管理会计（高等教育出版社）
于增彪（清华大学） 改编 余绪缨（厦门大学） 审校 CHAPTER 16
COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOL
QUESTIONS FOR WRITING AND DISCUSSION
1. CVP analysis allows managers to focus on
selling prices, volume, costs, profits, and sales mix. Many different “what if” questions can be asked to assess the effect on profits of changes in key variables. 2. The units-sold approach defines sales vo-lume in terms of units of product and gives answers in these same terms. The sales-revenue approach defines sales volume in terms of revenues and provides answers in these same terms. 3. Break-even point is the level of sales activity
where total revenues equal total costs, or where zero profits are earned. 4. At the break-even point, all fixed costs are
covered. Above the break-even point, only variable costs need to be covered. Thus, contribution margin per unit is profit per unit, provided that the unit selling price is greater than the unit variable cost (which it must be for break-even to be achieved). 5. Profit = $7.00 ? 5,000 = $35,000
6. Variable cost ratio = Variable costs/Sales.
Contribution margin ratio = Contribution margin/Sales. Contribution margin ratio = 1 – Variable cost ratio. 7. Break-even revenues = $20,000/0.40 =
$50,000
8. No. The increase in contribution is $9,000
(0.30 ? $30,000), and the increase in adver-tising is $10,000. 9. Sales mix is the relative proportion sold of
each product. For example, a sales mix of 3:2 means that three units of one product are sold for every two of the second product. 10. Packages of products, based on the ex-pected sales mix, are defined as a single product. Selling price and cost information for this package can then be used to carry out CVP analysis. 11. Package contribution margin: (2 ? $10) + (1
? $5) = $25. Break-even point = $30,000/$25 = 1,200 packages, or 2,400 units of A and 1,200 units of B. 12. Profit = 0.60($200,000 – $100,000) =
$60,000 13. A change in sales mix will change the contri-bution margin of the package (defined by the sales mix) and, thus, will change the units needed to break even. 14. Margin of safety is the sales activity in
excess of that needed to break even. The higher the margin of safety, the lower the risk. 15. Operating leverage is the use of fixed costs
to extract higher percentage changes in
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profits as sales activity changes. It is achieved by increasing fixed costs while lo-wering variable costs. Therefore, increased leverage implies increased risk, and vice versa.
16. Sensitivity analysis is a “what if” technique
that examines the impact of changes in un-derlying assumptions on an answer. A com-pany can input data on selling prices, varia-ble costs, fixed costs, and sales mix and set up formulas to calculate break-even points and expected profits. Then, the data can be varied as desired to see what impact changes have on the expected profit. 17. By specifically including the costs that vary
with nonunit drivers, the impact of changes in the nonunit drivers can be examined. In traditional CVP, all nonunit costs are lumped together as “fixed costs.” While the costs are fixed with respect to units, they vary with re-spect to other drivers. ABC analysis reminds us of the importance of these nonunit drivers and costs. 18. JIT simplifies the firm’s cost equation since
more costs are classified as fixed (e.g., di-rect labor). Additionally, the batch-level vari-able is gone (in JIT, the batch is one unit). Thus, the cost equation for JIT includes fixed costs, unit variable cost times the number of units sold, and unit product-level cost times the number of products sold (or related cost
driver). JIT means that CVP analysis ap-proaches the standard analysis with fixed and unit-level costs only.
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EXERCISES
16–1
1. e 2. c 3. d
4. b 5. a
16–2
1. f 2. d 3. b 4. a
5. g 6. e 7. c
16–3
1. 2. 3.
Units = Fixed cost/Contribution margin = $10,350/($15 – $12) = 3,450 Sales (3,450 ? $15)
Variable costs (3,450 ? $12) Contribution margin Fixed costs
Operating income Units
$51,750 41,400 $ 10,350 10,350 $ 0 = (Target income + Fixed cost)/Contribution margin
= ($9,900 + $10,350)/($15 – $12) = $20,250/$3 = 6,750
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16–4
1. 2. 3. 4.
Contribution margin per unit = $15 – $12 = $3 Contribution margin ratio = $3/$15 = 0.20, or 20% Variable cost ratio = $60,000/$75,000 = 0.80, or 80% Revenue = Fixed cost/Contribution margin ratio = $10,350/0.20 = $51,750
Revenue = (Target income + Fixed cost)/Contribution margin ratio = ($9,900 + $10,350)/0.20 = $101,250
16–5
1. 2.
0.15($15)(Units) $2.25(Units) $10,350 Units = $15(Units) – $12(Units) – $10,350
= $3(Units) – $10,350 = $0.75(Units) = 13,800
$ 207,000 165,600 $ 41,400 10,350 $ 31,050 Sales (13,800 ? $15)
Variable costs (13,800 ? $12) Contribution margin Fixed costs
Operating income
$31,050 does equal 15% of $207,000, so the answer of 13,800 units is correct.
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16–6
1. Before-tax income = (After-tax income)/(1 – Tax rate) = $6,000/(1 – 0.40) = $10,000
Units = (Target income + Fixed cost)/Contribution margin = ($10,000 + $10,350)/($15 – $12) = 6,783*
*The answer is 6,783.3333, and so it must be rounded to a whole unit. You may prefer that students round up the answer to 6,784, instead, since it is better to be marginally above break-even than marginally below it.
2. Before-tax income = (After-tax income)/(1 – Tax rate) = $6,000/(1 – 0.50) = $12,000
3.
Units = (Target income + Fixed cost)/Contribution margin = ($12,000 + $10,350)/($15 – $12) = 7,450 Before-tax income = (After-tax income)/(1 – Tax rate) = $6,000/(1 – 0.30) = $8,571 Units = (Target income + Fixed cost)/Contribution margin = ($8,571 + $10,350)/($15 – $12) = 6,307
16–7
1. 2. 3.
Break-even units = Fixed costs/(Price – Variable cost) = $150,000/($2.45 – $1.65) = $150,000/$0.80 = 187,500
Units = ($150,000 + $12,600)/($2.45 – $1.65) = $162,600/$0.80 = 203,250
Unit variable cost = $1.65
Unit variable manufacturing cost = $1.65 – $0.17 = $1.48
The unit variable cost is used in cost-volume-profit analysis, since it includes all of the variable costs of the firm.
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