Question

Break-Even in Units, Target Income, New Unit Variable Cost, Degree of Operating Leverage, Percent Change in Operating Income

Reagan, Inc., has developed a chew-proof dog bed—the Tuff-Pup. Fixed costs are $208,000 per year. The average price for the Tuff-Pup is $37, and the average variable cost is $24 per unit. Currently, Reagan produces and sells 20,000 Tuff-Pups annually.

Required:

1. How many Tuff-Pups must be sold to break even?
units

2. If Reagan wants to earn $72,800 in profit, how many Tuff-Pups must be sold?
units

Feedback

1. See Cornerstone 16.2.

2. Combine desired profit with fixed costs in the formula.

Prepare a variable-costing income statement to verify your answer.

Reagan, Inc.
Variable-Costing Income Statement
Sales	$
Less: Variable cost
Contribution margin	$
Less: Fixed expenses
Operating income	$

Feedback

Remember a contribution margin income statement calculates contribution-margin not gross profit.

3. Suppose that Reagan would like to lower the break-even units to 10,400. The company does not believe that the price or fixed cost can be changed. Calculate the new unit variable cost that would result in break-even units of 10,400. If required, round your intermediate computations and final answer to the nearest cent.
$

4. What is Reagan’s current contribution margin and operating income?

Current contribution margin	$
Current operating income	$

Calculate the degree of operating leverage. Round your answer to three decimal places.

If sales increased by 10 percent next year, what would the percent change in operating income be? Use your rounded answer to the question above in your computations, and round your final percentage answer to two decimal places (for example, 45.555% would be entered as "45.56").
%

What would the new total operating income for next year be? Round your answer to the nearest dollar.

Answer 1

1. How many Tuff-Pups must be sold to break even?
Break even = 208000/(37-24) = 16000 Units

2. If Reagan wants to earn $72,800 in profit, how many Tuff-Pups must be sold?
Required unit = (208000+72800)/13 = 21600 units

Prepare a variable-costing income statement to verify your answer.

Reagan, Inc.
Variable-Costing Income Statement
Sales (21600*37)	$799200
Less: Variable cost	518400
Contribution margin	$280800
Less: Fixed expenses	208000
Operating income	$72800

3. Suppose that Reagan would like to lower the break-even units to 10,400. The company does not believe that the price or fixed cost can be changed. Calculate the new unit variable cost that would result in break-even units of 10,400. If required, round your intermediate computations and final answer to the nearest cent.
Break even = Fixed cost/Contribution margin per unit

10400 = 208000/37-X

384800-10400X = 208000

X(Variable cost) = 17

4. What is Reagan’s current contribution margin and operating income?

Current contribution margin	13*20000 = 260000
Current operating income	260000-208000 = 52000

Calculate the degree of operating leverage. Round your answer to three decimal places.

Degree of operating leverage = 260000/52000 = 5 Times

If sales increased by 10 percent next year, what would the percent change in operating income be? Use your rounded answer to the question above in your computations, and round your final percentage answer to two decimal places (for example, 45.555% would be entered as "45.56").
5*10 = 50%

What would the new total operating income for next year be? Round your answer to the nearest dollar.

New operating income = 52000*1.5 = $78000