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1、Chapter 08,Operating and Financial Leverage经营杠杆和财务杠杆,Operating Leverage(经营杠杆),One potential“effect”caused by the presence of operating leverage is that a change in the volume of sales results in a“more than proportional”change in operating profit(or loss).,Operating Leverage-The use of fixed operati
2、ng costs by the firm.,Impact of Operating Leverage on Profits,Firm F Firm V Firm 2FSales$10$11$19.5Operating CostsFixed 7 2 14 Variable 2 7 3Operating ProfitFC/total costs FC/sales,(in thousands),Impact of Operating Leverage on Profits,Now,subject each firm to a 50%increase in sales for next year.Wh
3、ich firm do you think will be more“sensitive”to the change in sales(i.e.,show the largest percentage change in operating profit,EBIT)?Firm F;Firm V;Firm 2F.,Impact of Operating Leverage on Profits,Firm F Firm V Firm 2FSalesOperating Costs Fixed VariableOperating ProfitPercentage Change in EBIT*,(in
4、thousands),*(EBITt-EBIT t-1)/EBIT t-1,Impact of Operating Leverage on Profits,Firm F is the most“sensitive”firm-for it,a 50%increase in sales leads to a 400%increase in EBIT.Our example reveals that it is a mistake to assume that the firm with the largest absolute or relative amount of fixed costs a
5、utomatically shows the most dramatic effects of operating leverage.Later,we will come up with an easy way to spot the firm that is most sensitive to the presence of operating leverage.,Break-Even Analysis,When studying operating leverage,“profits”refers to operating profits before taxes(i.e.,EBIT)an
6、d excludes debt interest and dividend payments.,Break-Even Analysis-A technique for studying the relationship among fixed costs,variable costs,sales volume,and profits.Also called cost/volume/profit(C/V/P)analysis.,Break-Even Chart,QUANTITY PRODUCED AND SOLD,0 1,000 2,000 3,000 4,000 5,000 6,000 7,0
7、00,Total Revenues,Profits,Fixed Costs,Variable Costs,Losses,REVENUES AND COSTS($thousands),175,250,100,50,Total Costs,Break-Even(Quantity)Point,How to find the quantity break-even point:EBIT=P(Q)-V(Q)-FC EBIT=Q(P-V)-FC P=Price per unit V=Variable costs per unit FC=Fixed costs Q=Quantity(units)produc
8、ed and sold,Break-Even Point-The sales volume required so that total revenues and total costs are equal;may be in units or in sales dollars.,Break-Even(Quantity)Point,Breakeven occurs when EBIT=0 Q(P-V)-FC=EBIT QBE(P-V)-FC=0 QBE(P-V)=FC QBE=FC/(P-V),a.k.a.Unit Contribution Margin,Break-Even(Sales)Po
9、int,How to find the sales break-even point:SBE=FC+(VCBE)SBE=FC+(QBE)(V)or SBE*=FC/1-(VC/S),*Refer to text for derivation of the formula,Break-Even Point Example,Basket Wonders(BW)wants to determine both the quantity and sales break-even points when:Fixed costs are$100,000Baskets are sold for$43.75 e
10、achVariable costs are$18.75 per basket,Break-Even Point(s),Breakeven occurs when:QBE=FC/(P-V)QBE=$100,000/($43.75-$18.75)QBE=4,000 UnitsSBE=(QBE)(V)+FCSBE=(4,000)($18.75)+$100,000SBE=$175,000,Break-Even Chart,QUANTITY PRODUCED AND SOLD,0 1,000 2,000 3,000 4,000 5,000 6,000 7,000,Total Revenues,Profi
11、ts,Fixed Costs,Variable Costs,Losses,REVENUES AND COSTS($thousands),175,250,100,50,Total Costs,Degree of Operating Leverage(DOL经营杠杆系数),DOL at Q units of output(or sales),Degree of Operating Leverage-The percentage change in a firms operating profit(EBIT)resulting from a 1 percent change in output(sa
12、les).,=,Percentage change in operating profit(EBIT),Percentage change in output(or sales),Computing the DOL,DOLQ units,Calculating the DOL for a single product or a single-product firm.,=,Q(P-V),Q(P-V)-FC,=,Q,Q-QBE,Computing the DOL,DOLS dollars of sales,Calculating the DOL for a multiproduct firm.,
13、=,S-VC,S-VC-FC,=,EBIT+FC,EBIT,Break-Even Point Example,Lisa Miller wants to determine the degree of operating leverage at sales levels of 6,000 and 8,000 units.As we did earlier,we will assume that:Fixed costs are$100,000Baskets are sold for$43.75 eachVariable costs are$18.75 per basket,Computing BW
14、s DOL,DOL6,000 units,Computation based on the previously calculated break-even point of 4,000 units,=,=,DOL8,000 units,Interpretation of the DOL,A 1%increase in sales above the 8,000 unit level increases EBIT by 2%because of the existing operating leverage of the firm.,=,DOL8,000 units,Interpretatio
15、n of the DOL,2,000 4,000 6,000 8,000,1,2,3,4,5,QUANTITY PRODUCED AND SOLD,0,-1,-2,-3,-4,-5,DEGREE OF OPERATINGLEVERAGE(DOL),QBE,Interpretation of the DOL,DOL is a quantitative measure of the“sensitivity”of a firms operating profit to a change in the firms sales.The closer that a firm operates to its
16、 break-even point,the higher is the absolute value of its DOL.When comparing firms,the firm with the highest DOL is the firm that will be most“sensitive”to a change in sales.,Key Conclusions to be Drawn from the previous slide and our Discussion of DOL,DOL and Business Risk(经营杠杆与经营风险),DOL is only on
17、e component of business risk and becomes“active”only in the presence of sales and production cost variability.DOL magnifies the variability of operating profits and,hence,business risk.,Business Risk-The inherent uncertainty in the physical operations of the firm.Its impact is shown in the variabili
18、ty of the firms operating income(EBIT).,Application of DOL for Our Three Firm Example,Use the data in Slide 08-5 and the following formula for Firm F:DOL=(EBIT+FC)/EBIT,=,DOL$10,000 sales,Application of DOL for Our Three Firm Example,Use the data in Slide 08-5 and the following formula for Firm V:DO
19、L=(EBIT+FC)/EBIT,=,DOL$11,000 sales,Application of DOL for Our Three-Firm Example,Use the data in Slide 08-5 and the following formula for Firm 2F:DOL=(EBIT+FC)/EBIT,=,DOL$19,500 sales,Application of DOL for Our Three-Firm Example,The ranked results indicate that the firm most sensitive to the prese
20、nce of operating leverage is Firm F.Firm FDOL=Firm VDOL=Firm 2FDOL=Firm F will expect a 400%increase in profit from a 50%increase in sales(see Slide 08-7 results).,Financial Leverage(财务杠杆),Financial leverage is acquired by choice.Used as a means of increasing the return to common shareholders.,Finan
21、cial Leverage-The use of fixed financing costs by the firm.,EBIT-EPS Break-Even,or Indifference,Analysis,Calculate EPS for a given level of EBIT at a given financing structure.,EBIT-EPS Break-Even Analysis-Analysis of the effect of financing alternatives on earnings per share.The break-even point is
22、 the EBIT level where EPS is the same for two(or more)alternatives.(每股收益相等时的息税前盈余水平),(EBIT-I)(1-t)-Pref.Div.,#of Common Shares,EPS,=,EBIT-EPS Chart,Current common equity shares=50,000$1 million in new financing of either:All C.S.sold at$20/share(50,000 shares)All debt with a coupon rate of 10%All P.
23、S.with a dividend rate of 9%Expected EBIT=$500,000Income tax rate is 30%,Basket Wonders has$2 million in LT financing(100%common stock equity).,EBIT-EPS Calculation with New Equity Financing,EBIT$500,000$150,000*Interest 0 0EBT$500,000$150,000Taxes(30%x EBT)150,000 45,000EAT$350,000$105,000Preferred
24、 Dividends 0 0EACS$350,000$105,000#of Shares 100,000 100,000EPS$3.50$1.05,Common Stock Equity Alternative,*A second analysis using$150,000 EBIT rather than the expected EBIT.,EBIT-EPS Chart,0 100 200 300 400 500 600 700,EBIT($thousands),Earnings per Share($),0,1,2,3,4,5,6,Common,EBIT-EPS Calculation
25、 with New Debt Financing,EBIT$500,000$150,000*Interest 100,000 100,000EBT$400,000$50,000Taxes(30%x EBT)120,000 15,000EAT$280,000$35,000Preferred Dividends 0 0EACS$280,000$35,000#of Shares 50,000 50,000EPS$5.60$0.70,Long-term Debt Alternative,*A second analysis using$150,000 EBIT rather than the expe
26、cted EBIT.,EBIT-EPS Chart,0 100 200 300 400 500 600 700,EBIT($thousands),Earnings per Share($),0,1,2,3,4,5,6,Common,Debt,Indifference pointbetween debt andcommon stockfinancing,EBIT-EPS Calculation with New Preferred Financing,EBIT$500,000$150,000*Interest 0 0EBT$500,000$150,000Taxes(30%x EBT)150,00
27、0 45,000EAT$350,000$105,000Preferred Dividends 90,000 90,000EACS$260,000$15,000#of Shares 50,000 50,000EPS$5.20$0.30,Preferred Stock Alternative,*A second analysis using$150,000 EBIT rather than the expected EBIT.,0 100 200 300 400 500 600 700,EBIT-EPS Chart,EBIT($thousands),Earnings per Share($),0,
28、1,2,3,4,5,6,Common,Debt,Indifference pointbetween preferred stock and common stock financing,Preferred,Degree of Financial Leverage(DFL财务杠杆系数),DFL at EBIT of X dollars,Degree of Financial Leverage-The percentage change in a firms earnings per share(EPS)resulting from a 1 percent change in operating
29、profit.,=,Percentage change in earnings per share(EPS),Percentage change in operating profit(EBIT),Computing the DFL,DFL EBIT of$X,Calculating the DFL,=,EBIT,EBIT-I-PD/(1-t),EBIT=Earnings before interest and taxesI=InterestPD=Preferred dividendst=Corporate tax rate,What is the DFL for Each of the Fi
30、nancing Choices?,DFL$500,000,Calculating the DFL for NEW equity*alternative,=,*The calculation is based on the expected EBIT,=,What is the DFL for Each of the Financing Choices?,DFL$500,000,Calculating the DFL for NEW debt*alternative,=,*The calculation is based on the expected EBIT,=,=,What is the
31、DFL for Each of the Financing Choices?,DFL$500,000,Calculating the DFL for NEW preferred*alternative,=,*The calculation is based on the expected EBIT,=,=,Variability of EPS,Preferred stock financing will lead to the greatest variability in earnings per share based on the DFL.This is due to the tax d
32、eductibility of interest on debt financing.,DFLEquity=DFLDebt=DFLPreferred=,Which financing method will have the greatest relative variability in EPS?,Financial Risk,Debt increases the probability of cash insolvency over an all-equity-financed firm.For example,our example firm must have EBIT of at l
33、east$100,000 to cover the interest payment.Debt also increased the variability in EPS as the DFL increased from 1.00 to 1.25.,Financial Risk-The added variability in earnings per share(EPS)-plus the risk of possible insolvency-that is induced by the use of financial leverage.,Total Firm Risk,CVEPS i
34、s a measure of relative total firm riskCVEBIT is a measure of relative business riskThe difference,CVEPS-CVEBIT,is a measure of relative financial risk,Total Firm Risk-The variability in earnings per share(EPS).It is the sum of business plus financial risk.,Total firm risk=business risk+financial ri
35、sk,Degree of Total Leverage(DTL总杠杆系数),DTL at Q units(or S dollars)of output(or sales),Degree of Total Leverage-The percentage change in a firms earnings per share(EPS)resulting from a 1 percent change in output(sales).,=,Percentage change in earnings per share(EPS),Percentage change in output(or sal
36、es),Computing the DTL,DTL S dollarsof sales,DTL Q units(or S dollars)=(DOL Q units(or S dollars)x(DFL EBIT of X dollars),=,EBIT+FC,EBIT-I-PD/(1-t),DTL Q units,Q(P-V),Q(P-V)-FC-I-PD/(1-t),=,DTL Example,Lisa Miller wants to determine the Degree of Total Leverage at EBIT=$500,000.As we did earlier,we w
37、ill assume that:Fixed costs are$100,000Baskets are sold for$43.75 eachVariable costs are$18.75 per basket,Computing the DTL for All-Equity Financing,DTL S dollarsof sales,=,DTLS dollars=(DOL S dollars)x(DFLEBIT of$S)DTLS dollars=,=,Computing the DTL for Debt Financing,DTL S dollarsof sales,=,DTLS do
38、llars=(DOL S dollars)x(DFLEBIT of$S)DTLS dollars=,=,Risk versus Return,Compare the expected EPS to the DTL for the common stock equity financing approach to the debt financing approach.Financing E(EPS)DTL Equity$Debt$Greater expected return(higher EPS)comes at the expense of greater potential risk(higher DTL)!,
