Question

Acct 6003 Chapter 3 Homework

Use the following information to work the problems. Each problem stands alone.

Bernard Windows is a small company that installs windows. Its cost structure is as follows:

Selling price for each window installation                              $500

Variable cost of each window installation                              $400

Annual fixed costs                                                            $150,000

#1. This is also TRY IT 3-2 on page 75.

Calculate (a) the breakeven point in units and revenue and (b) the number of windows Bernard Windows must install and the revenues needed to earn a target operating income of $100,000.

#2. TRY IT 3-3 on page 77.

Same information as above but now tax rate is 30%. Calculate the number of windows Bernard Windows must install and the revenues needed to earn a target net income of $63,000.

#3. TRY IT 3-4 on page 82. Calculate the margin of safety in units and dollars and the margin of safety percentage if the company expects to sell 2,400 windows in the year.

#4. TRY IT 3-5 on page 84. Number of units sold is 2500.

Bernard is considering changing its sales compensation for next year. Bernard would pay salespeople a 5% commission next year and reduce fixed costs by $62,500. Calculate the degree of operating leverage at sales of 2,500 units under the two options. Comment briefly on the result.

#5. TEY IT 3-6 on page 87.

Bernard Windows plans to sell two different brands of windows-- Chad and Musk--- and budgets the following:

Chad Musk Total

Expected sales                                                  2500                                       1000 3500

Revenues (500 and 350 per unit) $1,250,000 $350,000 $1,600,000

Variable cost ( 400 and 275 per unit) $1,000,000 $275,000 $1,275,000

Contribution margin (100 and 75 ) 250,000 $75,000 $325,000

Fixed costs $195,000

Operating income $130,000

Calculate the break even point for Bernard Windows in terms of the (a) number of units sold and (b) revenues.

Answer 1

1.(a). Breakeven point (in units) = Fixed cost / Contribution margin per unit

Contribution margin per unit = Selling price per unit - Variable cost per unit

= $500 - $400 = $100 per unit

Breakeven point ( in units) = $150,000 / $100 per unit

Breakeven point ( in units) = 1500 units

Breakeven point ( in revenue) = Fixed Cost / Contribution margin ratio

Contribution margin ratio = ( Selling price per unit - Variable cost per unit) / Selling price per unit * 100

= ($500 - $400) / $500 * 100

= 20%

Breakeven point ( in revenue) = $150,000 / 20%

Breakeven point ( in revenue) = $750,000

(b). Let x be the unknown quantity of units Bernard Windows must sell to earn an operating income of $100,000. Selling price is $500

Revenue - Variable cost - Fixed cost = operating income

($500 * x) - ($400*x) - $150,000 = $100,000

($100* x) = $250,000

x = $250,000 / $100 per unit = 2,500 units

Quantity of units required to be sold = 2,500 units

Revenue to earn an operating income of $100,000 is

Revenue = Number of units required to be sold * Selling Price

Revenue = 2,500 * $500 = $1,250,000

2. Target operating income = Target net income / (1 - Tax Rate)

= $63,000 / (1 - 0.30)

= $90,000

In other words, to earn a target net income of $63,000, Bernard Windows Target operating income is $90,000.

Proof: Target operating income $90,000

Tax at 30% ( $90,000*0.30) $27,000

Target net income $63,000

Calculation of number of units Bernard Windows must sell:

Quantity of units required to be sold = Fixed cost + Target operating income / Contribution margin per unit

= $150,000 + $90,000 / $100 = $2,400 units

Quantity of units required to be sold = 2,400 units

Revenue to earn net income of $63,000 is:

Revenue = Number of units required to be sold * Selling price

= 2,400 * $500

Revenue = $1,200,000

3. Margin of Safety = Budgeted revenue - Breakeven revenue

= $1,200,000 - $750,000

Margin of Safety = $450,000

Margin of safety (in units) = Budgeted Sales (units) - Breakeven Sales (units)

= 2,400 - 1,500

Margin of safety (in units) = 900 units

The margin of safety indicated that sales would have to decrease by 900 units and revenue by $450,000 before the breakeven point is reached.

Margin of safety percentage = Margin of safety in dollars / Budgeted revenues

= $450,000 / $1,200,000 * 100 = 37.5%

This result means that revenue would have to decrease substantially, by 60%, to reach the breakeven revenues.

4. At any given level of sales,

Degree of operating leverage = Contribution margin / Operating income

The following table shows the degree of operating leverage at sales 2,500 units for the two options.

	Option 1 No Commission	Option 2 5% Commission
1. Selling price	$500	$500
2. Variable cost($400; $400 = 0.05*$500)	$400	$425
3.Contribution margin per unit	$100	$75
4.Contribution margin (row 3. * 2,500)	$250,000	$187,500
5.Fixed Cost	$150,000	$87,500
6.Operating income	$100,000	$100,000
7.Degree of operating leverage (row 4 / row 6)	$250,000/ $100,000 = 2.50	$187,500/ $100,000 = 1.875

The result indicates that when sales are 2,500 units, a 1% change in sales and contibution margin will result in 2.5% change in operating income for option 1.

For option 2, a 1% change in sales and contribution margin will result in onlyn 1.875% change in operating income. The degree of operating leverage at a given level of sales helps manager to calculate effect of sales fluctuations on operating income.

5. Let we assume that the budgeted sales mix (2,500 units of chad windows sold for every 1,000 units of Musk windows sold, that is a ratio of 5:2) will not change at different levels of total unit sales.

	Number of units of Chad Windows and Musk Windows in each bundle	Contribution Margin per unit for Chad Windows and Mask Windows	Contribution margin of the bundle
Chad Windows	5	$100	$500
Musk windows	2	$75	$150
Total			$650

To calculate breakeven point, we calculate the number of bundles Bernard needs to sell.

Breakeven point in bundles = Fixed cost / Contribution margin per bundle

= $195,000 / $650 = 300 bundles

a. Breakeven point in units of Chad Windows and Musk windows is as follows:

Chad windows: 300 bundles * 5 units per bundle = 1,500 units

Musk windows: 300 bundles * 2 units per bundle = 600 units

Total number of units to breakeven = 1,500 + 600 = 2,100 units

b. The breakeven point in dollars for Chad windows and Musk windows is as follows:

Chad windows: 1,500 units * $500 per unit = $750,000

Musk windows: 600 units * $350 per unit = $210,000

Breakeven revenue = $750,000 + $210,000 = $960,000