11. Degree of leverage (LO2 and 5) The Harding Company manufactures skates. The
company’s income statement for 20X1 is as follows:
HARDING COMPANY
Income Statement
For the Year Ended December 31, 20X1
Sales (10,500 skates @ $60 each)…………………………… $630,000
Less: Variable costs (10,500 skates at $25)………………. 262,500
Fixed costs……………………………………………………….. 200,000
Earnings before interest and taxes (EBIT)……………….. 167,500
Interest expense……………………………………………………. 62,500
Earnings before taxes (EBT)………………………………….. 105,000
Income tax expense (30%)…………………………………….. 31,500
Earnings after taxes (EAT)…………………………………….. $ 73,500
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:
Harding Company
a.
( VC)
DOL ( VC) FC
10,500($60 $25)
10,500($60 $25) $200,000
10,500($35)
10,500($35) $200,000
$367,500 $367,500 2.19x
Q P
Q P
–
=– –
–
=– –
=–
5-11. (Continued)
b.
EBIT $167,500
DFL EBIT $167,500 $62,500
$167,500 1.60x
$105,000
I
= =
– –
= =
c.
( VC)
DCL ( VC) FC
10,500($60 $25)
10,500($60 $25) $200,000 $62,500
$10,500($35) $367,500 3.50x
$10,500($35) $262,500 $105,000
Q P
Q P I
–
=– – –
–
=– – –
= = =
–
d.
$200,000 $200,000
BE 5,714 skates
$60 $25 $35
= = =
–
12. Break-even point and degree of leverage (LO2 and 5) Healthy Foods Inc. sells 50-pound
bags of grapes to the military for $10 a bag. The fixed costs of this operation are $80,000,
while the variable costs of grapes are $0.10 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 Healthy Foods 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?
5-12. Solution:
Healthy Foods Inc.
a.
$80,000 $80,000
BE 16,000 bags
$10 ($0.10 50) $5
= = =
– ´
b. 12,000 bags 25,000 bags
c.
( VC)
DOL ( VC) FC
20,000($10 $5)
DOL at 20,000 20,000 ($10 $5) $80,000
$100,000 5.00x
$20,00
Q P
Q P
–
=– –
–
=– –
= =
Leverage goes down because we are further away from the break-even point, thus
the firm is operating on a larger profit base and leverage is reduced.
5-12. (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
e. What is the degree of combined leverage at both sales levels?
5-13. Solution:
United Snack Company
a.
$176,250 $176, 250
BE 14,100 bags
$20 ($.15 50) $12.50
= = =
– ´
b.
7,000 bags 20,000 bags
Sales @ $20 per bag $140,000 $400,000
5-13. (Continued)
c.
( VC)
DOL ( VC) FC
19,000($20 $7.50)
DOL at 19,000 19,000 ($20 $7.50) $176,250
$237,500 3.88x
$61,250
Q P
Q P
–
=– –
–
=– –
= =
24,000 ($20 $7.50)
DOL at 24,000 24, 000($20 $7.50) $176, 250
$300, 000 2.42x
$123,750
–
=– –
= =
Leverage goes down because we are further away from the break-even point, thus
the firm is operating on a larger profit base and leverage is reduced.
5-13. (Continued)
d.
EBIT
DFL EBIT I
=–
First determine the profit or loss (EBIT) at 19,000 bags and at 24,000 bag:
19,000 bags 24,000 bags
$61,250
DFL at 19,000 $61, 250 $15, 000
1.32x
=–
=
$123,750
DFL at 24,000 $123,750 $15,000
1.14x
=–
=
e.
( VC)
DCL ( VC) FC
Q P
Q P I
–
=– – –
19,000 ($20 $7.50)
DCL at 19,000
19,000($20 $7.50) $176, 250 $15,000
$237,500 5.14x
$46, 250
–
=– – –
= =
24,000 ($20 $7.50)
DCL at 24,000 24, 000($20 $7.50) $176,250 $15,000
$300, 000 2.76x
$108,750
–
=– – –
= =
b. Sales (205,000 $8.80)……………………………………………………. $1,804,000
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)
60,000 $ 120,000 $50,000 $170,000 $360,000 $190,000
80,000 160,000 50,000 210,000 480,000 270,000
a. Compute DOL based on the following formula:
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. There may be a slight difference due to rounding.
( VC)
DOL ( VC) FC
Q P
Q P
–
=– –
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
$80, 000
42%
190, 000 1.27
20, 000 33%
60, 000
=
= = =
b.
( VC)
DOL ( VC) FC
Q P
Q P
–
=– –
60,000
Total revenue $360,000 $6
Units sold 60,000
Total variable costs $120,000
VC $2
Units sold 60,000
FC $50,000
60,000 ($6 $2) $240,000
DOL 60,000($6 $2) $50,000 $240,000 $50,000
$240,000 1.26
$190,000
Q
P
=
= = =
= = =
=
–
= =
– – –
= =
16. Earnings per share and financial leverage (LO4) Lenow’s Drug Stores and Hall’s
Pharmaceuticals are competitors in the discount drug chain store business. The separate
capital structures for Lenow and Hall are presented next.
Lenow Hall
Debt @ 10%……………………. $100,000 Debt @ 10%…………………….. $200,000
Common stock, $10 par……. 200,000 Common stock, $10 par…….. 100,000
Total……………………………….. $300,000 Total………………………………… $300,000
Shares…………………………….. 20,000 Common shares………………… 10,000
5-16. Solution:
a. Lenow Drug Stores and Hall Pharmaceuticals
EBIT $ 20,000 $ 20,000
Less: Interest 10,000 20,000
EBT 10,000 0
5-16. (Continued)
b. Before-tax return on assets = 6.67 percent, 10 percent, and 40 percent at the
respective levels of EBIT. When the before-tax return on assets (EBIT/Total
assets) is less than the cost of debt (10 percent), Lenow does better with less debt
17. P/E ratio (LO6) The capital structure for Cain Supplies is presented next. Compute the
stock price for Cain if it sells at 19 times earnings per share and EBIT is $50,000. The tax
rate is 20 percent.
Cain
Debt @ 9%…………………….. $100,000
Common stock, $10 par……. 200,000
Total…………………………… $300,000
Common shares………………. 20,000