Problem 5-20 CVP Applications: Break-Even Analysis; Cost Structure; Target Sales

Question

Problem 5-20 CVP Applications: Break-Even Analysis; Cost Structure; Target Sales [LO5-1, LO5-3 LO5-4, LO5-5, LO5-6, LO5-8 Northwood Company manufactures basketballs. The company has a ball that sells for $30. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, vanable expenses are high, totaling $2100 per ball of which 70%S direct labor cost Last year, the company sold 53,000 of these bals, with the following results Sales (53,089 balls) Variable expenses Contribution nargin Fixed expenses $1,598,800 1,113,800 477,800 378,e08 Net operating income 99,000 1. Compute (a) last year's CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year's sales level 2 Due to an increase in labor rates, the company estimates that next years variable expenses will increase by $1 50 per ball if this change takes place and the selling price per ball remains constant at $30.00, what will be next years CM ratio and the break even point in balls? 3 Reter to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next NM Ad

Explanation / Answer

Requirement 1)

a)

The contribution margin ratio is calculated as below:

Contribution Margin Ratio = Contribution Margin/Sales*100

Using the values provided in the question, we get,

Contribution Margin Ratio = 477,000/1,590,000*100 = 30%

____

The break-even point in balls is determined as follows:

Break-Even Point in Balls = Fixed Cost/Contribution Margin Per Unit = 378,000/(477,000/53,000) = 42,000 balls

____

Part b)

The degree of operating leverage is calculated as follows:

Degree of Operating Leverage = Contribution Margin/Net Operating Income = 477,000/99,000 = 4.82

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Tabular Representation:

____

Requirement 2)

The new contribution margin ratio and break-even point in balls is arrived as below:

New Contribution Margin Ratio = (Revised Contribution Margin Per Ball)/Selling Price Per Unit*100 = (30 - 22.50)/30*100 = 25%

New Break-Even Point in Balls = Fixed Cost/New Contribution Margin Per Unit = 378,000/(30 - 22.50) = 50,400 balls

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Tabular Representation:

____

Requirement 3)

The number of balls to be sold next year is calculated with the use of following formula:

Number of Balls to be Sold Next Year = (Fixed Cost + Desired Income)/(New Contribution Margin Per Unit) = (378,000 + 99,000)/(30 - 22.50) = 63,600 balls

____

Requirement 4)

The revised selling price is determined as follows:

Desired Contribution Margin Ratio = (Revised Selling Price Per Unit - New Variable Cost Per Unit)/Revised Selling Price Per Unit*100

Substituting values in the above formula, we get,

30% = (Revised Selling Price Per Unit - 22.50)/Revised Selling Price Per Unit*100

Rearranging values, we get,

.30*Revised Selling Price = Revised Selling Price Per Unit - 22.50

Solving further, we get,

Revised Selling Price = 22.50/(1 - .30) = $32.14

CM Ratio 30% Unit Sales to Break Even 42,000 balls Degree of Operating Leverage 4.82

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