CHAPTER 15Analysis and Impactof Leverage CHAPTER ORIENTATIONThischapter focusesonuseful aidsfor thefinancial manager indeterminingthefirm's proper financial structure. It includes the definitions of the different kinds of risk, a review of breakeven analysis, the concepts of operating leverage, financial leverage, the combination of both leverages, and their effect on EPS (earnings per share).CHAPTER OUTLINEI. Business risk and financial riskA. Riskisdefinedasthelikelyvariabilityassociatedwithexpectedrevenue streams.1. The variations in the income stream can be attributed toa. The firm's exposure to business riskb. The firm's decision to incur financial riskB. Businessriskisdefinedasthevariabilityof thefirm'sexpectedearnings before interest and taxes.1. Business risk is measured by the firm's corresponding expected coefficient of variation.2. Dispersion in operating income does not cause business risk. It is the result of several influences, suchasthecompanys cost structure, product demand characteristics, and intra-industry competition. C. Financial risk is a direct result of the firm's financing decision. It refers to the additional variability in earnings available to the firms common stockholders and the additional chance of insolvency borne by the common shareholder when financial leverage is used.981. Financial leverageisthefinancingofaportionofthefirm'sassets with securities bearing a fixed rate of return in hopes of increasing the return to the common shareholders.2. Financial riskispassedontothecommonshareholderswhomust bear most of the inconsistencies of returns to the firmafter the deduction of fixed payments.II. Break-even AnalysisA. The objective of break-even analysis is to determine the break-even quantity of output bystudyingtherelationships amongthe firms cost structure, volume of output, and operating profit.1. The break-even quantity of output results in an EBIT level equal to zero.B. Use of the model enables the financial officer to1. Determine the quantity of output that must be soldtocover all operating costs.2. Calculate the EBIT achieved at various output levels.C. Some potential applications include1. Capital expenditure analysis as a complementary technique to discounted cash flow evaluation models2. Pricing policy3. Labor contract negotiations4. Evaluation of cost structure5. Financial decision makingD. Essential elements of the break-even model 1. Production costs must be separated into fixed costs and variable costs. Fixed costs do not vary as the sales volume or the quantity of output changes.Examples includea. Administrative salariesb. Depreciationc. Insurance premiumsd Property taxese. Rent2. Variable costs vary in total as output changes. Variable costs are fixed per unit of output.Examples includea. Direct materialsb. Direct laborc. Energy cost associated withproduction d. Packaging99e. Freight-outf. Sales commissions3. Inordertoimplement thebreak-even model, it is necessaryfor the financial manager toa. Identify the most relevant output range for planning purposes.b. Approximate all costs in the semifixed and semivariable range and allocate them to the fixed and variable cost categories.4. Total revenue and volume of outputa. Total revenue (sales dollars) is equal to the selling price per unit multiplied by the quantity sold.b. Volume of output refers to the firms level of operations and is expressed as a unit quantity or sales dollars.E. Finding the break-even point1. The break-evenmodel is just anadaptationof thefirm's income statement expressed assales - (total variable costs + total fixed costs) = profit2. Three ways to find the break-even point are explained.a. Trial and error(1) Select an arbitrary output level.(2) Calculate the corresponding EBIT amount.(3) When EBIT equals zero, the break-even point has been found.b. Contribution margin analysis(1) Unit sellingprice- unit variablecost =contribution margin(2) Fixed cost divided by the contribution margin per unit equals the break-even quantity in units.c. Algebraic analysis(l) QB=the break-even level of units sold, P =the unit sales price,F =the total fixed cost for the period,V =unit variable cost.(2) Then,QB =V PF100F. The break-even point in sales dollars1. It isconvenient tocalculatethebreak-evenpoint intermsofsales dollars if thefirmdeals withmorethanoneproduct. It canbe computed by using data from the firm's annual report.2. Sincevariable costandsellingprice perunit areassumedconstant, the ratio of total variable costs to total sales is a constant for any level of sales.G. Limitations of break-even analysis1. Assumes linear cost-volume-profit relationship.2. Thetotal revenuecurveispresumedtoincreaselinearlywiththe volume of output.3. Assumes constant production and sales mix.4. This is a static form of analysis.III. Operating LeverageA. Operating leverage is the responsiveness of a firm's EBIT to fluctuations in sales. Operating leverage results when fixed operating costs are present in the firm's cost structure.B. This responsivenesscan be measured as follows:level sales base the from leverageoperating of degree=DOLs =sales inchange %EBIT inchange %C. If unit costs are available, the DOL can be measured by DOLs = F V) Q(PV) Q(P D. If ananalytical income statement is the only information available, the following formula is used:DOLs = EBITcosts fixed before revenue = F VC SVC S Note:All three formulas provide the same results.E. Implications of operating leverage1. At eachpoint abovethebreak-evenlevel, thedegreeof operating leverage decreases.2. At the break-even level of sales, the degree of operating leverage is undefined.3. OperatingleverageispresentwhenthepercentagechangeinEBIT divided by the percentage change in sales is greater than one.4. The degree of operating leverage is attributed to the business risk that a firm faces.101IV. Financial LeverageA. To see if financial leverage has been used to benefit the common shareholder, the focus will be on the responsiveness of the company's earnings per share (EPS) to changes in its EBIT.B. The firm is using financial leverage and is exposing its owners to financial risk whenEBIT inchange %EPS inchange % is greater than 1.00C. A measure of the firm's use of financial leverage is as follows:level EBIT base the from leveragefinancial of degree=DFLEBIT=EBIT inchange %EPS inchange %1. The degree of financial leverage concept can be either in the positive or negative direction.2. The greater the degree of financial leverage, the greater the fluctuations in EPS.D. An easier way to measure financial leverage isDFLEBIT = I EBITEBITwhere I is the sum of all fixed financing costsV. Combining operating and financial leverageA. Changes insales revenues causegreater changes in EBIT. If the firm chooses to use financial leverage, changes in EBIT turn into larger variations inbothEPSandEAC.Combining operating and financial leverage causes rather large variations in EPS.B. One way to measure the combined leverage can be expressed aslevel sales base the from leveragecombined of degree= DCLs = sales inchange %EPS inchange %If the DCL is equal to 5.0 times, then a 1% change in sales will result in a 5% change in EPS.C. Thedegreeof combinedleverageis theproduct of thetwoindependent leverage measures. Thus:DCLS =(DOLS )x(DFLEBIT)102D. Another way to compute DCLs is with the following equation:DCLs =I F V) Q(PV) Q(P E. Implications of combining operating and financial leverage1. Total riskcanbemanagedbycombiningoperatingandfinancial leverage in different degrees.2. Knowledge of the various leverage measures helps to determine the proper level of overall risk that should be accepted.ANSWERS TOEND-OF-CHAPTER QUESTIONS15-1. Businessriskistheuncertaintythat envelopsthefirm'sstreamofearnings before interest and taxes (EBIT).One possible measure of business risk is the coefficient of variation in the firm's expected level of EBIT.Business risk is the residual effect of the: (1) company's cost structure, (2) product demandcharacteristics, (3) intra-industry competitive position.The firm's asset structure is the primary determinant of its business risk.Financial risk can be identified by its two key attributes: (1) the added risk of insolvency assumed by the common stockholder when the firm choosestousefinancial leverage; (2) theincreasedvariabilityinthestreamof earnings available to the firm's common stockholders.15-2. Financial leverage is financing a portion of the firm's assets with securities bearing a fixed(limited) rateof return. Anytimethefirmusespreferredstocktofinance assets, financial leverage is employed.15-3. Operatingleverageistheuseoffixedoperatingcostsinthefirm'scoststructure. When operating leverage is present, any percentage fluctuation in sales will result in a greater percentage fluctuation in EBIT.15-4. Break-evenanalysis, asitistypicallypresented, categorizesalloperatingcostsas beingeitherfixedorvariable. Baseduponthisdivisionofcosts, thebreak-even point is computed.The computation procedure for the cash break-even point omits anynoncashexpensesthat thefirmmight incur. Typical examplesof noncash expenses include depreciation and prepaid expenses.The ordinary break-even point willalwaysexceedthecash break-even point, provided some noncash chargesare present.15-5. The most important shortcomings of break-even analysis are:(1) Thecost-volume-profitrelationshipis assumedtobelinear over theentire range of output.(2) All of the firm's production is assumed to be salable at the fixed selling price.(3)The sales mix and production mix is assumed constant.103(4) Thelevel of total fixedcostsandthevariablecost tosalesratioisheld constant over all output and sales ranges.15-6. Total riskexposureistheresult ofthefirm'suseofbothoperatingleverageand financial leverage. Business riskandfinancial riskproducethis total risk. A company that is normally exposed to a high degree of business risk may manage its financial structure in such a way as to minimize financial risk.A firm that enjoys a stable pattern in its earnings before interest and taxes might reasonably elect to use a high degree of financial leverage. This would increase both its earnings per share and its rate of return on the common equity investment.15-7. By taking the degree of combined leverage times the sales change of a negative 15 percent, the earnings available to the firm's common shareholders will decline by 45 percent.15-8. Asthesalesof afirmincrease, twothingsoccurthat biasthecost andrevenue functions toward a curvilinear shape. First, sales will increase at a decreasing rate. Asthemarketapproachessaturation, thefirmmustcutitspricetogeneratesales revenue.Second, as production approaches capacity, inefficiencies occur that result inhigherlaborandmaterialcosts. Furthermore, thefirm's operatingsystemmay have to bear higher administrative and fixed costs.The result is higher per unit costs as production output increases.SOLUTIONS TOEND-OF-CHAPTER PROBLEMSSolutions To Problem Set A15-1A.Product Line Sales V.C. C.M. C.M. RatioPiano 61,250 41,650 19,600 32%Violin 37,500 22,500 15,000 40%Cello 98,750 61,225 37,525 38%Flute 52,500 25,725 26,775 51%Total 250,000 151,100 98,900 40%Break-even PointS* = F/(1-VC/S) = 50,000/(1-VC/S) = 50,000/.4 = 125,000S* =

,_

SVC1F=

,_

$250,000$151,100150,000=.450,000 = 125,00010415-2A. Break-even Quantity = QBQB=V) (PFQB=(.70)($30) - $30$360,000QB= 40,000 bottles15-3A. Degree of Operating Leverage = DOLSDOLS=F] V) [Q(PV) Q(P V = 70% x $30 =$21DOLS=] 000 , 360 $ ) 21 $ 30 ($ 000 , 50 [) 21 $ 30 ($ 000 , 50 DOLS= 5 times15-4A.(a)Jake's Sarasota JeffersonLawn Chairs Sky Lights WholesaleSales $600,640.00 $2,450,000 $1,075,470Variable Costs $326,222 .60$1,120,000 $957,000Revenue before fixed costs $274,417.40 $1,330,000 $118,470Fixed costs $120,350 .00$850,000 $89,500EBIT $154,067 .40$480,000 $28,970(b)Jake's Lawn Chairs:QB =V PF=38 . 17 $ 32 $350 , 120 $=62 . 14 $350 , 120 $= 8,232Sarasota Skylights:QB =400 $ 875 $000 , 850 $=475 $000 , 850 $= 1,789Jefferson Wholesale:QB =87 $ 77 . 97 $500 , 89 $=77 . 10 $500 , 89 $= 8,310(c)Jake's Sarasota JeffersonLawn Chairs Skylights Wholesale105EBITCosts FixedBefore Revenue =40 . 067 , 154 $40 . 417 , 274 $$480,000$1,330,000970 , 28 $470 , 118 $= 1.78 times 2.77 times 4.09 times(d) Jefferson Wholesale, since its degree of operating leverage exceeds that of the other two companies.15-5A.(a)EBITCosts Fixed Before Revenue=000 , 750 , 13 $000 , 950 , 22 $= 1.67 times(b)I EBITEBIT=000 , 350 , 1 $ 000 , 750 , 13 $000 , 750 , 13 $=000 , 400 , 12 $000 , 750 , 13 $= 1.11 times(c) DCL45,750,000= (1.67) (1.11)= 1.85 times (d) S* =SVC1F=000 , 750 , 45 $000 , 800 , 22 $1000 , 200 , 9 $=498 . 1000 , 200 , 9 $=502 .000 , 200 , 9 $=$18,326,693.23 (e) (25%) (1.85) = 46.25%15-6A. (a) QB = V PF=58 $ 85 $000 , 170 $=27 $000 , 170 $= 6,296 pairs of shoes (b) S* = SVC1F=85 $58 $1000 , 170 $= 682 . 1000 , 170 $= 318 .000 , 170 $= $534,591.20 (c)7,000 9,000 15,000Pairs of Shoes Pairs of Shoes Pairs of ShoesSales $595,000 $765,000 $1,275,000Variable Costs 406,000 522,000 870,000Revenue before fixed costs $189,000 $243,000 $405,000Fixed costs 170,000 170,000 170,000EBIT $19,000 $73,000 $235,000106(d)7,000 9,000 15,000 Pairs of Shoes Pairs of Shoes Pairs of Shoes000 , 19 $000 , 189 $ 000 , 73 $000 , 243 $ 000 , 235 $000 , 405 $= 9.95 times 3.33 times1.72 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-7A.(a)QB=V PF=110 $ 180 $000 , 630 $=70 $000 , 630 $ =9000 Units(b) S* = 9000 units $180=$1,620,000Alternatively,S* = SVC1F=180 $110 $1000 , 630 $=6111 . 0 1000 , 630 $= 3889 .000 , 630 $= $1,619,954Note:$1,619,954 differs from $1,620,000 due to rounding.(c) 12,000 15,000 20,000units units unitsSales $2,160,000 $2,700,000 $3,600,000Variable Costs 1,320,000 1,650,000 2,200,000Revenue before fixed costs 840,000 1,050,000 1,400,000Fixed costs 630,000 630,000 630,000EBIT $210,000 $420,000 $770,000(d) 12,000 units 15,000 units 20,000 units000 , 210 $000 , 840 $000 , 420 $000 , 050 , 1 $000 , 770 $000 , 400 , 1 $= 4 times = 2.5 times = 1.82 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-8A.(a)107Blacksburg Lexington WilliamsburgFurniture Cabinets ColonialsSales $1,125,000 $1,600,000 $520,000Variable costs 926,250 880,000 188,500Revenue before fixed costs $198,750 $720,000 $331,500Fixed costs 35,000 100,000 70,000EBIT $163,750 $620,000 $261,500(b): FurnitureBlacksburgQB=V PF= 35 . 12 $ 00 . 15 $000 , 35 $= 65 . 2 $000 , 35 $= 13,208 units: CabinetsLexingtonQB=220 $ 400 $000 , 100 $=180 $000 , 100 $=556 units : Colonialsrg WilliamsbuQB=50 . 14 $ 00 . 40 $000 , 70 $=50 . 25 $000 , 70 $=2745 units(c)Blacksburg Lexington WilliamsburgFurniture Cabinets ColonialsEBITCosts FixedBefore Revenue750 , 163 $750 , 198 $000 , 620 $000 , 720 $500 , 261 $500 , 331 $=1.21 times 1.16 times 1.27 times(d) Williamsburg Colonials, since its degree of operating leverage exceeds that of the other two companies.15-9A.(a) {S-(VC+F)} (1-T)=$50,000( ) T 1 FSVCS S ;'1]1

+ ,_

= $50,000[S VC - } (1 T)=$50,000{$375,000 - $206,250 F}(0.6)=$50,000($168,750 - F)(0.6)=$50,000F=$85,416.67(b) QB

=V PF =85 . 14 $ 00 . 27 $67 . 416 , 85 $=15 . 12 $67 . 416 , 85 $ = 7,030 units108S*=SVC1F = 55 . 167 . 416 , 85 $= $189,815 15-10A.(a) Find the EBIT level at the forecast sales volume:SEBIT=.26Therefore, EBIT=(0.26)($3,250,000)=$845,000Next, find total variable costs:SVC=0.5,so, VC=(0.5)$3,250,000=$1,625,000Now, solve for total fixed costs:S - (VC+F)=$845,000$3,250,000 - ($1,625,000+F)=$845,000F=$780,000(b) S*=5 . 0 1000 , 780 $=$1,560,000 15-11A.(a)EBITcosts Fixed before Revenue=000 , 500 , 8 $000 , 500 , 16 $ =1.94 times(b)I EBITEBIT =000 , 500 , 7 $000 , 500 , 8 $ =1.13 times(c) DCL$30,000,000=(1.94) (1.13)=2.19 times(d) S*=SVC1F=mm0 . 30 $5 . 13 $1000 , 000 , 8 $=45 . 0 1000 , 000 , 8 $=55 . 0000 , 000 , 8 $= $14,545,455(e) (25%) (2.19)=54.75% 15-12A.Giventhedatafor thisproblem, several approachesarepossiblefor findingthe break-even point in units.The approach below seems to work well with students.Step (1) Compute the operating profit margin:109Operating Profit Margin x Operating Asset Turnover = Return on operating assets(M)x(5)=0.25 M=.05Step(2) Compute the sales level associated with the given output level:0 $20,000,00Sales=5Sales=$100,000,000Step(3) Compute EBIT:(.05)($100,000,000)=$5,000,000Step(4) Computerevenuebeforefixedcosts. Sincethedegreeof operating leverage is 4 times, revenue before fixed costs (RBF) is 4 times EBIT as follows:RBF=(4) ($5,000,000)=$20,000,000Step(5) Compute total variable costs:(Sales) - (Total variable costs)=$20,000,000$100,000,000 - (Total variable costs)=$20,000,000Total variable costs=$80,000,000Step(6) Compute total fixed costs:RBF-Fixed costs=$5,000,000$20,000,000-fixed costs=$5,000,000Fixed costs=$15,000,000Step(7)Find the selling price per unit, and the variable cost per unit:P=000 , 000 , 10000 , 000 , 100 $=$10.00V=000 , 000 , 10000 , 000 , 80 $=$8.00Step(8) Compute the break-even point:QB =V PF = ) 8 ($ ) 10 ($000 , 000 , 15 $ = 2 $000 , 000 , 15 $ = 7,500,000 units 11015-13A.(a) QB =V PF=126 $ 180 $000 , 540 $=54 $000 , 540 $=10,000units (b)S* =SVC1F= 180 $126 $1000 , 540 $ =7 . 0 1000 , 540 $=3 .000 , 540 $= $1,800,000

(c) 12,000 15,000 20,000UnitsUnits UnitsSales $2,160,000 $2,700,000 $3,600,000Variable costs 1,512,000 1,890,000 2,520,000Revenue before fixed costs $648,000 $810,000 $1,080,000Fixed costs 540,000 540,000 540,000EBIT $108,000 $270,000 $540,000(d) 12,000 units 15,000 units 20,000 units000 , 108 $000 , 648 $=6 times000 , 270 $000 , 810 $=3 times000 , 540 $000 , 080 , 1 $=2 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-14A.(a) Oviedo Gainesville AthensSeedsSodPeachesSales $1,400,000 $2,000,000 $1,200,000Variable costs 1,120,000 1,300,000 840,000Revenue before fixed costs $280,000 $700,000 $360,000Fixed costs 25,000 100,000 35,000EBIT $255,000 $600,000 $325,000(b) Oviedo Seeds:QB =V PF= 20 . 11 $ 00 . 14 $000 , 25 $= 80 . 2 $000 , 25 $= 8,929 unitsGainesville Sod:QB=130 $ 200 $000 , 100 $=70 $000 , 100 $= 1,429 unitsAthens Peaches:QB=50 . 17 $ 00 . 25 $000 , 35 $=50 . 7 $000 , 35 $= 4,667 units(c)111Oviedo GainesvilleSeeds Sod000 , 255 $000 , 280 $=1.098 times000 , 600 $000 , 700 $=1.167 times AthensPeaches000 , 325 $000 , 360 $=1.108 times(d) Gainesville Sod, since its degree of operating leverage exceeds that of the other two companies.15-15A.(a) {S - [VC + F]}(1 - T)=$40,000( ) T 1 FSVCS S ;'1]1

+ ,_

= $40,000{($400,000)-($160,000)-F}(0.6)=$40,000($240,000-F)(0.6)=$40,000F=$173,333.33(b) QB=V PF=12 $33 . 333 , 173 $=14,444 units S* =SVC1F =40 . 0 133 . 333 , 173 $ =$288,888.8815-16A.(a) {S-[VC + F] }(1-T)=$80,000( ) T 1 FSVCS S ;'1]1

+ ,_

= $80,000{($2,000,000) - (1,400,000) - F}(.6)=$80,000($600,000 - F) (.6)=$80,000$360,000 - .6F=$80,000F=$466,666.67(b) QB=V PF=24 $67 . 666 , 466 $=19,444 units 112S*=SVC1F=7 . 167 . 666 , 466 $=3 .67 . 666 , 466 $= $1,555,555.5715-17A.(a) S (1 - 0.75) - $300,000=$240,0000.25S=$540,000S=$2,160,000=(P Q)Now, solve the above relationship for P:200,000 (P) = $2,160,000P = $10.80(b) Sales $2,160,000Less:Total variable costs 1,620,000Revenue before fixed costs $540,000Less:Total fixed costs 300,000EBIT $240,00015-18A.(a) S(1 - .6)-$300,000=$250,000.4S=$550,000S=$1,375,000=(P Q) Solve the above relationship for P.200,000 (P) = $1,375,000P = $6.875(b) Sales $1,375,000Less:Total variable costs 825,000Revenue before fixed costs $550,000Less:Total fixed costs 300,000EBIT $250,00011315-19A.(a)First, find the EBIT level at the forecast sales volume:=0.28So: EBIT=(0.28) $3,750,000=$1,050,000Next, find total variable costs:=0.5So: VC=(0.50) $3,750,000=$1,875,000Then, solve for total fixed costs:S - (VC + F)=$1,050,000$3,750,000 - ($1,875,000 + F)=$1,050,000F=$825,000(b) S* =5 . 0 1000 , 825 $=$1,650,00015-20A.(a)QB=V PF=150 $000 , 180 $=1,200 units(b) S*=SVC1F=70 . 0 1000 , 180 $=$600,000(c) DOL$2,500,000=000 , 180 $ ) 350 $ 500 ($ 000 , 5) 350 $ 500 ($ 000 , 5 000 , 570 $000 , 750 $=1.316 times(d) (20%)x(1.316)=26.32% Increase11415-21A.(a) QB

=V PF=15 $ 25 $000 , 50 $=10 $000 , 50 $=5,000 units(b) S*= SVC1F=25 $15 $1000 , 50 $=6 . 0 1000 , 50 $=4 .000 , 50 $=$125,000 (c) 4000 units 6000 units 8000 unitsSales $100,000 $150,000 $200,000Variable costs 60,000 90,000 120,000Revenue before fixed costs $40,000 $60,000 $80,000Fixed costs 50,000 50,000 50,000EBIT $-10,000 $ 10,000 $ 30,000(d) 4000 units 6000 units 8000 units000 , 10 $000 , 40 $=-4X000 , 10 $000 , 60 $=6X000 , 30 $000 , 80 $=2.67X(e) The degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-22A. Compute the present level of break-even output:QB=V PF=7 $ 12 $000 , 120 $=24,000 unitsCompute the new level of fixed costs at the break-even output:S V F = 0($12) (24,000) - ($5) (24,000) - F = 0$288,000 - $120,000 - F = 0$168,000 = FCompute the addition to fixed costs:$168,000 - $120,000 = $48,000 addition11515-23A. DOL$360,000=000 , 120 $ ) 7 $ 12 ($ 000 , 30) 7 $ 12 ($ 000 , 30 =000 , 30 $000 , 150 $=5 times Any percentage change in sales will magnify EBIT by a factor of 5.15-24A.(a) DOL$480,000 =000 , 120 ) 7 $ 12 ($ 000 , 40) 7 $ 12 ($ 000 , 40 =000 , 80 $000 , 200 $ =2.5 times(b) DFL$80,000=000 , 30 $ 000 , 80 $000 , 80 $ =1.6 times (c) DCL$480,000=000 , 30 $ 000 , 120 $ ) 7 $ 12 ($ 000 , 40) 7 $ 12 ($ 000 , 40 =000 , 50 $000 , 200 $=4 times Alternatively:(DOLS)x(DFLEBIT)=DCLS (2.5) x (1.6)=4 times 15-25A. The taskis tofindthebreak-evenpoint inunits for thefirm. Several approaches are possible, but the one presented below makes intuitive sense to students.Step(1) Compute the operating profit margin:(Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets(M) x (5)=0.15M=0.03Step(2) Compute the sales level associated with the given output level:$3,000,000Sales=5Sales=$15,000,000 Step(3) Compute EBIT:(0.03) ($15,000,000)=EBIT=$450,000116Step(4) Compute revenue before fixed costs.Since the degree of operating leverage is 8 times, revenue before fixed costs (RBF) is 8 times EBIT as follows:RBF=(8) ($450,000)=$3,600,000Step(5) Compute total variable costs:Sales - Total variable costs=$3,600,000$15,000,000 - Total variable costs=$3,600,000Total variable costs=$11,400,000Step(6) Compute total fixed costs:RBF - Fixed costs=$450,000$3,600,000 - Fixed costs=$450,000Fixed costs=$3,150,000Step(7) Find the selling price per unit, and the variable cost per unit:P=000 , 600 , 1000 , 000 , 15 $ =$9.375V=000 , 600 , 1000 , 400 , 11 $=$7.125Step(8) Compute the break-even point:QB=V PF=) 125 . 7 ($ ) 375 . 9 ($000 , 150 , 3 $=25 . 2 $000 , 150 , 3 $=1,400,000 units 15-26A. Compute the present level of break-even output:QB

=V PF=14 $ 20 $000 , 300 $=50,000 unitsCompute the new level of fixed costs at the break-even output.S V F = 0($20) (50,000) - ($12) (50,000) F = 0$400,000=FCompute the addition to fixed costs:$400,000 - $300,000=$100,000 addition 15-27A.(a)EBITcosts fixed before Revenue =000 , 000 , 1 $000 , 000 , 3 $=3 times117(b)I EBITEBIT=000 , 800 $000 , 000 , 1 $=1.25 times(c) DCL$12,000,000 =(3) (1.25)=3.75 times(d) S*=SVC1F=$12m$9m1$2,000,000= 75 . 0 1000 , 000 , 2 $=25 . 0000 , 000 , 2 $=$8,000,00015-28A.(a)EBITcosts fixed before Revenue=000 , 000 , 4 $000 , 000 , 8 $=2 times(b)I EBITEBIT=000 , 500 , 2 $000 , 000 , 4 $=1.6 times(c) DCL$16,000,000=(2) (1.6)=3.2 times(d) (20%) (3.2)=64% Increase(e) S*=SVC1F=$16m$8m1$4,000,000=5 . 0 1000 , 000 , 4 $=$8,000,000 11815-29A.a. A BC D Total Sales $40,000 $50,000 $20,000 $10,000 $120,000Variable costs* 24,000 34,000 16,000 4,000 78,000Contribution margin $16,000 $16,000 $ 4,000 $ 6,000 $ 42,000Contribution margin ratio 40% 32% 20% 60% 35%*Variable costs=(Sales) (1 - contribution margin ratio)b. 35%c.. Break-even point in sales dollars:S*=SVC1F=65 . 0 1400 , 29 $=35 . 0400 , 29 $=$84,00015-30A.AB C D TotalSales $30,000 $44,000 $40,000$6,000 $120,000Variable costs* 18,000 29,920 32,000 2,400 82,320Contribution margin $12,000 $14,080 $8,000 $3,600 $37,680Contribution margin ratio 40% 32% 20% 60% 31.4%*Variable costs=(sales) (1- contribution margin ratio).b. 31.4%c.. Break-even point in sales dollars:S*=SVC1F=314 . 0400 , 29 $=$93,631 Toledo'smanagement wouldprefer thesalesmixidentifiedinproblem15-29A. That sales mix provides a higher EBIT ($12,600 vs. $8,280) and a lower break-even point ($84,000 vs. $93,631).SOLUTION TO INTEGRATIVE PROBLEM:In solving for the break-even point in units, the following step-by-step approach seems to be the most logical to students and the easiest for them to understand.COMPUTE BREAK-EVEN POINT:STEP 1: Compute the operating profit margin:Operating Profit Margin [M] x Operating Asset Turnover = Return on operating assetsM x 7 = 35%M = 5%119STEP 2: Compute the sales level associated with the given output level:Operating Assets x Operating Asset Turnover = Sales$2,000,000 x 7 = SalesSales = $14,000,000STEP 3: Compute EBIT:Sales [STEP 2] x Operating Profit Margin [STEP 1] = EBIT$14,000,000 x 5% = EBITEBIT = $700,000STEP 4: Compute revenue before fixed costs:EBIT [STEP 3] x Degree of Operating Leverage = Revenue before Fixed Costs$700,000 x 5 = Revenue before Fixed CostsRevenue before Fixed Costs = $3,500,000STEP 5: Compute total variable costs:Sales [STEP 2] - Revenue before Fixed Costs [STEP 4] = Total Variable Costs$14,000,000 - $3,500,000 = Total Variable CostsTotal Variable Costs = $10,500,000STEP 6: Compute total fixed costs:Revenue before Fixed Costs [STEP 4] - EBIT [STEP 3] = Fixed Costs$3,500,000 - $700,000 = Fixed CostsFixed Costs = $2,800,000STEP 7: Find selling price per unit (P) and variable cost per unit (V):P = Sales [STEP 2] / Output in UnitsP = $14,000,000 / 50,000 unitsP = $280.00V = Total Variable Costs [STEP 5] / Output in UnitsV = $10,500,000 / 50,000 unitsV = $210.00120STEP 8: Compute break-even point (in units):QB = F [STEP 6] / (P - V) [STEP 7]QB = $2,800,000 / ($280.00 - $210.00)QB = 40,000 unitsAfterdeterminingthebreak-evenpoint usingtheapproachdescribedabove, thestudents have the information necessary to prepare an analytical income statement as follows:Sales [STEP 2] $14,000,000Variable Costs [STEP 5] 10,500,000Revenue before Fixed Costs $3,500,000Fixed Costs [STEP 6] 2,800,000EBIT $700,000Interest Expense 400,000Earnings Before Taxes $300,000Taxes (35%) 105,000Net Income $195,000Thereafter, the students have the data they need to answer questions (a) - (e) as follows:(a) Degree of financial leverage:DFLEBIT = EBIT / (EBIT - Interest)DFLEBIT = $700,000 / ($700,000 - $400,000)DFLEBIT = 2.33(b) Degree of Combined Leverage:DCLS = DOLS x DFLEBITDCLS = 5 x 2.33DCLS = 11.65(c) Break-even point in sales dollars:S* = SVC1FS* = 0 $14,000,000 $10,500,00- 1$2,800,000S* = $11,200,000(d) If sales increase 30%, by what percent would EBT increase?% increase in EBT = % increase in Sales x DCLS% increase in EBT = 30% x 11.65% increase in EBT = 350%121(e) Analytical Income Statement to verify effect of 30% increase in sales:Sales] $18,200,000Variable Costs 13,650,000Revenue Before Fixed Costs $4,550,000Fixed Costs [STEP 6] 2,800,000EBIT $1,750,000Interest Expense 400,000Earnings Before Taxes $1,350,000Taxes (35%) 472,500Net Income $877,500It may be useful to develop the following proof to assist in explaining the inter-relationships of the various values:% change in EBT = (EBTafter - EBTbefore) / EBTbefore% change in EBT = ($1,350,000 - $300,000) / $300,000% change in EBT = 350%which agrees with the following:% change in EBT = % change in Sales x DCLS% change in EBT = 30% x 11.65% change in EBT = 350%Solutions To Problem Set B15-1B. Break-even Quantity = QBQB=V) (PFP =units 40,000,0000 $20,000,00= $.50 per unitV =units 40,000,0000 $16,000,00= $.40 per unitthus,QB=) 40 . 0 $ 50 . 0 ($000 , 400 , 2 $QB= 24,000,000 units12215-2B. Degree of Combined Leverage = DCLSDegree of Operating Leverage = DOLSDegree of Financial Leverage = DFLEBITDOLS=F] V) [Q(PV) Q(P P =units 40,000,0000 $20,000,00= $.50 per unitV =units 40,000,0000 $16,000,00= $.40 per unitthus,DOLS=[ ] 000 , 400 , 2 $ ) 40 . 0 $ 50 . 0 ($ 000 , 000 , 40) 40 . 0 $ 50 . 0 ($ 000 , 000 , 40 DOLS= 2.50 timesDFLEBIT=1) (EBITEBITDFLEBIT=) 000 , 800 $ 000 , 600 , 1 ($000 , 600 , 1 $DFLEBIT= 2.00 timesandDCLS=I] F V) [Q(PV) Q(P DCLS= [ ] 000 , 800 $ 000 , 400 , 2 $ ) 40 . 0 $ 50 . 0 ($ 000 , 000 , 40) 40 . 0 $ 50 . 0 ($ 000 , 000 , 40 DCLS=000 , 800 $000 , 000 , 4 $DCLs= 5.00 times15-3B.(a) QB=V PF=115 $ 175 $000 , 650 $=60 $000 , 650 $=10,833 Units123(b) S* = (10,833 units) ($175)=$1,895,775Alternatively,S*=SVC1F =175 $115 $1000 , 650 $=6571 . 0 1000 , 650 $= 3429 .000 , 650 $= $1,895,596Note:$1,895,596 differs from $1,895,775 due to rounding.(c) 10,000 16,000 20,000units units unitsSales $1,750,000 $2,800,000 $3,500,000Variable costs 1,150,000 1,840,000 2,300,000Revenue before fixed costs 600,000 960,000 1,200,000Fixed costs 650,000 650,000 650,000EBIT -$50,000 $310,000 $550,000(d) 10,000 units 16,000 units 20,000 units000 , 50 $000 , 600 $ =-12 times$310,000$960,000=3.1 times000 , 550 $000 , 200 , 1 $ =2.2 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-4B.(a) Durham Raleigh CharlotteFurniture Cabinets ColonialsSales $1,600,000 $1,957,500 $525,000Variable costs 1,100,000 1,080,000 236,250Revenue before fixed costs $500,000 $877,500 $288,750Fixed costs 40,000 150,000 60,000EBIT $460,000 $727,500 $228,750(b) QB=V PF=75 . 13 $ 00 . 20 $000 , 40 $=25 . 6 $000 , 40 $= 6,400 unitsQB=240 $ 435 $000 , 150 $=195 $000 , 150 $=769 units QB=75 . 15 $ 00 . 35 $000 , 60 $ =25 . 19 $000 , 60 $ =3,117 units(c)124Durham RaleighCharlotteFurniture FurnitureColonials=000 , 460 $000 , 500 $=500 , 727 $500 , 877 $=750 , 228 $750 , 288 $=1.09 times 1.21 times 1.26 times(d) Charlotte Colonials, since its degree of operating leverage exceeds that of the other two companies.15-5B.(a) {S-[VC+F]} (1 - T)=$55,000( ) T 1 FSVCS S ;'1]1

+ ,_

=$55,000{$400,008 - [257,148 + F ]}(0.55)=$55,000($142,860 - F)(0.55)=$55,000F=$42,860(b) QB

=V PF=00 . 18 $ 00 . 28 $860 , 42 $=00 . 10 $860 , 42 $= 4,286 unitsS* =SVC1F =643 . 0 1860 , 42 $ = $120,056 15-6B. (a) Find the EBIT level at the forecast sales volume:SEBIT=.28Therefore, EBIT=(0.28)($3,750,000)=$1,050,000Next, find total variable costs:SVC=0.55,so: VC=(0.55)$3,750,000=$2,062,500Now, solve for total fixed costs:S - (VC+F)=$1,050,000$3,750,000 - ($1,687,500+F)=$1,050,000F=$637,500(b) S* =55 . 0 1500 , 637 $=$1,416,667 12515-7B. (a) =000 , 000 , 14 $000 , 000 , 24 $=1.71 times(b)I EBITEBIT =000 , 850 , 12 $000 , 000 , 14 $ =1.09 times(c) DCL$40,000,000=(1.71) (1.09)=1.86 times(d) S* =SVC1F=$40m$16m10 $10,000,00=4 . 0 1000 , 000 , 10 $= 6 . 0000 , 000 , 10 $=$16,666,667 (e) (20%) (1.86)=37.2% 15-8B. Giventhedataforthisproblem,severalapproachesare possiblefor findingthe break-even point in units.The approach below seems to work well with students.Step(1) Compute the operating profit margin:(Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets(M)x(5)=0.25 M=.05Step(2) Compute the sales level relative to the given output level:0 $18,000,00Sales=5Sales=$90,000,000Step(3) Compute EBIT:(.05)($90,000,000)=$4,500,000Step(4) Computerevenue before fixed costs. Since the degree of operating leverage is 6 times, revenue before fixed costs (RBF) is 6 times EBIT as follows:RBF=(6) ($4,500,000)=$27,000,000126Step(5) Compute total variable costs:(Sales) - (Total variable costs)=$27,000,000$90,000,000 - (Total variable costs)=$27,000,000Total variable costs=$63,000,000Step(6) Compute total fixed costs:RBF-Fixed costs=$4,500,000$27,000,000-fixed costs=$4,500,000Fixed costs=$22,500,000Step(7) Find the selling price per unit, and the variable cost per unit:P=000 , 000 , 7000 , 000 , 90 $=$12.86V=000 , 000 , 7000 , 000 , 63 $=$9.00Step(8) Compute the break-even point:QB =V PF =) 9 ($ ) 86 . 12 ($000 , 500 , 22 $=86 . 3 $000 , 500 , 22 $ =5,829,016 units 15-9B.(a) QB =V PF =140 $ 175 $000 , 550 $=35 $000 , 550 $=15,714 units (b) S*=SVC1F=175 $140 $1000 , 550 $=8 . 0 1000 , 550 $ =2 .000 , 550 $ =$2,750,000

(c) 12,000 15,000 20,000UnitsUnits UnitsSales $2,100,000 $2,625,000 $3,500,000Variable costs 1,680,000 2,100,000 2,800,000Revenue before fixed costs $420,000 $525,000 $700,000Fixed costs 550,000 550,000 550,000EBIT -$130,000 -$25,000 $150,000127(d) 12,000 units 15,000 units 20,000 units000 , 130 $000 , 420 $= -3.2 times000 , 25 $000 , 525 $= -21 times000 , 150 $000 , 700 $= 4.67 times15-10B.(a) Farm City Empire GoldenSeeds Sod PeachesSales $1,800,000 $1,710,000 $1,400,000Variable costs 1,410,000 1,305,000 950,000Revenue before fixed costs $390,000 $ 405,000 $450,000Fixed costs 30,000 110,000 33,000EBIT $360,000 $295,000 $417,000(b) Farm City:QB =V PF= 75 . 11 $ 00 . 15 $000 , 30 $= 25 . 3 $000 , 30 $= 9,231 unitsEmpire Sod:QB =145 $ 190 $000 , 110 $=45 $000 , 110 $ =2,444 unitsGolden Peaches:QB=19 $ 00 . 28 $000 , 33 $=9 $000 , 33 $=3,667 units(c) Farm City Empire GoldenSeeds Sod Peaches000 , 360 $000 , 390 $=1.083 times000 , 295 $000 , 405 $= 1.373 times000 , 417 $000 , 450 $= 1.079 times(d)Empire Sod, since its degree of operating leverage exceeds that of the other two companies.15-11B.(a) {S [VC + F]} (1-T) = $38,000( ) T 1 FSVCS S ;'1]1

+ ,_

=$38,000 [($420,002)-($222,354)-F](0.65)=$38,000($197,648-F)(0.65)=$38,000F=$139,186.46128(b) QB

=V PF=8 $46 . 186 , 139 $=17,398 units S* =SVC1F=5294 . 0 146 . 186 , 139 $=$295,76415-12B.(a) {S [VC + f]} (1 T) = $70,000( ) T 1 FSVCS S ;'1]1

+ ,_

=$70,000[ ($2,500,050) - (1,933,372) - F ] (.55)=$70,000($566,678 - F)(.55)=$70,000($311,672.9 - .55F)=$70,000F=$439,405.27(b) QB

=V PF=17 $27 . 405 , 439 $=25,847 units S* =SVC1F=.7733 17 $439,405.2=.22677 $439,405.2= $1,938,268=2267 .27 . 405 , 439 $15-13B.(a) S (1 - 0.8) - $335,000=$270,0000.2S=$605,000S=$3,025,000=(P Q)Now, solve the above relationship for P:175,000 (P) = $3,025,000P = $17.29(b) Sales $3,025,750Less:Total variable costs 2,420,600Revenue before fixed costs $605,150Less:Total fixed costs 335,000EBIT $270,15012915-14B.(a) S(1-.75)-$300,000=$250,000.25S =$550,000S=$2,200,000=(P Q)Solve the above relationship for P:190,000 (P)=$2,200,000P=$11.58(b) Sales $2,200,000Less:Total variable costs 1,650,000Revenue before fixed costs $550,000Less:Total fixed costs 300,000EBIT $250,00015-15B.(a) First, find the EBIT level at the forecast sales volume:SEBIT=0.25So: EBIT=(0.25) $4,250,000=$1,062,500Next, find total variable costs:=0.4So: VC=(0.40) $4,250,000=$1,700,000Then, solve for total fixed costs:S - (VC + F)=$1,062,500$4,250,000 - ($1,700,000 + F)=$1,062,500F=$1,487,500 (b) S* =4 . 1500 , 487 , 1 $ = $2,479,16715-16B.(a) QB

=V PF=125 $000 , 200 $=1,600 units(b) S*=SVC1F=0.7368 1$200,000=$759,878130(c) DOL$2,850,000=000 , 200 $ ) 350 $ 475 ($ 000 , 6) 350 $ 475 ($ 000 , 6 000 , 550 $000 , 750 $= 1.364 times(d) (13%)x(1.364) = 17.73%Increase15-17B.(a) QB

=V PF=17 $ 28 $000 , 55 $=11 $000 , 55 $=5,000 units(b) S* =SVC1F=28 $17 $1000 , 55 $=607 . 0 1000 , 55 $=393 .000 , 55 $= $139,949 (c) 4,000 units 6,000 units 8,000 unitsSales $112,000 $168,000 $224,000Variable costs 68,000 102,000 136,000Revenue before fixed costs $44,000 $66,000 $88,000Fixed costs 55,000 55,000 55,000EBIT -$11,000 $ 11,000 $ 33,000(d) 4000 units 6000 units 8000 units000 , 11 $000 , 44 $= -4X000 , 11 $000 , 66 $=6X000 , 33 $000 , 88 $= 2.67X(e) The degree of operating leverage decreases as the firm's sales level rises above the break-even point.15-18B. Compute the present level of break-even output:QB

=V PF=6 $ 13 $000 , 135 $=19,286 unitsCompute the new level of fixed costs at the break-even output:S V F = 0($13) (19,286) - ($5) (19,286) - F = 0$250,718 - $96,430 - F = 0$154,288 = FCompute the addition to fixed costs:$154,288 - $135,000 = $19,288 addition13115-19B. DOL$520,000=000 , 135 $ ) 6 $ 13 ($ 000 , 40) 6 $ 13 ($ 000 , 40 =000 , 145000 , 280 $ =1.93 times Any percentage change in sales will magnify EBIT by a factor of 1.93.15-20B.(a) DOL$650,000=000 , 135 ) 6 $ 13 ($ 000 , 50) 6 $ 13 ($ 000 , 50 =000 , 215 $000 , 350 $=1.63 times(b) DFL$215,000=000 , 60 $ 000 , 215 $000 , 215 $=1.39 times (c) DCL$650,000 =000 , 60 $ 000 , 135 $ ) 6 $ 13 ($ 000 , 50) 6 $ 13 ($ 000 , 50 =000 , 155 $000 , 350 $=2.26 times Alternatively:DOLSxDFLEBIT=DCLS 1.63 x 1.39 = 2.26 times15-21B. The taskis tofindthebreak-evenpoint inunits for thefirm. Several approaches are possible, but the one presented below makes intuitive sense to students.Step(1) Compute the operating profit margin:(Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets(M) x (6)=0.16M=0.0267Step(2) Compute the sales level associated with the given output level:$3,250,000Sales=6Sales=$19,500,000 Step(3) Compute EBIT:(0.0267) ($19,500,000)=EBIT=$520,000Step(4) Computerevenue before fixed costs. Since the degree of operating leverage is 9 times, revenue before fixed costs (RBF) is 9 times EBIT as follows:132RBF=(9) ($520,000)=$4,680,000Step(5) Compute total variable costs:Sales - Total variable costs=$4,680,000$19,500,000 - Total variable costs=$4,680,000Total variable costs=$14,820,000Step(6) Compute total fixed costs:RBF - Fixed costs=$520,000$4,680,000 - Fixed costs=$520,000Fixed costs=$4,160,000Step(7) Find the selling price per unit, and the variable cost perunit:P=000 , 700 , 1000 , 500 , 19 $ =$11.471V=000 , 700 , 1000 , 820 , 14 $=$8.718Step(8)Compute the break-even point:QB= V PF=) 718 . 8 ($ ) 471 . 11 ($000 , 160 , 4 $=753 . 2 $000 , 160 , 4 $= 1,511,079 units 15-22B. Compute the present level of break-even output:QB

=V PF=13 $ 25 $000 , 375 $=31,250 unitsCompute the new level of fixed costs at the break-even output.S V F = 0($25) (31,250) - ($11) (31,250) - F = 0$437,500=FCompute the addition to fixed costs:$437,500 - $375,000=$62,500 addition 15-23B.(a)EBITcosts fixed before Revenue=000 , 250 , 1 $000 , 250 , 4 $=3.4 times(b)I EBITEBIT= 000 , 000 , 1 $000 , 250 , 1 $= 1.25 times(c) DCL$13,750,000 =(3.4) (1.25)=4.25 times(d) S*=SVC1F=$13.75m$9.5m13,000,000133=0.6909 1$3,000,000=0.3091$3,000,000=$9,705,59715-24B.(a)EBITcosts fixed before Revenue=000 , 000 , 5 $000 , 000 , 11 $=2.2 times(b)I EBITEBIT=000 , 250 , 3 $000 , 000 , 5 $=1.54 times(c) DCL$18,000,000=(2.2) (1.54)=3.39 times(d) (15%) (3.39)=50.9%(e) S*=SVC1F=$18m$7m1$6,000,000=389 . 0 1000 , 000 , 6 $ =$9,819,96715-25B.a. AB C D Total Sales $38,505 $61,995 $29,505 $19,995 $150,000Variable costs* 23,103 42,157 23,604 7,998 96,862Contribution margin $15,402 $19,838 $ 5,901 $ 11,997 $ 53,138Contribution margin ratio 40% 32% 20% 60% 35.43%*Variable costs=(Sales) (1 - contribution margin ratio)b. 35.43%c. Break-even point in sales dollars:S*=SVC1F =000 , 150 $862 , 96 $ 1 =$98,80013415-26B.a.A B CD Total Sales $49,995 $62,505 $25,00512,495 $150,000Variable costs* 29,997 42,503 20,004 4,998 97,502Contribution margin $19,998 $20,002 $5,001 $7,497 $52,498Contribution margin ratio 40% 32% 20% 60% 35%*Variable costs=(sales) (1- contribution margin ratio).b. 35%c. Break-even point in sales dollars:S*=SVC1F=35 . 0000 , 35 $=$100,000 Wayne'smanagement wouldprefer thesalesmixidentifiedinproblem15-25B. That first salesmixprovidesahigher EBIT($18,138vs. $17,498) andalower break-even point ($98,800 vs. $100,000).135