Problem 520 CVP Applications BreakEven Analysis Cost Structu

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

Solution

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%

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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

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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:

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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:

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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

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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