Elephant Books: Publisher's Break-Even Analysis

How Much More Money Can Elephant Books Allocate to Advertising?

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Question

Elephant Books sells paperback books for $7 each. The variable cost per book is $5. At current annual sales of 200,000 books, the publisher is just breaking even. It is estimated that if the authors' royalties are reduced, the variable cost per book will drop by $1. Assume authors' royalties are reduced and sales remain constant; how much more money can the publisher put into advertising (a fixed cost) and still break even?

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A. B. C. D. E.

B

$7(200,000) - $5(200,000) - F = 0

F = $400,000.

$7(200,000) - $4(200,000) - F = 0

F = $600,000.

$600,000 - $400,000 = $200,000.

To determine how much more money the publisher can put into advertising while still breaking even, we need to calculate the contribution margin per book and then multiply it by the number of books sold.

The contribution margin per book is the difference between the selling price and the variable cost per book. Currently, the selling price is $7 and the variable cost per book is $5, so the contribution margin is:

Contribution margin = Selling price - Variable cost per book = $7 - $5 = $2

This means that for each book sold, the publisher has a $2 contribution to cover fixed costs and generate profit.

Next, we calculate the current contribution margin for the annual sales of 200,000 books:

Current contribution margin = Contribution margin per book * Number of books sold = $2 * 200,000 = $400,000

Since the publisher is currently breaking even, the current contribution margin of $400,000 covers the fixed costs.

Now, with the estimated reduction in authors' royalties, the variable cost per book will drop by $1. This means the new variable cost per book will be $5 - $1 = $4.

To find out how much more money can be put into advertising while still breaking even, we need to calculate the new contribution margin per book and multiply it by the number of books sold.

New contribution margin per book = Selling price - New variable cost per book = $7 - $4 = $3

The new contribution margin per book is $3, which means for each book sold, the publisher has a $3 contribution to cover fixed costs and generate profit.

To calculate the new contribution margin for the annual sales of 200,000 books:

New contribution margin = New contribution margin per book * Number of books sold = $3 * 200,000 = $600,000

Since the publisher wants to break even, the new contribution margin of $600,000 needs to cover the fixed costs and advertising expenses. However, we need to find the additional amount that can be allocated to advertising while still breaking even.

The additional amount that can be allocated to advertising is the difference between the new contribution margin and the current contribution margin:

Additional advertising amount = New contribution margin - Current contribution margin = $600,000 - $400,000 = $200,000

Therefore, the publisher can put an additional $200,000 into advertising and still break even.

The correct answer is option B: $200,000.

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