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Chapter 05: Operating and Financial Leverage
c.
Q (P VC)
DCL Q(P VC) FC I
20,000($60 $30)
20,000($60 $30) $400,000 $50,000
$600,000 $600,000 4x
$600,000 $400,000 $50,000 $150,000
−
=
− − −
−
=
− − −
= = =
−−
d.
$400,000 $400,000
BE 13,333 units
$60 $30 $30
= = =
−
11. Degree of leverage (LO2 & 5) The Harding Company manufactures skates. The
company's income statement for 2010 is as follows:
HARDING COMPANY
Income Statement
For the Year Ended December 31, 2010
Sales (10,000 skates @ $50 each) ................................
$500,000
Less: Variable costs (10,000 skates at $20) ..................
200,000
Fixed costs ..............................................................
150,000
Earnings before interest and taxes (EBIT) ...................
150,000
Interest expense ...........................................................
60,000
Earnings before taxes (EBT) .......................................
90,000
Income tax expense (40%) ..........................................
36,000
Earnings after taxes (EAT) ..........................................
$ 54,000
Given this income statement, compute the following:
a. Degree of operating leverage.
b. Degree of financial leverage.
c. Degree of combined leverage.
d. Break-even point in units (number of skates).
5-11. Solution:
Chapter 05: Operating and Financial Leverage
Harding Company
Q = 10,000, P = $50, VC = $20, FC = $150,000, I = $60,000
a.
Q(P VC)
DOL Q(P VC) FC
10,000($50 $20)
10,000($50 $20) $150,000
10,000($30)
10,000($30) $150,000
$300,000 $300,000 2.00x
$300,000 $150,000 $150,000
−
=
−−
−
=
−−
=
−
= = =
−
5-11. (Continued)
b.
EBIT $150,000
DFL EBIT I $150,000 $60,000
$150,000 1.67x
$90,000
==
−−
==
c.
Q (P VC)
DCL Q(P VC) FC I
10,000($50 $20)
10,000($50 $20) $150,000 $60,000
−
=
− − −
−
=
− − −
Chapter 05: Operating and Financial Leverage
d.
$150,000 $150,000
BE 5,000 skates
$50 $20 $30
= = =
−
12. Break-even point and degree of leverage (LO2 & 5) Mo & Chris's Delicious Burgers,
Inc., sells food to Military Cafeterias for $15 a box. The fixed costs of this operation are
$80,000, while the variable cost per box is $10.
a. What is the break-even point in boxes?
b. Calculate the profit or loss on 15,000 boxes and on 30,000 boxes.
c. What is the degree of operating leverage at 20,000 boxes and at 30,000 boxes?
Why does the degree of operating leverage change as the quantity sold increases?
d. If the firm has an annual interest expense of $10,000, calculate the degree of
financial leverage at both 20,000 and 30,000 boxes.
e. What is the degree of combined leverage at both sales levels?
5-12. Solution:
Moe & Chris’ Delicious Burgers, Inc.
a.
$80,000 $80,000
BE 16,000 boxes
$15 $10 $5
= = =
−
b.
15,000
boxes
30,000 boxes
Sales @ $15 per box
$225,000
$450,000
Less: Variables Costs ($10)
($150,000)
($300,000)
Fixed Costs
($ 80,000)
($ 80,000)
Profit or Loss (EBIT)
($ 5,000)
$ 70,000
c.
Q(P VC)
DOL Q(P VC) FC
20,000($15 $10)
DOL at 20,000 20,000 ($15 $10) $80,000
$100,000 5.0x
$20,000
−
=
−−
−
=
−−
==
Chapter 05: Operating and Financial Leverage
30,000 ($15 $10)
DOL at 30,000 30,000($15 $10) $80,000
$150,000 2.14x
$70,000
−
=
−−
==
base and leverage is reduced.
5-12. (Continued)
d.
EBIT
DFL EBIT I
=
−
$70,000:
20,000 boxes
Sales @ $15 per bag
$300,000
Less: Variable Costs ($10)
(200,000)
Fixed Costs
80,000
Profit or Loss (EBIT)
$ 20,000
$20,000
DFL at 20,000 $20,000 $10,000
$20,000 2.0x
$10,000
=
−
==
$70,000
DFL at 30,000 $70,000 $10,000
$70,000 1.17x
$60,000
=
−
==
Chapter 05: Operating and Financial Leverage
e.
Q (P VC)
DCL Q(P VC) FC I
−
=
− − −
20,000 ($15 $10)
DCL at 20,000
20,000($15 $10) $80,000 $10,000
$100,000 10.0x
$10,000
−
=
− − −
==
5-12. (Continued)
30,000 ($15 $10)
DCL at 30,000 30,000($15 $10) $80,000 $10,000
$150,000 2.50x
$60,000
−
=
− − −
==
13. Break-even point and degree of leverage (LO2 & 5) United Snack Company sells
50-pound bags of peanuts to university dormitories for $10 a bag. The fixed costs of this
operation are $80,000, while the variable costs of peanuts are $.10 per pound.
a. What is the break-even point in bags?
b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.
c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why
does the degree of operating leverage change as the quantity sold increases?
d. If United Snack Company has an annual interest expense of $10,000, calculate the
degree of financial leverage at both 20,000 and 25,000 bags.
e. What is the degree of combined leverage at both sales levels?
5-13. Solution: United Snack Company
a.
$80,000 $80,000
BE 16,000 bags
$10 ($.10 50) $5
= = =
−
b.
Chapter 05: Operating and Financial Leverage
12,000 bags
25,000 bags
Sales @ $10 per bag
$120,000
$250,000
Less: Variables Costs ($5)
(60,000)
(125,000)
Fixed Costs
(80,000)
(80,000)
Profit or Loss (EBIT)
($ 20,000)
$ 45,000
5-13. (Continued)
c.
Q(P VC)
DOL Q(P VC) FC
20,000($10 $5)
DOL at 20,000 20,000 ($10 $5) $80,000
$100,000 5.00x
$20,000
−
=
−−
−
=
−−
==
25,000 ($10 $5)
DOL at 25,000 25,000($10 $5) $80,000
$125,000 2.78x
$45,000
−
=
−−
==
Chapter 05: Operating and Financial Leverage
5-13. (Continued)
d.
EBIT
DFL EBIT I
=
−
First determine the profit or loss (EBIT) at 20,000 bags. As
indicated in part b, the profit (EBIT) at 25,000 bags is
$45,000:
20,000 bags
Sales @ $10 per bag
$200,000
Less: Variable Costs ($5)
100,000
Fixed Costs
80,000
Profit or Loss (EBIT)
$ 20,000
$20,000
DFL at 20,000 $20,000 $10,000
2.0x
=
−
=
$45,000
DFL at 25,000 $45,000 $10,000
1.29x
=
−
=
e.
Q (P VC)
DCL Q(P VC) FC I
−
=
− − −
20,000 ($10 $5)
DCL at 20,000
20,000($10 $5) $80,000 $10,000
$100,000 10.0x
$10,000
−
=
− − −
==
25,000 ($10 $5)
DCL at 25,000 25,000($10 $5) $80,000 $10,000
$125,000 3.57x
$35,000
−
=
− − −
==
Chapter 05: Operating and Financial Leverage
5-18
14. Nonlinear breakeven analysis (LO2) International Data Systems information on revenue
and costs is only relevant up to a sales volume of 100,000 units. After 100,000 units, the
market becomes saturated and the price per unit falls from $4.00 to $3.80. Also, there are
cost overruns at a production volume of over 100,000 units, and variable cost per unit goes
up from $2.00 to $2.20. Fixed costs remain the same at $50,000.
a. Compute operating income at 100,000 units.
b. Compute operating income at 200,000 units.
5-14. Solution:
International Data Systems
a.
Sales (100,000 $4) ........................................
$400,000
Total variable costs (100,000 $2) ..................
200,000
Fixed costs .......................................................
50,000
Operating income .............................................
$150,000
b.
Sales (200,000 $3.80) ...................................
$760,000
Total variable costs (200,000 $2.20) .............
440,000
Fixed costs .......................................................
50,000
Operating income .............................................
$270,000
Chapter 05: Operating and Financial Leverage
15. Use of different formulas for operating leverage (LO3) U.S. Steal has the following
income statement data:
Units
Sold
Total
Variable
Costs
Fixed
Costs
Total
Costs
Total
Revenue
Operating
Income
(Loss)
40,000
$ 80,000
$50,000
$130,000
$160,000
$30,000
60,000
120,000
50,000
170,000
240,000
70,000
a. Compute DOL based on the formula below (see page 128 for an example):
Percent change in operating income
DOL Percent change in units sold
=
b. Confirm that your answer to part a is correct by recomputing DOL using formula 5–3
on page 129. There may be a slight difference due to rounding.
Q(P VC)
DOL Q(P VC) FC
−
=
−−
Q represents beginning units sold (all calculations should be done at this level).
P can be found by dividing total revenue by units sold.
VC can be found by dividing total variable costs by units sold.
5-15. Solution:
U. S. Steal
a.
Percent change in operating income
DOL Percent change in units sold
$40,000 133%
30,000 2.66
20,000 50%
40,000
=
= = =
b.
Q(P VC)
DOL Q(P VC) FC
−
=
−−
Chapter 05: Operating and Financial Leverage
Q 40,000
Total revenue $160,000
P $4
Units sold 40,000
Total variable costs $80,000
VC $2
Units sold 40,000
FC $50,000
40,000 ($4 $2) $80,000
DOL 40,000($4 $2) $50,000 $80,000 $50,000
$80,000 2.67
$30,000
=
= = =
= = =
=
−
==
− − −
==
16. Earnings per share and financial leverage (LO4) Cain Auto Supplies and Able Auto
Parts are competitors in the aftermarket for auto supplies. The separate capital structures
for Cain and Able are presented below.
Cain
Able
Debt @ 10% .......................
$ 50,000
Debt @ 10% ..................
$100,000
Common stock, $10 par ......
100,000
Common stock, $10 par.
50,000
