CHAPTER 15
Analysis and Impact
of Leverage
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) 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 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 operating fixed 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 saleable at the fixed selling price.
(3) The sales mix and production mix is assumed constant.
(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 / 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 Point
S = F/(1-VC/S) = 50,000/(1-VC/S) = 50,000/.4 = 125,000
S = = = = 125,000
15-2A.Break-even Quantity=QB
QB=
QB=
QB=40,000 bottles
15-3A.Degree of Operating Leverage = DOLS
DOLS=
V=70% x $30=$21
DOLS=
DOLS=5 times
15-4A.
(a)
Jake's Sarasota Jefferson
Lawn Chairs Sky Lights Wholesale
Sales $600,640.00 $2,450,000 $1,075,470
Variable Costs $326,222.60 $1,120,000 $957,000
Revenue before
fixed costs $274,417.40 $1,330,000 $118,470
Fixed costs $120,350.00 $850,000 $89,500
EBIT $ 154,067.40 $ 480,000 $ 28,970
(b)
Jake's Lawn Chairs: QB= =
= = 8,232
Sarasota Skylights: QB= = = 1,789
Jefferson Wholesale: QB= = = 8,310
(c)
Jake'sSarasotaJefferson
Lawn ChairsSkylightsWholesale
=
=1.78 times2.77 times4.09 times
(d)Jefferson Wholesale, since its degree of operating leverage exceeds that of the other two companies.
15-5A.
(a)==1.67 times
(b)===1.11 times
(c)DCL45,750,000=(1.67) (1.11) =1.85 times
(d)S*===
==$18,326,693.23
(e)(25%) × (1.85)=46.25%
15-6A.
(a)QB = = = = 6,296 pairs of shoes
(b)S* = = = = = $534,591.20
(c)
7,000 9,000 15,000
Pairs of Shoes Pairs of Shoes Pairs of Shoes
Sales $595,000 $765,000 $1,275,000
Variable Costs 406,000 522,000 870,000
Revenue before
fixed costs $189,000 $243,000 $405,000
Fixed costs 170,000 170,000 170,000
EBIT $ 19,000 $ 73,000 $ 235,000
(d)
7,0009,00015,000
Pairs of ShoesPairs of ShoesPairs of Shoes
=9.95 times3.33 times1.72 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= = = = 9000 Units
(b)S*=9000 units × $180 = $1,620,000
Alternatively,
S*= =
= = = $1,619,954
Note: $1,619,954 differs from $1,620,000 due to rounding.
(c)12,00015,00020,000
unitsunitsunits
Sales $2,160,000 $2,700,000 $3,600,000
Variable Costs 1,320,000 1,650,000 2,200,000
Revenue before
fixed costs 840,000 1,050,000 1,400,000
Fixed costs 630,000 630,000 630,000
EBIT $ 210,000 $ 420,000 $ 770,000
(d)12,000 units15,000 units20,000 units
=4 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.
15-8A. (a)
BlacksburgLexingtonWilliamsburg
FurnitureCabinetsColonials
Sales $1,125,000 $1,600,000 $520,000
Variable costs 926,250 880,000 188,500
Revenue before
fixed costs $198,750 $720,000 $331,500
Fixed costs 35,000 100,000 70,000
EBIT $163,750 $620,000 $261,500
(b)
QB== = = 13,208 units
QB= = = 556 units
QB= = = 2745 units
(c)
BlacksburgLexingtonWilliamsburg
FurnitureCabinetsColonials
= 1.21 times1.16 times1.27 times
(d)Williamsburg Colonials, since its degree of operating leverage exceeds that of the other two companies.
15-9A.
(a)
{S- (V + F)} (1-T) = $50,000
{S – [S + F]} (1-T) = $50,000
{$375,000 - $206,250 – F} (0.6) = $50,000
($168,750 - F) (0.6) = $50,000
F = $85,416.67
(b)QB = = = = 7,030 units
S* = = = $189,815
15-10A.(a)Find the EBIT level at the forecast sales volume:
= .26
Therefore, EBIT = (0.26) ($3,250,000) = $845,000
Next, find total variable costs:
= 0.5,
so,VC = (0.5) $3,250,000 = $1,625,000
Now, solve for total fixed costs:
S - (VC + F) = $845,000
$3,250,000 - ($1,625,000 + F) = $845,000
F = $780,000
(b)S* = = $1,560,000
15-11A.
(a) = = 1.94 times
(b) = = 1.13 times
(c)DCL$30,000,000= (1.94) × (1.13) = 2.19 times
(d)S* = = = = = $14,545,455
(e)(25%) × (2.19) = 54.75%
15-12A. 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 associated with the given output level:
= 5
Sales = $100,000,000
Step (3)Compute EBIT:
(.05) ($100,000,000) = $5,000,000
Step (4)Compute revenue before fixed costs. Since the degree of operating leverage is 4 times, revenue before fixed costs (RBF) is 4 times EBIT as follows:
RBF = (4) ($5,000,000) = $20,000,000
Step (5)Compute total variable costs:
(Sales) - (Total variable costs) = $20,000,000
$100,000,000 - (Total variable costs) = $20,000,000
Total variable costs = $80,000,000
Step (6)Compute total fixed costs:
RBF - Fixed costs = $5,000,000
$20,000,000 - fixed costs = $5,000,000
Fixed costs = $15,000,000
Step (7)Find the selling price per unit, and the variable cost per unit:
P = = $10.00
V = = $8.00
Step (8)Compute the break-even point:
QB = = = = 7,500,000 units
15-13A.
(a)QB = = = = 10,000 units
(b) S* = = = =
=$1,800,000
(c) 12,00015,00020,000
UnitsUnitsUnits
Sales$2,160,000$2,700,000$3,600,000
Variable costs1,512,0001,890,0002,520,000
Revenue before fixed costs$ 648,000$ 810,000$1,080,000
Fixed costs540,000540,000540,000
EBIT$ 108,000$ 270,000$ 540,000
(d)12,000 units15,000 units20,000 units
= 6 times= 3 times= 2 times
Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.
15-14A.
(a)OviedoGainesvilleAthens
Seeds Sod Peaches
Sales$1,400,000$2,000,000$1,200,000
Variable costs1,120,0001,300,000840,000
Revenue before fixed costs$280,000$ 700,000$ 360,000
Fixed costs25,000100,00035,000
EBIT$ 255,000$ 600,000$ 325,000
(b)Oviedo Seeds: QB= = =
=8,929 units
Gainesville Sod: QB= =
=1,429 units
Athens Peaches: QB= =
=4,667 units
(c)
OviedoGainesville
SeedsSod
= 1.098 times= 1.167 times
Athens
Peaches
= 1.108 times
(d)Gainesville Sod, since its degree of operating leverage exceeds that of the other two companies.
15-15A.
(a){S - [V + F]} (1 - T) = $40,000
{S – [S + F]} (1-T) = $40,000
{($400,000) - ($160,000) - F} (0.6) = $40,000
($240,000 - F) (0.6) = $40,000
F = $173,333.33
(b)QB= = = 14,444 units
S*= = = $288,888.88
15-16A.
(a){S - [V + F] } (1-T) = $80,000
{S – [S + F]} (1-T) = $80,000
{($2,000,000) - (1,400,000) - F} (.6) = $80,000
($600,000 - F) (.6) = $80,000
$360,000 - .6F = $80,000
F = $466,666.67
(b)QB= = = 19,444 units
S* = = =
=$1,555,555.57
15-17A.
(a)S (1 - 0.75) - $300,000 = $240,000
0.25S = $540,000
S = $2,160,000 = (P × Q)
Now, solve the above relationship for P:
200,000 (P)=$2,160,000
P=$10.80
(b)Sales $2,160,000
Less: Total variable costs 1,620,000
Revenue before fixed costs $540,000
Less: Total fixed costs 300,000
EBIT $ 240,000
15-18A.
(a)S (1 - .6) - $300,000 = $250,000
.4S = $550,000
S = $1,375,000 = (P × Q)
Solve the above relationship for P.
200,000 (P)=$1,375,000
P=$6.875
(b)Sales $1,375,000
Less: Total variable costs 825,000
Revenue before fixed costs $550,000
Less: Total fixed costs 300,000
EBIT $ 250,000
15-19A.
(a) First, find the EBIT level at the forecast sales volume:
= 0.28
So:EBIT = (0.28) $3,750,000 = $1,050,000
Next, find total variable costs:
= 0.5
So:VC = (0.50) $3,750,000 = $1,875,000
Then, solve for total fixed costs:
S - (VC + F) = $1,050,000
$3,750,000 - ($1,875,000 + F) = $1,050,000
F = $825,000
(b)S*= = $1,650,000
15-20A.
(a) QB= = = 1,200 units
(b)S* = = = $600,000
(c)DOL$2,500,000 =
= 1.316 times
(d)(20%) x (1.316) = 26.32%
15-21A.
(a)QB = = = = 5,000 units
(b)S* = = = = = $125,000
(c)4000 units6000 units8000 units
Sales $100,000 $150,000 $200,000
Variable costs 60,000 90,000 120,000
Revenue before fixed costs $ 40,000 $ 60,000 $ 80,000
Fixed costs 50,000 50,000 50,000
EBIT $-10,000 $ 10,000 $ 30,000
(d)4000 units6000 units8000 units
= -4X = 6X = 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 = = = 24,000 units
Compute 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 = F
Compute the addition to fixed costs:
$168,000 - $120,000 = $48,000 addition
15-23A.DOL$360,000=
== 5 times
Any percentage change in sales will magnify EBIT by a factor of 5.
15-24A.
(a)DOL$480,000=
= = 2.5 times
(b)DFL$80,000= = 1.6 times
(c)DCL$480,000=
== 4 times
Alternatively:
(DOLS) x (DFLEBIT) = DCLS
(2.5) x (1.6) = 4 times
15-25A.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 (5) = 0.15
M = 0.03
Step (2)Compute the sales level associated with the given output level:
= 5
Sales = $15,000,000
Step (3)Compute EBIT:
(0.03) ($15,000,000) = EBIT = $450,000
Step (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) = $3,600,000
Step (5)Compute total variable costs:
Sales - Total variable costs = $3,600,000
$15,000,000 - Total variable costs = $3,600,000
Total variable costs = $11,400,000
Step (6)Compute total fixed costs:
RBF - Fixed costs = $450,000
$3,600,000 - Fixed costs = $450,000
Fixed costs = $3,150,000
Step (7)Find the selling price per unit, and the variable cost per unit:
P = = $9.375
V = = $7.125
Step (8)Compute the break-even point:
QB = = =
= 1,400,000 units
15-26A.Compute the present level of break-even output:
QB = = = 50,000 units
Compute 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 = F
Compute the addition to fixed costs:
$400,000 - $300,000 = $100,000 addition
15-27A.
(a) = = 3 times
(b) = = 1.25 times
(c)DCL$12,000,000 = (3) × (1.25) = 3.75 times
(d)S* = = =
= = $8,000,000
15-28A.
(a) = = 2 times
(b) = = 1.6 times
(c)DCL$16,000,000 = (2) (1.6) = 3.2 times
(d)(20%) (3.2) = 64%
(e)S* = = =
= $8,000,000
15-29A.ABCDTotal
Sales$40,000$50,000$20,000$10,000$120,000
Variable costs*24,00034,00016,0004,00078,000
Contribution margin$16,000$16,000$ 4,000$ 6,000$ 42,000
Contribution margin ratio40%32%20%60%35%
*Variable costs = (Sales) (1 - contribution margin ratio)
Break-even point in sales dollars:
S* = = = = $84,000
15-30A. A B C D Total
Sales$30,000$44,000$40,000 $6,000$120,000
Variable costs*18,00029,92032,0002,40082,320
Contribution margin$12,000$14,080$ 8,000$ 3,600$ 37,680
Contribution margin ratio40%32%20%60%31.4%
*Variable costs = (sales) (1- contribution margin ratio).
Break-even point in sales dollars:
S* = = = $93,631
Toledo's management would prefer the sales mix identified in problem 15-29A. 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 assets
M x 7 = 35%
M = 5%
STEP 2:Compute the sales level associated with the given output level:
Operating Assets x Operating Asset Turnover = Sales
$2,000,000 x 7 = Sales
Sales = $14,000,000
STEP 3:Compute EBIT:
Sales [STEP 2] x Operating Profit Margin [STEP 1] = EBIT
$14,000,000 x 5% = EBIT
EBIT = $700,000
STEP 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 Costs
Revenue before Fixed Costs = $3,500,000
STEP 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 Costs
Total Variable Costs = $10,500,000
STEP 6:Compute total fixed costs:
Revenue before Fixed Costs [STEP 4] - EBIT [STEP 3] = Fixed Costs
$3,500,000 - $700,000 = Fixed Costs
Fixed Costs = $2,800,000
STEP 7:Find selling price per unit (P) and variable cost per unit (V):
P = Sales [STEP 2] / Output in Units
P = $14,000,000 / 50,000 units
P = $280.00
V = Total Variable Costs [STEP 5] / Output in Units
V = $10,500,000 / 50,000 units
V = $210.00
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] $14,000,000
Variable Costs [STEP 5] 10,500,000
Revenue before Fixed Costs $3,500,000
Fixed Costs [STEP 6] 2,800,000
EBIT $700,000
Interest Expense 400,000
Earnings Before Taxes $300,000
Taxes (35%) 105,000
Net Income $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 = 5 x 2.33
DCLS = 11.65
(c)Break-even point in sales dollars:
S* =
S* =
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%
(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 inter-relationships of the various values:
% change in EBT = (EBTafter - EBTbefore) / EBTbefore
% change in EBT = ($1,350,000 - $300,000) / $300,000
% change in EBT = 350%
which agrees with the following:
% change in EBT = % change in Sales x DCLS
% change in EBT = 30% x 11.65
% change in EBT = 350%
SOLUTIONS TO PROBLEM SET B
15-1B.Break-even Quantity=QB
QB=
P==$.50 per unit
V==$.40 per unit
thus,
QB=
QB=24,000,000 units
15-2B.Degree of Combined Leverage=DCLS
Degree of Operating Leverage=DOLS
Degree of Financial Leverage=DFLEBIT
DOLS=
P==$.50 per unit
V==$.40 per unit
thus,
DOLS=
DOLS=2.50 times
DFLEBIT=
DFLEBIT=
DFLEBIT=2.00 times
and
DCLS=
DCLS=
DCLS=
DCLS=5.00 times
15-3B.
(a)QB= = = = 10,833 Units
(b)S*=(10,833 units) × ($175) = $1,895,775
Alternatively,
S* = =
= = = $1,895,833
Note: $1,895,833 differs from $1,895,775 due to rounding.
(c)10,00016,00020,000
unitsunitsunits
Sales $1,750,000 $2,800,000 $3,500,000
Variable costs 1,150,000 1,840,000 2,300,000
Revenue before fixed costs 600,000 960,000 1,200,000
Fixed costs 650,000 650,000 650,000
EBIT -$50,000 $ 310,000 $ 550,000
(d)10,000 units16,000 units20,000 units
= -12 times = 3.1 times = 2.2 times
Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point.
15-4B.
(a)DurhamRaleighCharlotte
FurnitureCabinetsColonials
Sales $1,600,000 $1,957,500 $525,000
Variable costs 1,100,000 1,080,000 236,250
Revenue before
fixed costs $500,000 $877,500 $288,750
Fixed costs 40,000 150,000 60,000
EBIT $460,000 $727,500 $228,750
(b)QB= = = = 6,400 units
QB= = = 769 units
QB= = = 3,117 units
(c)
DurhamRaleigh Charlotte
FurnitureFurniture Colonials
===
= 1.09 times1.21 times1.26 times
(d)Charlotte Colonials, since its degree of operating leverage exceeds that of the other two companies.
15-5B.
(a){S - [V + F]} (1 - T) = $55,000
{S – [S + F]} (1-T) = $55,000
{$400,008 - [257,148 + F ]} (0.55) = $55,000
($142,860 - F) (0.55) = $55,000
F = $42,860
(b)QB = = = = 4,286 units
S*= = = $120,056
15-6B.(a)Find the EBIT level at the forecast sales volume:
= .28
Therefore, EBIT = (0.28) ($3,750,000) = $1,050,000
Next, find total variable costs:
= 0.45,
so:VC = (0.45) $3,750,000 = $1,687,500
Now, solve for total fixed costs:
S - (VC + F) = $1,050,000
$3,750,000 - ($1,687,500 + F) = $1,050,000
F = $1,012,500
(b)S*= = $1,840,909
15-7B.
(a)= = 1.71 times
(b) = = 1.09 times
(c)DCL$40,000,000= (1.71) × (1.09) = 1.86 times
(d)S*==
= = = $16,666,667
(e)(20%) × (1.86) = 37.2%
15-8B.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:
= 5
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 6 times, revenue before fixed costs (RBF) is 6 times EBIT as follows:
RBF = (6) ($4,500,000) = $27,000,000
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:
P = = $12.86
V = = $9.00
Step (8)Compute the break-even point:
QB= =
= = 5,829,016 units
15-9B.
(a)QB= = = = 15,715 units
(b)S* = =
= = = $2,750,000
(c)12,00015,00020,000
UnitsUnitsUnits
Sales $2,100,000 $2,625,000 $3,500,000
Variable costs 1,680,000 2,100,000 2,800,000
Revenue before fixed costs $ 420,000 $ 525,000 $700,000
Fixed costs 550,000 550,000 550,000
EBIT -$130,000 -$25,000 $ 150,000
(d)12,000 units15,000 units20,000 units
= -3.2 times= -21 times= 4.67 times
15-10B.
(a)Farm CityEmpireGolden
SeedsSod Peaches
Sales $1,800,000 $1,710,000 $1,400,000
Variable costs 1,410,000 1,305,000 950,000
Revenue before fixed costs $390,000 $ 405,000 $ 450,000
Fixed costs 30,000 110,000 33,000
EBIT $ 360,000 $ 295,000 $ 417,000
(b)Farm City: QB = = = = 9,231 units
Empire Sod: QB = = = 2,444 units
Golden Peaches: QB= = = 3,667 units
(c)Farm CityEmpireGolden
SeedsSodPeaches
= 1.083 times= 1.373 times= 1.079 times
(d) Empire Sod, since its degree of operating leverage exceeds that of the other two companies.
15-11B.
(a){S – [V + F]} (1-T) = $38,000
{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
(b)QB = = = 17,398 units
S*= = = $295,766
15-12B.
(a){S – [V + f]} (1 – T) = $70,000
{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 == = 25,847 units
S*== =
=$1,938,552.66
15-13B.
(a)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:
175,000 (P)=$3,025,000
P=$17.29
(b)Sales $3,025,000
Less: Total variable costs 2,420,000
Revenue before fixed costs $605,000
Less: Total fixed costs 335,000
EBIT $ 270,000
15-14B.
(a)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
(b)Sales $2,200,000
Less: Total variable costs 1,650,000
Revenue before fixed costs $550,000
Less: Total fixed costs 300,000
EBIT $ 250,000
15-15B.
(a)First, find the EBIT level at the forecast sales volume:
= 0.25
So:EBIT = (0.25) $4,250,000 = $1,062,500
Next, find total variable costs:
= 0.6
So:VC = (0.60) $4,250,000 = $2,550,000
Then, solve for total fixed costs:
S - (VC + F) = $1,062,500
$4,250,000 - ($2,550,000 + F) = $1,062,500
F = $637,500
(b)S* = = $1,593,750
15-16B.
(a)QB = == 1,600 units
(b)S* = == $760,000
(c)DOL$2,850,000=
=1.364 times
(d)(13%) x (1.364)=17.73%
15-17B.
(a)QB = = = = 5,000 units
(b)S*= = = = = $140,000
(c)4,000 units6,000 units8,000 units
Sales $112,000 $168,000 $224,000
Variable costs 68,000 102,000 136,000
Revenue before fixed costs $ 44,000 $ 66,000 $ 88,000
Fixed costs 55,000 55,000 55,000
EBIT -$11,000 $ 11,000 $ 33,000
(d)4000 units6000 units8000 units
= -4X = 6X = 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 = = = 19,286 units
Compute 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 = F
Compute the addition to fixed costs:
$154,288 - $135,000 = $19,288 addition
15-19B.DOL$520,000=
= = 1.93 times
Any percentage change in sales will magnify EBIT by a factor of 1.93.
15-20B.
(a)DOL$650,000=
== 1.63 times
(b)DFL$215,000== 1.39 times
(c)DCL$650,000 =
= = 2.26 times
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:
= 6
Sales = $19,500,000
Step (3)Compute EBIT:
(0.0267) ($19,500,000) = EBIT = $520,000
Step (4)Compute revenue before fixed costs. Since the degree of operating leverage is 9 times, revenue before fixed costs (RBF) is 9 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:
P = = $11.471
V = = $8.718
Step (8)Compute the break-even point:
QB = = = = 1,511,079 units
15-22B. Compute the present level of break-even output:
QB = = = 31,250 units
Compute 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 = F
Compute the addition to fixed costs:
$437,500 - $375,000 = $62,500 addition
15-23B.
(a)= = 3.4 times
(b) = = 1.25 times
(c)DCL$13,750,000 = (3.4) × (1.25) = 4.25 times
(d)S* ==
== = $9,705,597
15-24B.
(a) = = 2.2 times
(b) = = 1.54 times
(c)DCL$18,000,000 = (2.2) × (1.54) = 3.39 times
(d)(15%) × (3.39) = 50.8%
(e)S* = =
= = $9,819,967
15-25B.ABCDTotal
Sales$38,505$61,995$29,505$19,995$150,000
Variable costs*23,10342,15723,6047,99896,862
Contribution margin$15,402$19,838$ 5,901$ 11,997$ 53,138
Contribution margin ratio40%32%20%60%35.43%
*Variable costs = (Sales) (1 - contribution margin ratio)
Break-even point in sales dollars:
S* = = = $98,799