Chapter 9, Problem 38P

1.

To determine

Compute the break-even point in total units and the number of units to be sold using weighted average contribution margin approach.

Explanation of Solution

Compute the break-even point in total units and the number of units to be sold using weighted average contribution margin approach.

Particulars	Total
Overall break-even point:
Fixed costs (A)	$400,000
Weighted average contribution per unit (B)$\left(\$15\times 80\%\right)+\left(\$40\times 20\right)$	$20.00
Break-even point $\left(\text{C}\right)=\frac{\left(\text{A}\right)}{\left(\text{B}\right)}$	20,000 units
Breakdown of overall breakeven sales in units:
Product A:  $\left(20,000\text{ units}\times 80\%\right)$	16,000 units
Product B:  $\left(20,000\text{ units}\times 20\%\right)$	4,000 units

Table (1)

2.

To determine

Compute the overall break even point using goal seek tool in excel.

Explanation of Solution

Compute the overall break-even point using goal seek tool in excel.

Step 1: Go to "Data," then "What-If Analysis," then "Goal Seek." The following window should appear:

Figure (1)

Step 2: After clicking OK the Goal seek function returns the value as shown below:

Figure (2)

3.

To determine

Compute the break-even in units and the breakdown of the total breakeven point into sales (in units) of each of the two products using sales basket approach.

Explanation of Solution

Compute the units of each product to be sold.

Contribution margin per sales basket
Product	Units	Unit price	Total
A	4 units	$15 per unit	$60.00
B	1 unit	$40 per unit	$40.00
Total contribution margin per sales basket (B)			$100.00
Overall break-even point
Fixed cost (A)			$400,000
Overall break-even point $\left(\text{C}\right)=\frac{\left(\text{A}\right)}{\left(\text{B}\right)}$			4,000 baskets
Overall breakeven point in units $\left(4,000\text{ baskets}\times \text{5 units per basket}\right)$			20,000
Breakdown of overall breakeven point:
Product	Units	Unit per basket	Total
A	4,000 baskets	4	16,000 units
B	4,000 baskets	1	4,000 units

Table (2)

4.

To determine

Compute the breakeven point in sales dollars using weighted average contribution margin ratio.

Explanation of Solution

Compute the breakeven point in terms of dollars using weighted average contribution margin ratio.

Step 1: Computation of total sales in dollars
Product		Units sold	Unit sales price	Total
A		18,000 units	$80 per unit	$1,440,000.00
B		4,500 unit	$140 per unit	$630,000.00
Total sales in dollars				$2,070,000
Step 2: Compute the weights assigned to each product
Product		Sales dollars (1)	Total sales in dollars (2)	Assigned weights $\left(3\right)=\frac{\left(1\right)}{\left(2\right)}$
A		$1,440,000.00	$2,070,000	0.6956522
B		$630,000.00	$2,070,000	0.3043478
Step 3: Computation of weighted average contribution margin ratio
Product	Assigned weights (1)	Sales per unit (2)	Contribution margin per unit (3)	Weighted average contribution margin ratio $\left(4\right)=\left(1\right)\times \frac{\left(3\right)}{\left(2\right)}$
A	0.6956522	$80	$15	0.13043478
B	0.3043478	$140	$40	0.08695652
				0.21739130
Break-even point overall dollars$\left(\frac{\text{\$400,000}}{0.21739130}\right)$					$1,840,000
Breakdown of total breakeven sales dollars, by product
Product A $\left( 0.6956522\times \text{\$1,840,000}\right)$					$1,280,000
Product B $\left( 0.3043478\times \text{\$1,840,000}\right)$					$560,000

Table (3)

5.

To determine

Describe the statement “For the multiproduct firm, there is no breakeven point independent of

the sales-mix assumption”.

Explanation of Solution

“For the multiproduct firm, there is no breakeven point independent of the sales mix assumption.” The companies dealing in multi products, it is presumed that the output that are sold in some standard mix are based either on relative physical units or relative sales dollars. If the individual products differ in terms of their contribution margins per unit (or contribution margin ratios), then the weighted-average contribution margin (and weighted-average contribution margin ratio) will change with respect to the changes in the sales mix. This, in turn, affects the breakeven point since that point is defined as the ratio of fixed costs to the weighted-average contribution margin per unit Certainly, if the unit contribution margins are the same for each product, then the assumed mix has no mathematical impact on the breakeven calculation.

6.

To determine

Explain the manner in which the break-even points will be affected by the increase in fixed costs. Explain the manner in which the percentage change in the break-even point will differ to the percentage change in fixed cost and explain the inference that could be drawn on the basis of calculation.

Explanation of Solution

Explain the manner in which the break-even points will be affected by the increase in fixed costs.

Change in the breakeven point (in total units) in response to a 10% change in fixed costs:
New level of fixed costs $\left(\$400,000+\$40,000\right)$(A)	$440,000
Original level of fixed costs (B)	$400,000
Change in fixed costs $\left(\text{C}\right)=\left(\text{A}\right)-\left(\text{B}\right)$	$40,000
Percentage change in fixed costs $\left(\text{D}\right)=\frac{\left(\text{C}\right)}{\left(\text{B}\right)}$	10.00%
New breakeven point $\frac{\$440,000}{\$20.00\text{ per unit}}$	22,000 units
Less: Original breakeven point (E)	20,000 units
Change in breakeven point (F)	2,000 units
Percentage change in break-even point $\left(\text{G}\right)=\frac{\left(\text{F}\right)}{\left(\text{E}\right)}$	10.00%

Table (4)

The percentage change in fixed costs of 10%t led to an identical percentage change in the breakeven point. Because of the linear cost functions assumed in a conventional CVP model, this finding can be generalized as follows: Keeping everything constant, a given percentage change (+ or −) in the amount of fixed costs leads to an equivalent percentage change in the breakeven point.