管理会计(英文版)课后习题答案(高等教育出版社)chapter 16

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 volume 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 advertising 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 expected 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 contribution 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 profits as sales activity changes. It is achieved by increasing fixed costs while lowering 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 underlying assumptions on an answer. A company can input data on selling prices, variable 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 respect 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., direct labor). Additionally, the batch-level variable 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 approaches the standard analysis with fixed and unit-level costs only. 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.    Units    = Fixed cost/Contribution margin             = $10,350/($15 – $12)             = 3,450 2.    Sales (3,450 $15)    $51,750     Variable costs (3,450 $12)        41,400     Contribution margin    $    10,350     Fixed costs        10,350             Operating income    $    0 3.    Units    = (Target income + Fixed cost)/Contribution margin             = ($9,900 + $10,350)/($15 – $12)             = $20,250/$3             = 6,750 16–4 1.    Contribution margin per unit = $15 – $12 = $3     Contribution margin ratio = $3/$15 = 0.20, or 20% 2.    Variable cost ratio = $60,000/$75,000 = 0.80, or 80% 3.    Revenue    = Fixed cost/Contribution margin ratio             = $10,350/0.20             = $51,750 4.    Revenue    = (Target income + Fixed cost)/Contribution margin ratio             = ($9,900 + $10,350)/0.20             = $101,250 16–5 1.            0.15($15)(Units)    = $15(Units) – $12(Units) – $10,350             $2.25(Units)    = $3(Units) – $10,350             $10,350    = $0.75(Units)             Units    = 13,800 2.    Sales (13,800 $15)    $    207,000     Variable costs (13,800 $12)        165,600     Contribution margin    $    41,400     Fixed costs        10,350             Operating income    $    31,050     $31,050 does equal 15% of $207,000, so the answer of 13,800 units is correct. 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     Units    = (Target income + Fixed cost)/Contribution margin             = ($12,000 + $10,350)/($15 – $12)             = 7,450 3.    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.    Break-even units    = Fixed costs/(Price – Variable cost)             = $150,000/($2.45 – $1.65)             = $150,000/$0.80             = 187,500 2.    Units    = ($150,000 + $12,600)/($2.45 – $1.65)             = $162,600/$0.80             = 203,250 3.    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. 16–8 1.    Before-tax income = $25,200/(1 – 0.40) = $42,000     Units    = ($150,000 + $42,000)/$0.80             = $192,000/$0.80             = 240,000 2.    Before-tax income = $25,200/(1 – 0.30) = $36,000     Units    = ($150,000 + $36,000)/$0.80             = $186,000/$0.80             = 232,500 3.    Before-tax income = $25,200/(1 – 0.50) = $50,400     Units    = ($150,000 + $50,400)/$0.80             = $200,400/$0.80             = 250,500 4.    215,000 – 187,500 = 27,500 pans             or     $526,750 – $459,375 = $67,375 16–9         A            B            C            D    Sales    $    5,000    $    15,600*    $    16,250*    $9,000 Variable costs        4,000        11,700        9,750        5,400* Contribution margin    $    1,000    $    3,900    $    6,500*    $3,600* Fixed costs        500*        4,000        6,100*        750     Operating income (loss)    $    500    $    (100)*    $    400    $2,850 Units sold    1,000*    1,300    125    90 Price/unit    $5    $12*    $130    $100* Variable cost/unit    $4*    $9    $78*    $60* Contribution margin/unit    $1*    $3    $52*    $40* Contribution margin ratio    20%*    25%*    40%    40%* Break-even in units    500*    1,334*    118*    19* *Designates calculated amount. Note: When the calculated break-even in units includes a fractional amount, it has been rounded up to the next whole unit. 16–10 1.    Variable cost ratio    = Variable costs/Sales             = $399,900/$930,000             = 0.43, or 43%     Contribution margin ratio    = (Sales – Variable costs)/Sales             = ($930,000 – $399,900)/$930,000             = 0.57, or 57% 2.    Break-even sales revenue = $307,800/0.57 = $540,000 3.    Margin of safety    = Sales – Break-even sales             = $930,000 – $540,000 = $390,000 4.    Contribution margin from increased sales = ($7,500)(0.57) = $4,275     Cost of advertising = $5,000     No, the advertising campaign is not a good idea, because the company’s operating income will decrease by $725 ($4,275 – $5,000). 16–11 1.            Income    = Revenue – Variable cost – Fixed cost             0    = 1,500P – $300(1,500) – $120,000             0    = 1,500P – $450,000 – $120,000             $570,000    = 1,500P             P    = $380 2.    $160,000/($3.50 – Unit variable cost) = 128,000 units     Unit variable cost = $2.25 16–12 1.    Contribution margin per unit    = $5.60 – $4.20*             = $1.40     *Variable costs per unit:     $0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20     Contribution margin ratio = $1.40/$5.60 = 0.25 = 25% 2.    Break-even in units = ($32,300 + $12,500)/$1.40 = 32,000 boxes     Break-even in sales    = 32,000 $5.60 = $179,200             or             = ($32,300 + $12,500)/0.25 = $179,200 3.    Sales ($5.60 35,000)    $    196,000     Variable costs ($4.20 35,000)        147,000     Contribution margin    $    49,000     Fixed costs        44,800             Operating income    $    4,200 4.    Margin of safety = $196,000 – $179,200 = $16,800 5.    Break-even in units = 44,800/($6.20 – $4.20) = 22,400 boxes     New operating income    = $6.20(31,500) – $4.20(31,500) – $44,800             = $195,300 – $132,300 – $44,800 = $18,200     Yes, operating income will increase by $14,000 ($18,200 – $4,200). 16–13 1.    Variable cost ratio = $126,000/$315,000 = 0.40     Contribution margin ratio = $189,000/$315,000 = 0.60 2.    $46,000 0.60 = $27,600 3.    Break-even revenue = $63,000/0.60 = $105,000     Margin of safety = $315,000 – $105,000 = $210,000 4.    Revenue    = ($63,000 + $90,000)/0.60             = $255,000 5.    Before-tax income = $56,000/(1 – 0.30) = $80,000     Note: Tax rate = $37,800/$126,000 = 0.30     Revenue = ($63,000 + $80,000)/0.60 = $238,333     Sales        $    238,333     Less: Variable expenses ($238,333 0.40)            95,333     Contribution margin        $    143,000     Less: Fixed expenses            63,000     Income before income taxes        $    80,000     Income taxes ($80,000 0.30)            24,000             Net income        $    56,000 16–14 1.    Operating income    = Revenue(1 – Variable cost ratio) – Fixed cost             (0.20)Revenue    = Revenue(1 – 0.40) – $24,000             (0.20)Revenue    = (0.60)Revenue – $24,000             (0.40)Revenue    = $24,000             Revenue    = $60,000     Sales        $    60,000     Variable expenses ($60,000 0.40)            24,000     Contribution margin        $    36,000     Fixed expenses            24,000             Operating income        $    12,000     $12,000 = $60,000 20% 2.    If revenue of $60,000 produces a profit equal to 20 percent of sales and if the price per unit is $10, then 6,000 units must be sold. Let X equal number of units, then:             Operating income    = (Price – Variable cost) – Fixed cost             0.20($10)X    = ($10 – $4)X – $24,000             $2X    = $6X – $24,000             $4X    = $24,000             X    = 6,000 buckets             0.25($10)X    = $6X – $24,000             $2.50X    = $6X – $24,000             $3.50X    = $24,000             X    = 6,857 buckets     Sales (6,857 $10)        $68,570     Variable expenses (6,857 $4)            27,428     Contribution margin        $41,142     Fixed expenses            24,000             Operating income        $17,142     $17,142* = 0.25 $68,570 as claimed     *Rounded down.     Note: Some may prefer to round up to 6,858 units. If this is done, the operating income will be slightly different due to rounding. 16–14    Concluded 3.    Net income    = 0.20Revenue/(1 – 0.40)             = 0.3333Revenue     0.3333Revenue    = Revenue(1 – 0.40) – $24,000     0.3333Revenue    = 0.60Revenue – $24,000     0.2667Revenue    = $24,000             Revenue    = $89,989 16–15 1.    Company A:    $100,000/$50,000 = 2     Company B:    $300,000/$50,000 = 6 2.            Company A            Company B        X = $50,000/(1 – 0.80)    X = $250,000/(1 – 0.40)     X = $50,000/0.20    X = $250,000/0.60     X = $250,000    X = $416,667     Company B must sell more than Company A to break even because it must cover $200,000 more in fixed costs (it is more highly leveraged). 3.    Company A:    2 50% = 100%     Company B:    6 50% = 300%     The percentage increase in profits for Company B is much higher than Company A’s increase because Company B has a higher degree of operating leverage (i.e., it has a larger amount of fixed costs in proportion to variable costs as compared to Company A). Once fixed costs are covered, additional revenue must cover only variable costs, and 60 percent of Company B’s revenue above break-even is profit, whereas only 20 percent of Company A’s revenue above break-even is profit. 16–16 1.                Variable        Units in    Package     Product        Price*    –    Cost    =    CM            Mix        =        CM        Scientific    $25    $12    $13    1    $13     Business    20    9    11    5        55             Total                        $68 *$500,000/20,000 = $25     $2,000,000/100,000 = $20     X = ($1,080,000 + $145,000)/$68     X = $1,225,000/$68     X = 18,015 packages     18,015 scientific calculators (1 18,015)     90,075 business calculators (5 18,015) 2.    Revenue = $1,225,000/0.544* = $2,251,838     *($1,360,000/$2,500,000) = 0.544 16–17 1.    Sales mix is 2:1 (Twice as many videos are sold as equipment sets.) 2.                    Variable                Sales         Product        Price    –        Cost        =    CM            Mix        =    Total CM     Videos    $12    $4    $8    2    $16     Equipment sets    15    6    9    1        9             Total                    $25     Break-even packages = $70,000/$25 = 2,800     Break-even videos    = 2 2,800 = 5,600     Break-even equipment sets    = 1 2,800 = 2,800 3.            Switzer Company             Income Statement     For Last Year     Sales        $    195,000     Less: Variable costs            70,000     Contribution margin        $    125,000     Less: Fixed costs            70,000             Operating income        $    55,000     Contribution margin ratio = $125,000/$195,000 = 0.641, or 64.1%     Break-even sales revenue = $70,000/0.641 = $109,204 4.    Margin of safety = $195,000 – $109,204 = $85,796 16–18 1.    Sales mix is 2:1:4 (Twice as many videos will be sold as equipment sets, and four times as many yoga mats will be sold as equipment sets.) 2.                Variable        Sales         Product        Price    –        Cost        =    CM            Mix        =    Total CM     Videos    $12    $    4    $8    2    $16     Equipment sets    15    6    9    1    9     Yoga mats    18    13    5    4        20             Total                    $45     Break-even packages = $118,350/$45 = 2,630     Break-even videos    = 2 2,630 = 5,260     Break-even equipment sets    = 1 2,630 = 2,630     Break-even yoga mats    = 4 2,630 = 10,520 3.            Switzer Company             Income Statement     For the Coming Year     Sales        $555,000     Less: Variable costs            330,000     Contribution margin        $225,000     Less: Fixed costs            118,350             Operating income        $106,650     Contribution margin ratio = $225,000/$555,000 = 0.4054, or 40.54%     Break-even revenue = $118,350/0.4054 = $291,934 4.    Margin of safety = $555,000 – $291,934 = $263,066 16–19 1.    Contribution margin/unit = $410,000/100,000 = $4.10     Contribution margin ratio = $410,000/$650,000 = 0.6308     Break-even units = $295,200/$4.10 = 72,000 units     Break-even revenue    = 72,000 $6.50 = $468,000             or             = $295,200/0.6308 = $467,977* *Difference due to rounding error in calculating the contribution margin ratio. 2.    The break-even point decreases:     X = $295,200/(P – V)     X = $295,200/($7.15 – $2.40)     X = $295,200/$4.75     X = 62,147 units     Revenue = 62,147 $7.15 = $444,351 3.    The break-even point increases:     X = $295,200/($6.50 – $2.75)     X = $295,200/$3.75     X = 78,720 units     Revenue = 78,720 $6.50 = $511,680 16–19    Concluded 4.    Predictions of increases or decreases in the break-even point can be made without computation for price changes or for variable cost changes. If both change, then the unit contribution margin must be known before and after to predict the effect on the break-even point. Simply giving the direction of the change for each individual component is not sufficient. For our example, the unit contribution changes from $4.10 to $4.40, so the break-even point in units will decrease.     Break-even units = $295,200/($7.15 – $2.75) = 67,091     Now, let’s look at the break-even point in revenues. We might expect that it, too, will decrease. However, that is not the case in this particular example. Here, the contribution margin ratio decreased from about 63 percent to just over 61.5 percent. As a result, the break-even point in revenues has gone up.         Break-even revenue = 67,091 $7.15 = $479,701 5.    The break-even point will increase because more units will need to be sold to cover the additional fixed expenses.     Break-even units = $345,200/$4.10 = 84,195 units     Revenue = $547,268 16–20 1.     Break-even point = 2,500 units; + line is total revenue and x line is total costs. 16–20    Continued 2.    a.    Fixed costs increase by $5,000:         Break-even point = 3,750 units 16–20    Continued     b.    Unit variable cost increases to $7:         Break-even point = 3,333 units 16–20    Continued     c.    Unit selling price increases to $12:         Break-even point = 1,667 units 16–20    Continued     d.    Both fixed costs and unit variable cost increase:         Break-even point = 5,000 units 16–20    Continued 3.    Original data:     Break-even point = 2,500 units 16–20    Continued     a.    Fixed costs increase by $5,000:         Break-even point = 3,750 units 16–20    Continued     b.    Unit variable cost increases to $7:         Break-even point = 3,333 units 16–20    Continued     c.    Unit selling price increases to $12:         Break-even point = 1,667 units 16–20    Concluded     d.    Both fixed costs and unit variable cost increase:         Break-even point = 5,000 units 4.    The first set of graphs is more informative since these graphs reveal how costs change as sales volume changes. 16–21 1.    Unit contribution margin = $1,060,000/50,000 = $21.20     Break-even units = $816,412/$21.20 = 38,510 units     Operating income = 30,000 $21.20 = $636,000 2.    CM ratio = $1,060,000/$2,500,000 = 0.424 or 42.4%     Break-even point = $816,412/0.424 = $1,925,500     Operating income = ($200,000 0.424) + $243,588 = $328,388 3.    Margin of safety = $2,500,000 – $1,925,500 = $574,500 4.    $1,060,000/$243,588 = 4.352 (operating leverage)     4.352 20% = 0.8704     0.8704 $243,588 = $212,019     New operating income level = $212,019 + $243,588 = $455,607 5.    Let X = Units             0.10($50)X    = $50.00X – $28.80X – $816,412             $5X    = $21.20X – $816,412             $16.20X    = $816,412             X    = 50,396 units 6.    Before-tax income = $180,000/(1 – 0.40) = $300,000     X = ($816,412 + $300,000)/$21.20 = 52,661 units 16–22 1.            Variable    Sales    Package         Product            Price    –        Cost            =    CM            Mix        =        CM        Vases    $40    $30    $10    2    $20     Figurines    70    42    28    1        28             Total                    $48     Break-even packages = $30,000/$48 = 625     Break-even vases = 2 625 = 1,250     Break-even figurines = 625 2.    The new sales mix is 3 vases to 2 figurines.             Variable    Sales    Package         Product            Price    –        Cost            =    CM            Mix        =        CM        Vases    $40    $30    $10    3    $30     Figurines    70    42    28    2        56             Total                    $86     Break-even packages = $35,260/$86 = 410     Break-even vases = 3 410 = 1,230     Break-even figurines = 2 410 = 820 16–23     1.    d     2.    c     3.    a     4.    d     5.    e     6.    b     7.    c problems 16–24 1.    Unit contribution margin = $825,000/110,000 = $7.50     Break-even point = $495,000/$7.50 = 66,000 units     CM ratio = $7.50/$25    = 0.30     Break-even point    = $495,000/0.30 = $1,650,000             or             = $25 66,000 = $1,650,000 2.    Increased CM ($400,000 0.30)    $    120,000     Less: Increased advertising expense        40,000     Increased operating income    $    80,000 3.    $315,000 0.30 = $94,500 4.    Before-tax income = $360,000/(1 – 0.40) = $600,000     Units    = ($495,000 + $600,000)/$7.50             = 146,000 5.    Margin of safety    = $2,750,000 – $1,650,000 = $1,100,000             or             = 110,000 units – 66,000 units = 44,000 units 6.    $825,000/$330,000 = 2.5 (operating leverage)     20% 2.5 = 50% (profit increase) 16–25 1.    Sales mix:     Squares:    $300,000/$30 = 10,000 units     Circles:    $2,500,000/$50 = 50,000 units                             Sales    Total     Product        P        –        V*        =    P – V            Mix        =        CM        Squares    $30    $10    $20    1    $    20     Circles    50    10    40    5        200             Package                    $220 *$100,000/10,000 = $10     $500,000/50,000 = $10     Break-even packages = $1,628,000/$220 = 7,400 packages     Break-even squares = 7,400 1 = 7,400     Break-even circles = 7,400 5 = 37,000 2.    Contribution margin ratio = $2,200,000/$2,800,000 = 0.7857             0.10Revenue    = 0.7857Revenue – $1,628,000             0.6857Revenue    = $1,628,000             Revenue    = $2,374,216 3.    New mix:                             Sales    Total     Product        P        –        V        =    P – V            Mix        =        CM        Squares    $30    $10    $20    3    $    60     Circles    50    10    40    5        200             Package                    $260     Break-even packages = $1,628,000/$260 = 6,262 packages     Break-even squares = 6,262 3 = 18,786     Break-even circles = 6,262 5 = 31,310     CM ratio = $260/$340* = 0.7647     *(3)($30) + (5)($50) = $340 revenue per package             0.10Revenue    = 0.7647Revenue – $1,628,000             0.6647Revenue    = $1,628,000             Revenue    = $2,449,225 16–25    Concluded 4.    Increase in CM for squares (15,000 $20)    $    300,000     Decrease in CM for circles (5,000 $40)        (200,000)     Net increase in total contribution margin    $    100,000     Less: Additional fixed expenses        45,000             Increase in operating income    $    55,000     Gosnell would gain $55,000 by increasing advertising for the squares. This is a good strategy. 16–26 1.    Currently:     Sales (830,000 $0.36)    $    298,800     Variable expenses        224,100     Contribution margin    $    74,700     Fixed expenses        54,000             Operating income    $    20,700     New contribution margin = 1.5 $74,700 = $112,050     $112,050 – promotional spending – $54,000 = 1.5 $20,700     Promotional spending = $27,000 2.    Here are two ways to calculate the answer to this question:     a.    The per-unit contribution margin needs to be the same:         Let P* represent the new price and V* the new variable cost.                 (P – V)    = (P* – V*)                 $0.36 – $0.27    = P* – $0.30                 $0.09    = P* – $0.30                 P*    = $0.39     b.    Old break-even point = $54,000/($0.36 – $0.27) = 600,000         New break-even point = $54,000/(P* – $0.30) = 600,000         P* = $0.39     The selling price should be increased by $0.03. 16–26    Concluded 3.    Projected contribution margin (700,000 $0.13)    $91,000     Present contribution margin        74,700     Increase in operating income    $16,300     The decision was good because operating income increased by $16,300.     (New quantity $0.13) – $54,000 = $20,700     New quantity = 574,615     Selling 574,615 units at the new price will maintain profit at $20,700. 16–27 1.            Service            P        –        V        =        P – V            Mix    =        Total        Residential    $540.00a    $221.64c    $318.36    2    $636.72     Commercial    160.00b    124.52c    35.48    1        35.48             Package                    $672.20     a$13.50 10 4     b$40 4     cCost per acre for four applications             Residential    Commercial     Chemicals    $    70.00    $    70.00    [$40 + (3 $10)]     Labor*    80.00    18.00     Operating expenses**    55.12    20.00     Supplies**        16.52        16.52             Total    $    221.64    $    124.52     *10/3 $6.00 4; 3/4 $6.00 4     **The per-acre amount 4 applications     X    = F/(P – V)             = $39,708/$672.20 = 59* packages     Residential:    2 59 =    118 acres     Commercial:    1 59 =    59 acres     Average number of residential customers = 118/0.10 = 1,180     *Rounded 16–27    Concluded 2.    Hours needed to service break-even volume (in packages):     Residential:    10/3 4 2    =    26.67*    hours     Commercial:    3/4 4 1    =        3.00    hours                         29.67    hours per package     Total hours required = 29.67 59 = 1,751 hours     Hours per employee = 8 140 = 1,120     Employees needed = 1,751/1,120 = 1.6 laborers     One employee is not sufficient.     Volume/Employee = 1,120/29.67 = 38 packages. Thus, if volume exceeds 38 composite units (76 residential and 38 commercial), a second laborer is needed (at least part time).     *Rounded     Note: Adding another employee could affect the costs used in the initial analysis; for example: (1) another truck might be added (increasing fixed costs and the break-even point; (2) a two-man crew might be used (increasing variable costs); (3) the new employee might work evenings/weekends (no change in either fixed or variable costs). CVP used for planning is often an iterative process—the original solution may raise problems that may call for a recalculation, altering plans further. 3.    The mix is redefined to be 1.2:0.8:1.0.         Product        P        –        V        =        P – V            Mix    =    Total CM     Res.-1    $135.00    $    77.91*    $    57.09    1.2    $    68.51     Res.-4    540.00    221.64    318.36    0.8    254.69     Comm.    160.00    124.52    35.48    1.0        35.48             Package                    $    358.68     *Variable cost for one-time residential application:     Chemicals    $40.00     Labor    20.00     Operating expenses    13.78     Supplies        4.13             Total    $77.91     X = F/(P – V) = $39,708/$358.68 = 111 packages     Residential (one application): 1.2 111 = 133 acres     Residential (four applications): 0.8 111 = 89 acres     Commercial: 1 111 = 111 acres 16–28 1.    Contribution margin ratio = $487,548/$840,600 = 0.58 2.    Revenue = $250,000/0.58 = $431,034 3.            Operating income    = CMR Revenue – Total fixed cost             0.08R/(1 – 0.34)    = 0.58R – $250,000             0.1212R    = 0.58R – $250,000             0.4588R    = $250,000             R    = $544,900 4.    $840,600 110% =    $924,660     $353,052 110% =        388,357                 $536,303     CMR = $536,303/$924,660 = 0.58     The contribution margin ratio remains at 0.58. 5.    Additional variable expense = $840,600 0.03 = $25,218     New contribution margin = $487,548 – $25,218 = $462,330     New CM ratio = $462,330/$840,600 = 0.55     Break-even point = $250,000/0.55 = $454,545     The effect is to increase the break-even point. 6.    Present contribution margin    $    487,548     Projected contribution margin ($920,600 0.55)        506,330     Increase in contribution margin/profit    $    18,782     Fitzgibbons should pay the commission because profit would increase by $18,782. 16–29 1.    Let X be a package of three Grade I cabinets and seven Grade II cabinets. Then:             0.3X($3,400) + 0.7X($1,600)    = $1,600,000             X    = 748 packages     Grade I:    0.3 748 = 224 units     Grade II:    0.7 748 = 524 units 2.        Product        P        –        V        =        P – V            Mix    =    Total CM     Grade I    $3,400    $2,686    $714    3    $2,142     Grade II    1,600    1,328    272    7        1,904             Package                    $4,046     Direct fixed costs—Grade I    $    95,000     Direct fixed costs—Grade II    95,000     Common fixed costs        35,000             Total fixed costs    $    225,000     $225,000/$4,046 = 56 packages     Grade I: 3 56 = 168; Grade II: 7 56 = 392 16–29    Continued 3.        Product        P        –        V        =        P – V            Mix    =    Total CM     Grade I    $3,400    $2,444    $956    3    $2,868     Grade II    1,600    1,208    392    7        2,744             Package                    $5,612             Package CM    = 3($3,400) + 7($1,600)             Package CM    = $21,400             $21,400X    = $1,600,000 – $600,000             X    = 47 packages remaining     141 Grade I (3 47) and 329 Grade II (7 47)     Additional contribution margin:     141($956 – $714) + 329($392 – $272)    $73,602     Increase in fixed costs        44,000     Increase in operating income    $29,602     Break-even: ($225,000 + $44,000)/$5,612 = 48 packages     144 Grade I (3 48) and 336 Grade II (7 48)     If the new break-even point is interpreted as a revised break-even for 2004, then total fixed costs must be reduced by the contribution margin already earned (through the first five months) to obtain the units that must be sold for the last seven months. These units would then be added to those sold during the first five months:     CM earned = $600,000 – (83* $2,686) – (195* $1,328) = $118,102     *224 – 141 = 83; 524 – 329 = 195     X = ($225,000 + $44,000 – $118,102)/$5,612 = 27 packages     From the first five months, 28 packages were sold (83/3 or 195/7). Thus, the revised break-even point is 55 packages (27 + 28)—in units, 165 of Grade I and 385 of Grade II. 16–29    Concluded 4.        Product        P        –        V        =        P – V            Mix    =    Total CM     Grade I    $3,400    $2,686    $714    1    $714     Grade II    1,600    1,328    272    1        272             Package                    $986     New sales revenue    $1,000,000 130% = $1,300,000             Package CM    = $3,400 + $1,600             $5,000X    = $1,300,000             X    = 260 packages     Thus, 260 units of each cabinet will be sold during the rest of the year.     Effect on profits:     Change in contribution margin:             $714(260 – 141) – $272(329 – 260)    $66,198     Increase in fixed costs:             $70,000(7/12)        40,833     Increase in operating income    $25,365     X    = F/(P – V)             = $295,000/$986             = 299 packages (or 299 of each cabinet)     The break-even point for 2006 is computed as follows:     X    = ($295,000 – $118,102)/$986             = $176,898/$986             = 179 packages (179 of each)     To this, add the units already sold, yielding the revised break-even point:     Grade I:    83 + 179 = 262     Grade II:    195 + 179 = 374 16–30 1.    R    = F/(1 – VR)             = $150,000/(1/3)             = $450,000 2.    Of total sales revenue, 60 percent is produced by floor lamps and 40 percent by desk lamps.     $360,000/$30 = 12,000 units     $240,000/$20 = 12,000 units     Thus, the sales mix is 1:1.         Product        P        –        V*        =        P – V            Mix    =    Total CM     Floor lamps    $30.00    $20.00    $10.00    1    $10.00     Desk lamps    20.00    13.33    6.67    1        6.67             Package                    $16.67     X    = F/(P – V)             = $150,000/$16.67             = 8,998 packages     Floor lamps:    1 8,998 = 8,998     Desk lamps:    1 8,998 = 8,998 3.    Operating leverage    = CM/Operating income             = $200,000/$50,000             = 4.0     Percentage change in profits = 4.0 40% = 160% 16–31 1.                Door Handles        Trim Kits        CM    $12 – $9 = $3        $8 – $5 = $3     CM ratio    $3/$12 = 0.25        $3/$8 = 0.375 2.    Contribution margin:             ($3 20,000) + ($3 40,000)    $    180,000     Less: Fixed costs        146,000             Operating income    $    34,000 3.    Sales mix (from Requirement 2): 1 door handle to 2 trim kits             Product        Price    –        V        =    CM        Sales Mix    =    Total CM     Door handle    $12    $9    $3    1    $3.00     Trim kit    8    5    3    2        6.00             Package                    $9.00     Break-even packages = $146,000/$9 = 16,222     Door handles    = 1 16,222 = 16,222     Trim kits    = 2 16,222 = 32,444 4.    Sales (70,000 $8)    $    560,000     Variable costs (70,000 $5)        350,000     Contribution margin    $    210,000     Fixed costs        111,000             Operating income    $    99,000     Yes, operating income is $65,000 higher than when both door handles and trim kits are sold. 16–32 1.    Break-even units = $300,000/$14* = 21,429     *$406,000/29,000 = $14     Break-even in dollars    = 21,429 $42** = $900,018             or             = $300,000/(1/3) = $900,000     The difference is due to rounding error.     **$1,218,000/29,000 = $42 2.    Margin of safety = $1,218,000 – $900,000 = $318,000 3.    Sales    $    1,218,000     Variable costs (0.45 $1,218,000)        548,100     Contribution margin    $    669,900     Fixed costs        550,000             Operating income    $    119,900     Break-even in units = $550,000/$23.10* = 23,810     Break-even in sales dollars = $550,000/0.55** = $1,000,000     *$669,900/29,000 = $23.10     **$669,900/$1,218,000 = 55% 16–33 1.    The annual break-even point in units at the Peoria plant is 73,500 units and at the Moline plant, 47,200 units, calculated as follows:     Unit contribution calculation:                     Peoria            Moline        Selling price    $150.00    $150.00     Less variable costs:             Manufacturing    (72.00)    (88.00)             Commission    (7.50)    (7.50)             G&A        (6.50)        (6.50)     Unit contribution    $    64.00    $    48.00     Fixed costs calculation:     Total fixed costs    =    (Fixed manufacturing cost + Fixed G&A)                     Production rate per day Normal working days             Peoria    =    [$30.00 + ($25.50 – $6.50)] 400 240                 =    $4,704,000             Moline    =    [$15.00 + ($21.00 – $6.50)] 320 240                 =    $2,265,600     Break-even calculation:     Break-even units    = Fixed costs/Unit contribution             Peoria    = $4,704,000/$64                 = 73,500 units             Moline    = $2,265,600/$48                 = 47,200 units 16–33    Concluded 2.    The operating income that would result from the divisional production manager’s plan to produce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is 96,000 units (400 240); however, the normal capacity at the Moline plant is 76,800 units (320 240). Therefore, 19,200 units (96,000 – 76,800) will be manufactured at Moline at a reduced contribution margin of $40 per unit ($48 – $8).     Contribution per plant:     Peoria (96,000 $64)    $    6,144,000     Moline (76,800 $48)    3,686,400     Moline (19,200 $40)        768,000     Total contribution    $    10,598,400     Less: Fixed costs        6,969,600             Operating income    $    3,628,800 3.    If this plan is followed, 120,000 units will be produced at the Peoria plant and 72,000 units at the Moline plant.     Contribution per plant:     Peoria (96,000 $64)    $    6,144,000     Peoria (24,000 $61)    1,464,000     Moline (72,000 $48)        3,456,000     Total contribution    $    11,064,000     Less: Fixed costs        6,969,600             Operating income    $    4,094,400 16–34 1.    Break-even dollars (in thousands)     X =    Variable cost of goods sold + Current fixed costs + Fixed cost of hiring +             Commissions     X    = 0.45aX + $6,120b + $1,890c + 0.1X + 0.05(X – $16,000)             = 0.60X + $6,120 + $1,890 – $800             = $18,025     a$11,700/$26,000 = 45%     bCurrent fixed costs (in thousands):     Fixed cost of goods sold    $2,870     Fixed advertising expenses    750     Fixed administrative expenses    1,850     Fixed interest expenses        650             Total    $6,120     cFixed cost of hiring (in thousands):     Salespeople (8 $80)    $    640     Travel and entertainment    600     Manager/secretary    150     Additional advertising        500             Total    $1,890 2.    Break-even formula set equal to net income (in thousands):     0.6(Sales – Var. COGS – Fixed costs – Commissions)    = Net income             0.6(X – 0.45X – $6,120 – 0.23X)    = $2,100             0.192X – $3,672    = $2,100             0.192X    = $5,772             X    = $30,063 3.    The general assumptions underlying break-even analysis that limit its usefulness include the following: all costs can be divided into fixed and variable elements; variable costs vary proportionally to volume; and selling prices remain unchanged. managerial decision caseS 16–35 1.    Break-even point = F/(P – V)     First process:    $100,000/($30 – $10) = 5,000 cases     Second process:    $200,000/($30 – $6) = 8,333 cases 2.            I    = X(P – V) – F             X($30 – $10) – $100,000    = X($30 – $6) – $200,000             $20X – $100,000    = $24X – $200,000             $100,000    = $4X             X    = 25,000     The manual process is more profitable if sales are less than 25,000 cases; the automated process is more profitable at a level greater than 25,000 cases. It is important for the manager to have a sales forecast to help in deciding which process should be chosen. 3.    The right to decide which process should be chosen belongs to the divisional manager. Danna has a moral obligation to report the correct information to her superior. By altering the sales forecast, Danna unfairly and unethically influenced the decision-making process. Managers certainly have a moral obligation to assess the impact of their decisions on employees, and every effort should be taken to be fair and honest with employees. Danna’s behavior, however, is not justified by the fact that it helped a number of employees retain their employment. First, Danna had no right to make the decision. Danna certainly has the right to voice her concerns about the impact of automation on the employees’ well-being. In so doing, perhaps the divisional manager would come to the same conclusion even though the automated system appears to be more profitable. Second, the choice to select the manual system may not be the best for the employees anyway. The divisional manager may possess more information, making the selection of the automated system the best alternative for all concerned, provided the sales volume justifies its selection. For example, if the automated system is viable, the divisional manager may have plans to retrain and relocate the displaced workers in better jobs within the company. Third, her motivation for altering the forecast seems more driven by her friendship for Jerry Johnson than any legitimate concerns for the layoff of other employees. Danna should examine her reasoning carefully to assess the real reasons for her behavior. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent. 16–35    Concluded 4.    Some standards that seem applicable are III-1 (conflict of interest), III-4 (nonsubversion of legitimate goals), III-6 (communication of favorable and unfavorable information), and IV-1 (communication of information fairly and objectively). 16–36 1.    Number of seats sold (expected):     Seats sold = Number of performances Capacity Percent sold                 Type of Seat                        A            B            C        Dream    570    3,024    3,690     Petrushka    570    3,024    3,690     Nutcracker    2,280    15,120    19,680     Sleeping Beauty    1,140    6,048    7,380     Bugaku        570        3,024        3,690                     5,130    30,240    38,130     Total revenues    = ($35 5,130) + ($25 30,240) + ($15 38,130)             = $179,550 + $756,000 + $571,950             = $1,507,500     Segmented revenues (Seat price Total seats):             A            B            C            Total    Dream    $19,950    $    75,600    $    55,350    $150,900 Petrushka    19,950    75,600    55,350    150,900 Nutcracker    79,800    378,000    295,200    753,000 Sleeping Beauty    39,900    151,200    110,700    301,800 Bugaku    19,950    75,600    55,350    150,900 16–36    Continued     Segmented variable-costing income statement:         Dream        Petrushka    Nutcracker Sales    $    150,900    $150,900    $753,000 Variable costs        42,500        42,500        170,000 Contribution margin    $    108,400    $108,400    $583,000 Direct fixed costs        275,500        145,500        70,500     Segment margin    $(167,100)    $    (37,100)    $512,500     Sleeping Beauty        Bugaku            Total    Sales    $    301,800    $    150,900    $    1,507,500 Variable costs        85,000        42,500        382,500 Contribution margin    $    216,800    $    108,400    $    1,125,000 Direct fixed costs        345,000        155,500        992,000 Segment margin    $(128,200)    $    (47,100)    $    133,000 Common fixed costs                        401,000     Operating (loss)                    $    (268,000) 2.    Contribution margin per ballet performance:     Dream    $108,400/5 = $21,680     Petrushka    $108,400/5 = $21,680     Nutcracker    $583,000/20 = $29,150     Sleeping Beauty    $216,800/10 = $21,680     Bugaku    $108,400/5 = $21,680     Segment break-even point:     X = F/(P – V)     Dream    $275,500/$21,680 =    13     Petrushka    $145,500/$21,680 =    7     Nutcracker    $70,500/$29,150 =    3     Sleeping Beauty    $345,000/$21,680 =    16     Bugaku    $155,500/$21,680 =    8 16–36    Continued 3.    Weighted contribution margin (package): Mix: 1:1:4:2:1     $21,680 + $21,680 + 4($29,150) + 2($21,680) + $21,680 = $225,000     X = F/(P – V)     X = ($992,000 + $401,000)/$225,000 = 6.19 or 7 (rounded up)     7 Dream, Petrushka, and Bugaku; 14 Sleeping Beauty; 28 Nutcracker     Provided the community will support the number of performances indicated in the break-even solution, I would alter the schedule to reflect the break-even mix. 4.    Additional revenue per performance:     114 $30 80% =    $    2,736     756 $20 80% =    12,096     984 $10 80% =        7,872             $    22,704     Increase in revenues ($22,704 5)    $113,520     Less: Variable costs ($8,300 5)        41,500     Increase in contribution margin    $    72,020     New mix 1:1:4:2:1:1     Contribution margin per matinee: $72,020/5 = $14,404     Adding the matinees will increase profits by $72,020.     New break-even point:     X    = F/(P – V)             = ($992,000 + $401,000)/($225,000 + $14,404)             = $1,393,000/$239,404 = 5.82 packages, or 6 (rounded up)             6    Dream, Petrushka, Bugaku, and Nutcracker matinees         12    Sleeping Beauty         24    Nutcracker 16–36    Concluded 5.    Current total segment margin    $    133,000     Add: Additional contribution margin    72,020     Add: Grant        60,000     Projected segment margin    $    265,020     Less: Common fixed costs        401,000             Operating (loss)    $    (135,980)     No, the company will not break even. This is a very thorny problem faced by ballet companies around the world. The standard response is to offer as many performances of The Nutcracker as possible. That action has already been taken here. Other actions that may help include possible increases in prices of the seats (particularly the A seats), offering additional performances of some of the other ballets, cutting administrative costs (they seem somewhat high), and offering a less expensive ballet (direct costs of Sleeping Beauty are quite high). Research Assignment 16–37 Answers will vary.