Solution manual financial management 10e by keown chapter 15

CHAPTER 15 Analysis and Impact of Leverage CHAPTER ORIENTATION This chapter focuses on useful aids for the financial manager in determining the firm'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 OUTLINE I Business risk and financial risk A Risk is defined as the likely variability associated with expected revenue streams B C The variations in the income stream can be attributed to a The firm's exposure to business risk b The firm's decision to incur financial risk Business risk is defined as the variability of the firm's expected earnings before interest and taxes Business risk is measured by the firm's corresponding expected coefficient of variation Dispersion in operating income does not cause business risk It is the result of several influences, such as the company’s cost structure, product demand characteristics, and intra-industry competition Financial risk is a direct result of the firm's financing decision It refers to the additional variability in earnings available to the firm’s common stockholders and the additional chance of insolvency borne by the common shareholder when financial leverage is used Financial leverage is the financing of a portion of the firm's assets with securities bearing a fixed rate of return in hopes of increasing the return to the common shareholders 98 II Financial risk is passed on to the common shareholders who must bear most of the inconsistencies of returns to the firm after the deduction of fixed payments Break-even Analysis A The objective of break-even analysis is to determine the break-even quantity of output by studying the relationships among the firm’s cost structure, volume of output, and operating profit B C D The break-even quantity of output results in an EBIT level equal to zero Use of the model enables the financial officer to Determine the quantity of output that must be sold to cover all operating costs Calculate the EBIT achieved at various output levels Some potential applications include Capital expenditure analysis as a complementary technique to discounted cash flow evaluation models Pricing policy Labor contract negotiations Evaluation of cost structure Financial decision making Essential elements of the break-even model Production costs must be separated into fixed costs and variable costs Fixed costs not vary as the sales volume or the quantity of output changes Examples include a Administrative salaries b Depreciation c Insurance premiums d Property taxes e Rent Variable costs vary in total as output changes Variable costs are fixed per unit of output Examples include a Direct materials b Direct labor c Energy cost associated with production d Packaging e Freight-out f Sales commissions 99 E In order to implement the break-even model, it is necessary for the financial manager to a 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 Total revenue and volume of output a Total revenue (sales dollars) is equal to the selling price per unit multiplied by the quantity sold b Volume of output refers to the firm’s level of operations and is expressed as a unit quantity or sales dollars Finding the break-even point The break-even model is just an adaptation of the firm's income statement expressed as sales - (total variable costs + total fixed costs) = profit Three ways to find the break-even point are explained a b c 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 Contribution margin analysis (1) Unit selling price - unit variable cost = contribution margin (2) Fixed cost divided by the contribution margin per unit equals the break-even quantity in units Algebraic analysis (l) (2) 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 Then, QB = F P−V 100 F G III The break-even point in sales dollars It is convenient to calculate the break-even point in terms of sales dollars if the firm deals with more than one product It can be computed by using data from the firm's annual report Since variable cost and selling price per unit are assumed constant, the ratio of total variable costs to total sales is a constant for any level of sales Limitations of break-even analysis Assumes linear cost-volume-profit relationship The total revenue curve is presumed to increase linearly with the volume of output Assumes constant production and sales mix This is a static form of analysis Operating Leverage A 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 responsiveness can be measured as follows: degree of operating % change in EBIT leverage from the = DOLs = % change in sales base sales level C If unit costs are available, the DOL can be measured by Q(P − V) DOLs = Q(P − V) − F D If an analytical income statement is the only information available, the following formula is used: DOLs = revenue before fixed costs S − VC = EBIT S − VC − F Note: All three formulas provide the same results E Implications of operating leverage At each point above the break-even level, the degree of operating leverage decreases At the break-even level of sales, the degree of operating leverage is undefined Operating leverage is present when the percentage change in EBIT divided by the percentage change in sales is greater than one The degree of operating leverage is attributed to the business risk that a firm faces 101 IV Financial Leverage A 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 when % change in EPS is greater than 1.00 % change in EBIT C A measure of the firm's use of financial leverage is as follows: degree of financial % change in EPS leverage from the = DFLEBIT = % change in EBIT base EBIT level D The degree of financial leverage concept can be either in the positive or negative direction The greater the degree of financial leverage, the greater the fluctuations in EPS An easier way to measure financial leverage is DFLEBIT = EBIT EBIT − I where I is the sum of all fixed financing costs V Combining operating and financial leverage A Changes in sales revenues cause greater changes in EBIT If the firm chooses to use financial leverage, changes in EBIT turn into larger variations in both EPS and EAC Combining operating and financial leverage causes rather large variations in EPS B One way to measure the combined leverage can be expressed as degree of combined % change in EPS leverage from the = DCLs = % change in sales base sales level If the DCL is equal to 5.0 times, then a 1% change in sales will result in a 5% change in EPS C The degree of combined leverage is the product of the two independent leverage measures Thus: DCLS = (DOLS ) x (DFLEBIT) 102 D Another way to compute DCLs is with the following equation: Q(P − V) DCLs = Q(P − V) − F − I E Implications of combining operating and financial leverage Total risk can be managed by combining operating and financial leverage in different degrees Knowledge of the various leverage measures helps to determine the proper level of overall risk that should be accepted ANSWERS TO END-OF-CHAPTER QUESTIONS 15-1 Business risk is the uncertainty that envelops the firm's stream of earnings 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 demand characteristics, (3) intraindustry 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 chooses to use financial leverage; (2) the increased variability in the stream of 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) rate of return Anytime the firm uses preferred stock to finance assets, financial leverage is employed 15-3 Operating leverage is the use of fixed operating costs in the firm's cost structure When operating leverage is present, any percentage fluctuation in sales will result in a greater percentage fluctuation in EBIT 15-4 Break-even analysis, as it is typically presented, categorizes all operating costs as being either fixed or variable Based upon this division of costs, the break-even point is computed The computation procedure for the cash break-even point omits any noncash expenses that the firm might incur Typical examples of noncash expenses include depreciation and prepaid expenses The ordinary break-even point will always exceed the cash break-even point, provided some noncash charges are present 15-5 The most important shortcomings of break-even analysis are: (1) The cost-volume-profit relationship is assumed to be linear over the entire 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) The level of total fixed costs and the variable cost to sales ratio is held constant over all output and sales ranges 15-6 Total risk exposure is the result of the firm's use of both operating leverage and financial leverage Business risk and financial risk produce this 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 As the sales of a firm increase, two things occur that bias the cost and revenue functions toward a curvilinear shape First, sales will increase at a decreasing rate As the market approaches saturation, the firm must cut its price to generate sales revenue Second, as production approaches capacity, inefficiencies occur that result in higher labor and material costs Furthermore, the firm's operating system may have to bear higher administrative and fixed costs The result is higher per unit costs as production output increases SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions To Problem Set A 15-1A Product Line Piano Violin Cello Flute Sales 61,250 37,500 98,750 52,500 V.C 41,650 22,500 61,225 25,725 C.M 19,600 15,000 37,525 26,775 C.M Ratio 32% 40% 38% 51% Total 250,000 151,100 98,900 40% Break-even Point S* = F/(1-VC/S) = 50,000/(1-VC/S) = 50,000/.4 = 125,000 50,000 F 50,000 S* =  VC  =  $151,100  = = 125,000 1 −  1 −  S    $250,000  104 15-2A Break-even Quantity = QB QB = F (P − V) QB = $360,000 $30 - (.70)($30) QB = 40,000 bottles 15-3A Degree of Operating Leverage = DOLS DOLS = Q(P − V) [Q(P − V) − F] V 70% x $30 = =$21 DOLS = 50,000($30 − $21) [50,000($30 − $21) − $360,000] DOLS = times 15-4A (a) Sales Variable Costs Revenue before fixed costs Fixed costs EBIT Jake's Lawn Chairs $600,640.00 $326,222.60 Sarasota Sky Lights $2,450,000 $1,120,000 Jefferson Wholesale $1,075,470 $957,000 $274,417.40 $120,350.00 $ 154,067.40 $1,330,000 $850,000 $ 480,000 $118,470 $89,500 $ 28,970 (b) Jake's Lawn Chairs: QB = F = $120,350 $32 − $17.38 P−V = $120,350 = 8,232 $14.62 = $850,000 = $850,000 = 1,789 $875 − $400 $475 Jefferson Wholesale: QB = $89,500 = $89,500 = 8,310 $97.77 − $87 $10.77 Sarasota Skylights: QB (c) 105 Revenue Before Fixed Costs EBIT (d) Jake's Lawn Chairs Sarasota Skylights Jefferson Wholesale = $274,417.40 $154,067.40 $1,330,000 $480,000 $118,470 $28,970 = 1.78 times 2.77 times 4.09 times Jefferson Wholesale, since its degree of operating leverage exceeds that of the other two companies 15-5A (a) Revenue Before Fixed Costs EBIT (b) EBIT = EBIT − I (c) DCL45,750,000 (d) S* = $22,950,000 $13,750,000 $13,750,000 $13,750,000 − $1,350,000 = = $13,750,000 $12,400,000 1.67 times = 1.11 times = (1.67) (1.11) = 1.85 times = F VC 1− S = $9,200,000 502 = $9,200,000 $22,800,000 1− $45,750,000 = = $9,200,000 − 498 $18,326,693.23 (e) (25%) × (1.85) = 46.25% (a) QB = (b) F $170,000 $170,000 $170,000 VC = $58 = S* = = = $534,591.20 1− 1− − 682 318 S $85 15-6A $170,000 $170,000 F = = = 6,296 pairs of shoes $85 − $58 $27 P−V (c) Sales Variable Costs Revenue before fixed costs Fixed costs EBIT 7,000 Pairs of Shoes $595,000 406,000 $189,000 170,000 $ 19,000 106 9,000 Pairs of Shoes $765,000 522,000 $243,000 170,000 $ 73,000 15,000 Pairs of Shoes $1,275,000 870,000 $405,000 170,000 $ 235,000 (d) 7,000 Pairs of Shoes = 9,000 Pairs of Shoes 15,000 Pairs of Shoes $189,000 $19,000 $243,000 $73,000 $405,000 $235,000 9.95 times 3.33 times 1.72 times Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point 15-7A (a) QB = $630,000 $630,000 F = = $180 − $110 $70 P−V (b) S* = 9000 units × $180 = $1,620,000 = 9000 Units Alternatively, S* = = Note: F $630,000 VC = $110 1− 1− S $180 $630,000 $630,000 = = $1,619,954 − 0.6111 3889 $1,619,954 differs from $1,620,000 due to rounding (c) Sales Variable Costs Revenue before fixed costs Fixed costs EBIT (d) = 12,000 units $2,160,000 1,320,000 15,000 units $2,700,000 1,650,000 20,000 units $3,600,000 2,200,000 840,000 630,000 $ 210,000 1,050,000 630,000 $ 420,000 1,400,000 630,000 $ 770,000 12,000 units 15,000 units 20,000 units $840,000 $210,000 $1,050,000 $420,000 $1,400,000 $770,000 times = 2.5 times = 1.82 times Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point 107 STEP 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 units After determining the break-even point using the approach described above, the students have the information necessary to prepare an analytical income statement as follows: Sales [STEP 2] Variable Costs [STEP 5] Revenue before Fixed Costs Fixed Costs [STEP 6] EBIT Interest Expense Earnings Before Taxes Taxes (35%) Net Income $14,000,000 10,500,000 $3,500,000 2,800,000 $700,000 400,000 $300,000 105,000 $195,000 Thereafter, 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 DFLEBIT DCLS = x 2.33 DCLS = 11.65 (c) Break-even point in sales dollars: S* = F − VC S $2,800,000 S* = $10,500,000 1$14,000,000 S* = $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] $18,200,000 Variable Costs 13,650,000 Revenue Before Fixed Costs $4,550,000 Fixed Costs [STEP 6] 2,800,000 EBIT $1,750,000 Interest Expense 400,000 Earnings Before Taxes $1,350,000 Taxes (35%) 472,500 Net Income $877,500 It may be useful to develop the following “proof” to assist in explaining the interrelationships 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 B 15-1B Break-even Quantity = QB QB = F (P − V) P = $20,000,000 40,000,000 units = $.50 per unit V = $16,000,000 40,000,000 units = $.40 per unit QB = $2,400,000 ($0.50 − $0.40) QB = 24,000,000 units thus, 122 15-2B Degree of Combined Leverage Degree of Operating Leverage Degree of Financial Leverage = = = DCLS DOLS DFLEBIT DOLS = Q(P − V) [Q(P − V) − F] P = $20,000,000 = 40,000,000 units $.50 per unit V = $16,000,000 = 40,000,000 units $.40 per unit DOLS = 40,000,000 ($0.50 − $0.40) [ 40,000,000 ($0.50 − $0.40) − $2,400,000] DOLS = 2.50 times DFLEBIT = EBIT (EBIT − 1) DFLEBIT = $1,600,000 ($1,600,000 − $800,000) DFLEBIT = 2.00 times DCLS = Q(P − V) [Q(P − V) − F − I] DCLS = DCLS = $4,000,000 $800,000 DCLs = 5.00 times thus, and 40,000,000 ($0.50 − $0.40) [ 40,000,000 ($0.50 − $0.40) − $2,400,000 − $800,000] 15-3B (a) QB = $650,000 $650,000 F = = = 10,833 Units $175 − $115 $60 P−V 123 (b) S* = (10,833 units) × ($175) = $1,895,775 Alternatively, S* Note: = F VC 1− S $650,000 $115 = 1− $175 = $650,000 $650,000 = = $1,895,596 − 0.6571 3429 $1,895,596 differs from $1,895,775 due to rounding (c) 10,000 units $1,750,000 1,150,000 600,000 650,000 -$50,000 Sales Variable costs Revenue before fixed costs Fixed costs EBIT (d) 10,000 units 16,000 units $2,800,000 1,840,000 960,000 650,000 $ 310,000 16,000 units $600,000 = -12 times − $50,000 $960,000 = 3.1 times $310,000 20,000 units $3,500,000 2,300,000 1,200,000 650,000 $ 550,000 20,000 units $1,200,000 = 2.2 times $550,000 Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point 15-4B (a) Sales Variable costs Revenue before fixed costs Fixed costs EBIT (b) QB units Durham Furniture $1,600,000 1,100,000 Raleigh Cabinets $1,957,500 1,080,000 $500,000 40,000 $460,000 $877,500 150,000 $727,500 = Charlotte Colonials $525,000 236,250 $288,750 60,000 $228,750 $40,000 $40,000 F = = = 6,400 $20.00 − $13.75 $6.25 P−V QB = $150,000 $435 − $240 QB = $60,000 $35.00 − $15.75 124 = $150,000 = 769 units $195 = $60,000 $19.25 = 3,117 units (c) Durham Furniture = Raleigh Furniture $500,000 $460,000 = = 1.09 times $877,500 $727,500 Charlotte Colonials = 1.21 times $288,750 $228,750 1.26 times (d) Charlotte Colonials, since its degree of operating leverage exceeds that of the other two companies (a) {S - [VC + F]} (1 - T) = $55,000 15-5B  S −    VC   S + F      (1 − T ) = $55,000   S   {$400,008 - [257,148 + F ]} (0.55) = $55,000 ($142,860 - F) (0.55) = $55,000 F = $42,860 (b) 15-6B (a) QB = $42,860 F = = $42,860 = 4,286 units $28.00 − $18.00 $10.00 P−V F $42,860 VC = S* = = $120,056 1− − 0.643 S Find the EBIT level at the forecast sales volume: EBIT = 28 S Therefore, EBIT = (0.28) ($3,750,000) = $1,050,000 Next, find total variable costs: VC = 0.55, S so: VC = (0.55) $3,750,000 = $2,062,500 Now, solve for total fixed costs: S - (VC + F) = $1,050,000 $3,750,000 - ($1,687,500 + F) = $1,050,000 F = $637,500 125 $637,500 = $1,416,667 − 0.55 (b) S* = (a) = (b) EBIT EBIT − I (c) DCL$40,000,000= (1.71) × (1.09) = 1.86 times 15-7B (d) (e) 15-8B S* $24,000,000 = 1.71 times $14,000,000 = $14,000,000 $12,850,000 = 1.09 times = F $10,000,000 VC = $16m 1− 1− S $40m = $10,000,000 $10,000,000 = = $16,666,667 − 0.4 0.6 (20%) × (1.86) = 37.2% Given the data for this problem, several approaches are possible for finding the 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 = 05 Step (2) Compute the sales level relative to the given output level: Sales = $18,000,000 Sales = $90,000,000 Step (3) Compute EBIT: (.05) ($90,000,000) = $4,500,000 Step (4) Compute revenue before fixed costs Since the degree of operating leverage is times, revenue before fixed costs (RBF) is times EBIT as follows: RBF = (6) × ($4,500,000) = $27,000,000 126 Step (5) Compute total variable costs: (Sales) - (Total variable costs) = $27,000,000 $90,000,000 - (Total variable costs) = $27,000,000 Total variable costs = $63,000,000 Step (6) Compute total fixed costs: RBF - Fixed costs = $4,500,000 $27,000,000 - fixed costs = $4,500,000 Fixed costs = $22,500,000 Step (7) Find the selling price per unit, and the variable cost per unit: Step (8) P = $90,000,000 = $12.86 7,000,000 V = $63,000,000 = $9.00 7,000,000 Compute the break-even point: QB $22,500,000 ($12.86) − ($9) = F P−V = $22,500,000 $3.86 = F P−V = = 5,829,016 units 15-9B (a) (b) S* QB $550,000 = $550,000 = 15,714 units $175 − $140 $35 = F $550,000 VC = $140 1− 1− S $175 = $550,000 − 0.8 = (c) Sales Variable costs Revenue before fixed costs Fixed costs EBIT = $550,000 = $2,750,000 12,000 Units $2,100,000 1,680,000 $ 420,000 550,000 15,000 Units $2,625,000 2,100,000 $ 525,000 550,000 20,000 Units $3,500,000 2,800,000 $700,000 550,000 -$130,000 -$25,000 $ 150,000 127 (d) 12,000 units 15,000 units 20,000 units $420,000 = -3.2 times − $130,000 $525,000 = -21 times − $25,000 $700,000 = 4.67 times $150,000 Sales Variable costs Revenue before fixed costs Fixed costs Farm City Seeds $1,800,000 1,410,000 $390,000 30,000 Empire Sod $1,710,000 1,305,000 $ 405,000 110,000 Golden Peaches $1,400,000 950,000 $ 450,000 33,000 EBIT $ 360,000 $ 295,000 $ 417,000 15-10B (a) (b) Farm City: QB Empire Sod: QB = $30,000 F = = $30,000 = 9,231 units $15.00 − $11 75 $3.25 P−V = Golden Peaches: QB = (c) 15-11B (a) = 2,444 units $33,000 $33,000 = = 3,667 units $28.00 − $19 $9 Farm City Empire Golden Seeds Sod Peaches $390,000 = 1.083 times $360,000 (d) $110,000 $110 ,000 = $190 − $145 $45 $405,000 = 1.373 times $295,000 $450,000 = 1.079 times $417,000 Empire Sod, since its degree of operating leverage exceeds that of the other two companies {S – [VC + F]} (1-T) = $38,000  S −    VC   S  S  + F  (1 − T ) = $38,000     [($420,002) - ($222,354) - F] (0.65) = $38,000 ($197,648 - F) (0.65) = $38,000 F = $139,186.46 128 (b) QB S* 15-12B (a) = F = $139,186.46 = 17,398 units $8 P−V = F $139,186.46 VC = = $295,764 1− − 0.5294 S {S – [VC + f]} (1 – T) = $70,000  S −    VC   S  S  + F  (1 − T ) = $70,000     [ ($2,500,050) - (1,933,372) - F ] (.55) = $70,000 ($566,678 - F) (.55) = $70,000 ($311,672.9 - 55F) = $70,000 F = $439,405.27 (b) QB S* 15-13B (a) = F = $439,405.27 = 25,847 units $17 P−V = F $439,405.27 $439,405.27 VC = = 1− − 7733 2267 S = $1,938,268 = $439,405.27 2267 S (1 - 0.8) - $335,000 = $270,000 0.2S = $605,000 S = $3,025,000 = (P × Q) Now, solve the above relationship for P: (b) 175,000 (P) = $3,025,000 P = $17.29 Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs $3,025,750 2,420,600 $605,150 335,000 EBIT $ 270,150 129 15-14B (a) (b) S (1-.75) - $300,000 = $250,000 25S = $550,000 S = $2,200,000 = (P × Q) Solve the above relationship for P: 190,000 (P) = $2,200,000 P = $11.58 Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs $2,200,000 1,650,000 $550,000 300,000 EBIT $ 250,000 15-15B (a) First, find the EBIT level at the forecast sales volume: EBIT = 0.25 S So: EBIT = (0.25) $4,250,000 = $1,062,500 Next, find total variable costs: = 0.4 So: VC = (0.40) $4,250,000 = $1,700,000 Then, solve for total fixed costs: S - (VC + F) = $1,062,500 $4,250,000 - ($1,700,000 + F) = $1,062,500 F = $1,487,500 (b) S* = $1,487,500 − (a) QB = (b) F VC S* = 1− S = $2,479,167 15-16B F P−V = $200,000 = 1,600 units $125 = $200,000 = $759,878 − 0.7368 130 (c) (d) DOL$2,850,000 = 6,000($475 − $350) 6,000($475 − $350) − $200,000 $750,000 $550,000 = 1.364 times (13%) x (1.364) = 17.73% Increase 15-17B (a) (b) QB S* = F = $55,000 = $55,000 = 5,000 units $28 − $17 $11 P−V = F $55,000 $55,000 $55,000 VC = $17 = = = $139,949 1− 1− − 0.607 393 S $28 (c) Sales Variable costs Revenue before fixed costs Fixed costs 4,000 units $112,000 68,000 $ 44,000 55,000 6,000 units $168,000 102,000 $ 66,000 55,000 EBIT -$11,000 $ 11,000 (d) (e) 15-18B 4000 units 6000 units $44,000 = -4X − $11,000 $66,000 = 6X $11,000 8,000 units $224,000 136,000 $ 88,000 55,000 $ 33,000 8000 units $88,000 = 2.67X $33,000 The degree of operating leverage decreases as the firm's sales level rises above the break-even point Compute the present level of break-even output: QB = F = $135,000 = 19,286 units $13 − $6 P−V Compute the new level of fixed costs at the break-even output: S–V–F=0 ($13) (19,286) - ($5) (19,286) - F = $250,718 - $96,430 - F = $154,288 = F Compute the addition to fixed costs: $154,288 - $135,000 = $19,288 addition 131 15-19B DOL$520,000 = 40,000($13 − $6) 40,000($13 − $6) − $135,000 = $280,000 145,000 = 1.93 times Any percentage change in sales will magnify EBIT by a factor of 1.93 15-20B (a) DOL$650,000 = 50,000($13 − $6) 50,000($13 − $6) − 135,000 = $350,000 = 1.63 times $215,000 (b) DFL$215,000 = $215,000 = 1.39 times $215,000 − $60,000 (c) DCL$650,000 = 50,000 ($13 − $6) 50,000 ($13 − $6) − $135,000 − $60,000 = $350,000 = 2.26 times $155,000 Alternatively: DOLS x DFLEBIT = DCLS 1.63 x 1.39 = 2.26 times 15-21B The task is to find the break-even point in units for the firm 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) = 0.16 M = 0.0267 Step (2) Compute the sales level associated with the given output level: Sales = $3,250,000 Sales = $19,500,000 Step (3) Compute EBIT: (0.0267) ($19,500,000) = EBIT = $520,000 132 Step (4) Compute revenue before fixed costs Since the degree of operating leverage is times, revenue before fixed costs (RBF) is times EBIT as follows: RBF = (9) ($520,000) = $4,680,000 Step (5) Compute total variable costs: Sales - Total variable costs = $4,680,000 $19,500,000 - Total variable costs = $4,680,000 Total variable costs = $14,820,000 Step (6) Compute total fixed costs: RBF - Fixed costs = $520,000 $4,680,000 - Fixed costs = $520,000 Fixed costs = $4,160,000 Step (7) Find the selling price per unit, and the variable cost per unit: Step (8) P = $19,500,000 1,700,000 V = $14,820,000 = $8.718 1,700,000 = $11.471 Compute the break-even point: QB = $4,160,000 $4,160,000 F = = = 1,511,079 ($11 471) − ($8.718) $2.753 P−V units 15-22B Compute the present level of break-even output: F = $375,000 = 31,250 units QB = $25 − $13 P−V Compute the new level of fixed costs at the break-even output S–V–F=0 ($25) (31,250) - ($11) (31,250) - F = $437,500 = F Compute the addition to fixed costs: $437,500 - $375,000 = $62,500 addition 15-23B (a) $4,250,000 Revenue before fixed costs = = 3.4 times $1,250,000 EBIT (b) $1,250,000 EBIT = = 1.25 times $1,000,000 EBIT − I 133 (c) DCL$13,750,000 = (3.4) × (1.25) = 4.25 times (d) = F 3,000,000 VC = $9.5m 1− 1− S $13.75m = $3,000,000 $3,000,000 = = $9,705,597 − 0.6909 0.3091 S* 15-24B (a) $11,000,000 Revenue before fixed costs = = 2.2 times $5,000,000 EBIT (b) EBIT = EBIT − I (c) DCL$18,000,000 = (2.2) × (1.54) = 3.39 times (d) (15%) × (3.39) = 50.9% (e) S* $5,000,000 = 1.54 times $3,250,000 = F $6,000,000 VC = $7m 1− 1− S $18m = $6,000,000 − 0.389 15-25B.a Sales Variable costs* Contribution margin Contribution margin ratio = $9,819,967 A $38,505 23,103 $15,402 40% B $61,995 42,157 $19,838 32% C $29,505 23,604 $ 5,901 20% *Variable costs = (Sales) (1 - contribution margin ratio) b 35.43% c Break-even point in sales dollars: F VC S* = 1− S = 1− $96,862 $150,000 134 = $98,800 D Total $19,995 $150,000 7,998 96,862 $ 11,997 $ 53,138 60% 35.43% 15-26B.a Sales Variable costs* Contribution margin Contribution margin ratio A $49,995 29,997 $19,998 40% B $62,505 42,503 $20,002 32% C $25,005 20,004 $ 5,001 20% D 12,495 4,998 $ 7,497 60% Total $150,000 97,502 $ 52,498 35% *Variable costs = (sales) (1- contribution margin ratio) b 35% c Break-even point in sales dollars: F $35,000 VC = S* = = $100,000 1− 0.35 S Wayne's management would prefer the sales mix identified in problem 15-25B That first sales mix provides a higher EBIT ($18,138 vs $17,498) and a lower break-even point ($98,800 vs $100,000) 135 ... 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 As... increases SOLUTIONS TO END-OF -CHAPTER PROBLEMS Solutions To Problem Set A 15- 1A Product Line Piano Violin Cello Flute Sales 61,250 37,500 98,750 52,500 V.C 41,650 22,500 61,225 25,725 C.M 19,600 15, 000... $48,000 addition 115 15-23A DOL$360,000 = 30,000($12 − $7) 30,000($12 − $7) − $120,000 = $150 ,000 = times $30,000 Any percentage change in sales will magnify EBIT by a factor of 15- 24A (a) DOL$480,000