Relates to Clyde Corporation,which Produced and Sold