CVP Analysis and Marginal Analysis Paper 12

(b) The requirement is to determine how many units of product X (one of three products) Thomas would sell at the breakeven point. The solutions approach is first to find the number of composite units to breakeven; a composite unit consists of the number of units of each of the three products in the mix. Since Thomas sells three units of X for each unit of Z and two units of Y for each unit of X, they are selling six units of Y for each unit of Z; therefore, a composite unit consists of 3X, 6Y, and 1Z. The total contribution margin for one composite unit is X (3) ($1.00) = $ 3 Y (6) ($1.50) = $ 9 Z (1) ($3.00) = $ 3 $15 The breakeven point in terms of units of the product mix group is $600,000 $15 = 40,000 composite units Since there are three units of X in each composite unit, (40,000) (3) or 120,000 units of X are sold at breakeven.

(c) Breakeven analysis is based upon several simplified assumptions. Included in these assumptions is that variable costs are constant per unit and, for a multiproduct company, that a given sales mix is maintained for all volume changes. When absorption costing is used, operating income is a function of both production volume and sales volume. This is because an increase in inventory levels causes fixed costs to be held in inventory while a decrease in inventory levels causes fixed costs to be charged to cost of goods sold. These fluctuations can dramatically affect income and the breakeven point. On the other hand, when variable costing is used the same amount of fixed costs will be deducted from income whether or not inventory levels fluctuate. As a result, the breakeven point will be the same even if production does not equal sales. Hence, operating income under variable costing is a function only of sales, and assumption I. is incorrect.

(d) Under variable costing, both variable direct and variable indirect manufacturing costs are assigned to inventory. All fixed costs are considered sunk costs and thus are written off as an expense of the period. Additionally, variable selling and administrative costs are also treated as period costs and thus not assigned to inventory.

(a) The requirement is to determine what situation would cause variable costing net income to be higher than absorption costing net income. Answer (a) is correct because this difference in reported income is explained if units produced in 2012 are less than units sold in 2012. This is true because under variable costing, the amount of overhead included in cost of goods sold is the amount applied in 2012 (since all units produced were sold), whereas under absorption costing the overhead released to cost of goods sold includes that applied in 2012 as well as overhead included in the 2011 year-end inventory. Answer (b) is incorrect since a level of production lower than the activity level used to allocate overhead would result in underapplied overhead. Answer (c) is incorrect because the opposite situation results in overapplied overhead. Answer (d) is incorrect because production in excess of units sold would produce a higher absorption costing income than the variable costing income.

(c) The requirement is to identify the item that is an output from a strategic plan. Answer (c) is correct. A financial planning model is a mathematical model that attempts to forecast future financial results. Sets of projected financial statements are a major output from the model. Answer (a) is incorrect because strategic plans drive the financial planning process and must be developed before employing the financial planning model. Answers (b) and (d) are incorrect because the planning model does not provide outputs related to actual results.

Correct answer: (B)
Assume the company has variable costs of $10 per unit. If they mark this up by 60%, the selling price will be $16. A markdown of 10% makes the sales price $14.40 ($16 × 0.90). A selling price of $14.40 minus variable cost of $10 provides a contribution of $4.40 per unit, which is 30.6% of the selling price ($4.40 ÷ $14.40). Another way to approach the problem is by using algebra, as follows: The original sale prices are 1.60 times the variable costs (1 + .60), or 1.6VC. Markdowns are 10% off the sales price. Therefore, the marked down prices are 90% of the original sale prices. Therefore, the marked down sales price = 1.6VC × .9. When you combine the terms by multiplying 1.6 by .9, you get the markdown price = 1.44VC. Now, it is easy to calculate the contribution margin. If we say one single product has a variable cost of $1.00, then the marked down sales price for that one product must be 1.44 times $1.00, which is $1.44. The unit sale price = $1.44. The unit variable cost = $1.00. The unit contribution margin = $.44. So the contribution margin ratio is $.44 ÷ $1.44, which is .306 or 30.6%

Correct answer: (C)
Because the commission is a percentage of the sales price, it is also a variable cost and needs to be deducted from the sales price to calculate the contribution per unit. The commission is $2 ($40 × 0.05) and this makes the contribution per unit $16 ($40 − $22 − $2). The fixed costs are $9,331,200 and given a contribution of $16 per unit, a total of 583,200 units must be sold ($9,331,200 ÷ $16).

Correct answer: (A)
The breakeven point in units is Fixed Cost divided by the Unit Contribution Margin. Cost of Goods Sold is 75% variable cost, or $15,000,000 variable cost for the budgeted 600,000 units ($20,000,000 × 0.75). Sales, General and Administrative Expense is 40% variable cost, or $3,000,000 variable cost for 600,000 budgeted units ($7,500,000 × 0.40). Therefore, the contribution margin at a sales level of 600,000 units is $30,000,000 − $15,000,000 − $3,000,000, or $12,000,000. The Unit Contribution Margin is $12,000,000 divided by 600,000 units, or $20 per unit. Fixed costs equal 25% of COGS, or $20,000,000 × 0.25, plus 60% of SG&A Expense, or $7,500,000 × 0.60, for a total fixed cost of $9,500,000. Therefore, the breakeven point in units is $9,500,000 ÷ $20, which equals 475,000 units.

Correct answer: (D)
The breakeven point in revenue is Fixed Cost divided by the Contribution Margin Ratio. We calculated the Unit Contribution Margin in the previous answer as $20. The sales price per unit is $50. Therefore, the Contribution Margin Ratio is $20 ÷ $50, or 40%. We calculated total fixed costs in the previous problem as $9,500,000. Therefore, the breakeven point in revenue is $9,500,000 ÷ 0.40, or $23,750,000. The same answer could also be calculated by multiplying the 475,000 units found in the previous problem as the breakeven point in units by the price per unit of $50. 475,000 × $50 = $23,750,000.

Correct answer: (C)
The breakeven point in units is Fixed Cost divided by Unit Contribution Margin, so the unit contribution margin multiplied by the breakeven point in units will equal fixed costs. At a sales volume of 900,000 units, KJR contribution margin is $24,300,000, so the company unit contribution margin is $24,300,000 ÷ 900,000, or $27. The breakeven point in units is given as 750,000. Fixed cost is therefore the unit contribution margin multiplied by the breakeven point in units: $27 × 750,000, or $20,250,000.