Question

This year Best Company earned a disappointing 5.6% after-tax return on sales (net income/sales) from marketing 100,000 units of its only product. The company buys its product in bulk and repackages it for resale at the price of \(20 per unit. Best incurred the following costs this year

Total variable unit costs	\)800,000
Total variable packaging costs	\(100,000
Fixed costs	\)950,000
Income tax rate	25%

The marketing manager claims that next year’s results will be the same as this year’s unless some changes are made. The manager predicts the company can increase the number of units sold by 80% if it reduces the selling price by 20% and upgrades the packaging. This change would increase variable packaging costs by 20%. Increased sales would allow the company to take advantage of a 25% quantity purchase discount on the cost of the bulk product. Neither the packaging change nor the volume discount would affect fixed costs, which provide an annual output capacity of 200,000 units.

Required

1. Compute the break-even point in dollar sales under the (a) existing business strategy and (b) new strategy that alters both unit selling price and variable costs. (Round answers to the next whole dollar.)

2. Prepare a forecasted contribution margin income statement with two columns showing the expected results of (a) the existing strategy and (b) changing to the new strategy. The statements should report sales, total variable costs (unit and packaging), contribution margin, fixed costs, income before taxes, income taxes, and net income. Also, determine the after-tax return on sales for these two strategies.

Short answer

1. Break-even dollar sales:

Existing strategy:$1,727,273

New strategy:$1,727,273

1. Net income:

Existing strategy:$112,500

New strategy: $475,500

Step-by-step solution

Definition of Contribution Margin

The line item representing the sales revenue generated over the variable cost incurred in the production process is known as the contribution margin. Variable cost includes expenses relating to labor and material.

Break-even point for both business strategy

(a) Existing business strategy

Calculation of variable cost per unit:

Particular	Amount $	/	Units	=	Per unit
Total variable unit costs	$800,000	/	100,000	=	$8
Total variable packaging costs	$100,000	/	100,000	=	$1
					$9

Calculation of contribution margin ratio:

$\begin{array}{rcl}\mathbf{\text{Contributionmarginratio}}& \mathbf{=}& \frac{\mathbf{\text{Salespriceperunit}}\mathbf{-}\mathbf{\text{Variablecostperunit}}}{\mathbf{\text{Salespriceperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{20}\mathbf{-}\mathbf{\$}\mathbf{9}}{\mathbf{\$}\mathbf{20}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{55}\end{array}$

Break-even dollar sales:

$\begin{array}{rcl}\mathbf{\text{Break-evendollarsales}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginnratio}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{950}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{55}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{727}\mathbf{,}\mathbf{273}\end{array}$

(b) New business strategy:

$\begin{array}{rcl}\mathbf{\text{Newsellingprice}}& \mathbf{=}& \mathbf{\text{Existingsellingprice}}\mathbf{\times }\mathbf{80}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{20}\mathbf{\times }\mathbf{80}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{16}\end{array}$

Calculation of new variable cost:

Particular	Amount $	/	Units	X	Percentage after increase or decrease	=	Per unit
Total variable unit costs	$800,000	/	100,000	X	75%	=	$6
Total variable packaging costs	$100,000	/	100,000	X	120%	=	$1.2
				X			$7.2

Calculation of contribution margin ratio:

$\begin{array}{rcl}\mathbf{\text{Contributionmarginratio}}& \mathbf{=}& \frac{\mathbf{\text{Salespriceperunit}}\mathbf{-}\mathbf{\text{Variablecostperunit}}}{\mathbf{\text{Salespriceperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{16}\mathbf{-}\mathbf{\$}\mathbf{7}\mathbf{.}\mathbf{2}}{\mathbf{\$}\mathbf{16}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{55}\end{array}$

Break-even dollar sales:

$\begin{array}{rcl}\mathbf{\text{Break-evendollarsales}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginratio}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{950}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{55}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{727}\mathbf{,}\mathbf{273}\end{array}$

Contribution margin income statement for each strategy

Particular	Existing strategy	New strategy
Sales	$\left(100,000\times 20\right)$$2,000,000	$\left(180,000\times 16\right)$$2,880,000
Less: Variable cost	(900,000)	$\left(180,000\times 7.2\right)$(1,296,000)
Contribution margin	1,100,000	1,584,000
Less: Fixed cost	(950,000)	(950,000)
Pre-tax income	150,000	634,000
Less: Income tax	(37,500)	(158,500)
Net income	$112,500	$475,500