# Calculate Optimal Capital Structure

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```					Question 9
EBIT – EPS and capital structure. Data-Check is considering two capital structures.
The key information is shown in the following table. Assume a 40 percent tax rate.

Source of            Structure A                       Structure B
capital
Long-term debt       R100 000 at 16% coupon            R200 000 at 17% coupon
rate                              rate
Common stock         4 000 shares                      2 000 shares

a.Calculate two EBIT-EPS coordinates for each of the structures by selecting any two
EBIT values and finding their associated EPS.
b.Plot the two capital structures on a set of EBIT-EPS axes.
c.Indicate over what EBIT range, if any, each structure is preferred.
d.Discuss the leverage and risk aspects of each structure.
e.If the firm is fairly certain that its EBIT will exceed R75 000, which structure would you
recommend? Why?
Question 9:
CAPITAL STRUCTURE – LEVERAGE:
STRUCTURE A             STRUCTURE B

EBIT     ………     ………    ………     ………
- Int    ………     ………    ………     ………
EAIBT    ………     ……….   ………     ………
- Tax    ………     ………    ………..   ………
EAIT     ………     ………    ……….    ……….
EPS      ………     ………    ……….    ……….
………     ……….   ……….    ……….
=     ………     ……….   ……….    ………..
[(EBIT – I) X (1 – T)] – PD = [(EBIT – I) X (1 – T)] – PD
n                               n

[(EBIT –_____) X _____)] – _____ = [(EBIT – ____) X____] – _____
………………..                               ………………

____+EBIT – _____ – _____ =             ____EBIT – ____ –______
………………                                ………………

______EBIT – _____             =      _____EBIT – _______
……………..                                …………….

_________ EBIT – ________________= _______EBIT – ________

_________EBIT = ______________

EBIT = R______________
WHAT DOES THIS
MEAN?
• IF THE COMPANY’S EBIT IS
LESS THAN R52 000, THEN THE
CAPITAL STRUCTURE TO
CHOOSE IS STRUCTURE A.
• WHY? BECAUSE STRUCTURE A
HAS THE HIGHEST EPS AT AN
EBIT BELOW R52 000.
• IF THE COMPANY’S EBIT IS
GREATER THAN R52 000, THEN
THE CAPITAL STRUCTURE TO
CHOOSE IS STRUCTURE B.
• WHY? BECAUSE STRUCTURE B
HAS THE HIGHEST EPS AT AN
EBIT ABOVE R52 000.
AND WHAT OFTEN
HAPPENS AS A
RESULT?
• THE INEXPERIENCED FINANCIAL MANAGER
WILL THEN CHOOSE STRUCTURE B AS
LONG AS THE COMPANY’S EBIT IS GREATER
THAN R52 000.
• HOWEVER, THIS MAY BE SHORTSIGHTED.
STRUCTURE B HAS MORE DEBT (DOUBLE
THAT OF STRUCTURE A). IN ADDITION,
STRUCTURE B ALSO DEMANDS A HIGHER
INTEREST RATE AND THEREFORE A
GREATER AMOUNT OF INTEREST TO BE
PAID (R34 000 VERSUS R16 000).
• SO, STRUCTURE B IS A FAR MORE RISKY
STRUCTURE AND MUST THEREFORE BE
USED WITH CAUTION.
THE ILLUSION OF
WEALTH
• BY USING STRUCTURE B, THE COMPANY IS
STRUCTURE B ENABLES THE COMPANY TO
SHOW A MUCH HIGHER EPS AS LONG AS
THE COMPANY’S EBIT IS GREATER THAN
R52 000.
• HOW HAS THIS HAPPENED?
• INTEREST PAID ON DEBT IS TAX
DEDUCTIBLE. AS A RESULT, THE COMPANY
IS ABLE TO REDUCE ITS TAX BURDEN
BECAUSE THE INTEREST THAT IT PAYS
REDUCES ITS TAXABLE INCOME.
• THIS IS KNOWN AS THE “TAX SHIELD”
ACCORDING TO MODIGLIANI AND MILLER
(MM).
Question 10
EBIT-EPS and preferred stock. Litho-Print is considering two possible capital structures,
A and B, shown in the following table. Assume a 40 percent tax rate.

Source of capital   Structure A                Structure B
Long-term debt      R75 000 at 16% coupon      R50 000 at 15% coupon
rate                       rate
Preferred stock     R10 000 with an 18%        R15 000 with an 18%
annual dividend            annual dividend
Common stock        8 000 shares               10 000 shares

a.Calculate two EBIT-EPS coordinates for each of the structures by selecting any
two EBIT values and finding their associated EPS.
b.Graph the two capital structures on the same set of EBIT-EPS axes.
c.Discuss the leverage and risk associated with each of the structures.
d.Over what range of EBIT is each structure preferred?
e.Which structure do you recommend if the firm expects its EBIT to be R35,000?
Explain
Question 10
CAPITAL STRUCTURE AND LEVERAGE

STRUCTURE A        STRUCTURE B
EBIT      ______   ______    ______   _______
-   INT   ______   ______    ______   _______
EAIBT    ______    _______   _______ ________
- TAX ______       _______   _______ _______
EARNINGS ______    _______   _______ _______
- PD      _____    ______    _______ ______
EAIT     ______    _______   ________ _______

EPS       ______ _______     _______ _______
………. …………          ………. …………
= R____ R______    = R____ R______
Question 10 Contd:

CAPITAL STRUCTURE – LEVERAGE:

A
EPS                                        B
_____

_____

_____

_____

0         ________   ________
EBIT
X=?
[(EBIT – I) X (1 – T)] – PD = [(EBIT – I) X (1 – T)] – PD
n                               n

[(EBIT –……….) X …)] = [(EBIT – ………..) X …….]
………….                …………..

……………                 =    ……………………
…………                        …………..

…………. – …………..             = …………. – ……………

…..………..       = ……………..

EBIT = ………………
Question 11
Integrative – Optimal capital structure. Nelson Corporation has made the following
forecast of sales, with the associated probability of occurrence noted.

Sales               Probability
R200,00                         .20
300,000                         .60
400,000                         .20

The company has fixed operating costs of R100 000 per year, and variable
operating costs represent 40 percent of sales. The existing capital structure
consists of 25 000 shares of common stock that have a R10 per share book
value. No other capital items are outstanding. The marketplace has assigned the
following discount rates to risky earnings per share.

Coefficient of        Estimated required
variation of EPS          return, ks(%)
.43                       15%
.47                        16
.51                        17
.56                        18
.60                        22
.64                        24
The company is contemplating shifting its capital structure by substituting debt in the
capital structure for common stock. The three different debt ratios under consideration
are shown in the following table, along with an estimate of the corresponding required
interest rate on all debt.
Interest rate
Debt ratio             on
all debt
20%                  10%
40                      12
60                      14

The tax rate is 40 percent. The market value of the equity for a levered firm can be
found by using the simplified method.
a.Calculate the expected earnings per share (EPS), the standard deviation of EPS,
and the coefficient of variation of EPS for the three proposed capital structures.
b.Determine the optimal capital structure, assuming (1) maximisation of earnings per
share and (2) maximisation of share value.
c.Construct a graph showing the relationships in b.
Question 11:
DEBT     EQUITY

A

B

C

D

STRUCTURE B:
………..    ……….     …………
Sales           ……….     ………..    ………...
- FC            ……….     ………..    …………
- VC             ……..    ………..    …………
EBIT             ……...    ………     …………
- Int             …….      ……..    ……...
EAIBT            ………      ………     …………
- Tax             …….     ………     ……….
EAIT              …….     ………     ……….
EPS         =     …….     ………     ……….
……...    ………     ……….
=   ……….     ………..    …………

EPS = (………..x……..) + (………x……) + (……..x………)
= …………….
n
x    =      (xi – x)² x Pri
i=1

n

x    =      (EPSi – EPS)² x Pri
i=1

=    [(…………)² x ……]
+[(…………)² x ……]
+[(…………)² x ……]

=   R1,14

CVx   =    x
x

CVEPS =    EPS
EPS
=   ………

=   ………
P0    =   EPS
k
=   ………

=   ………
EPS      CV   k   P0
A
B
C
D
WHAT DOES THE
GRAPH TELL US?
• IF YOU WANTED TO MAXIMISE EARNINGS,
THEN YOU WILL CHOOSE STRUCTURE D.
• WHY? BECAUSE IT HAS THE HIGHEST EPS.
• IF YOU WANTED TO MAXIMISE SHARE
PRICE, THEN YOU WILL CHOOSE
STRUCTURE C.
• WHY? BECAUSE IT HAS THE HIGHEST
SHARE PRICE.
• SO, WHICH IS THE BETTER STRUCTURE TO
CHOOSE???
OURSELVES WHAT THE GOAL OF THE
FINANCIAL MANAGER IS?
• ANSWER = TO MAXIMISE THE WEALTH OF
THE SHAREHOLDERS.
SHAREHOLDERS
WEALTH
MAXIMISATION
• HOW DO WE MAXIMISE SHAREHOLDERS
WEALTH?
• IS IT THROUGH MAXIMISING EARNINGS OR
MAXIMISING THE SHARE PRICE???
• SHAREHOLDERS WEALTH IS MAXIMISED
THROUGH …
• SHARE PRICE.
• THEREFORE, THE COMPANY SHOULD
CHOOSE STRUCTURE C.
HOW COME THE GRAPH
HAS THE SHAPE IT DOES
(CURVES)?
• WHAT YOU HAVE SEEN IS THAT THE
COMPANY WAS ABLE TO GENERATE
HIGHER EPS BY MANIPULATING THE
CAPITAL STRUCTURE ONLY!
• THE COMPANY DID NOT MAKE MORE SALES.
IT DID NOT LOWER COSTS. ALL IT DID WAS
CHANGE (MANIPULATE) THE DEBT:EQUITY
RATIO.
• IN ESSENCE, THEY HAVE USED THE TAX
SHIELD ON INTEREST TO ACHIEVE THIS
INCREASE IN EPS.
CAPITAL
STRUCTURE THEORY
(MM)
•   ACCORDING TO MM, A COMPANY’S OPTIMAL
CAPITAL STRUCTURE IS 100% DEBT, NO EQUITY.
•   WHY?
•   BECAUSE, INTEREST IS TAX DEDUCTIBLE (TAX
SHIELD). DIVIDENDS ARE NOT TAX DEDUCTIBLE
– THEY ARE PAID AFTER TAX HAS BEEN PAID.
•   IN ADDITION, EQUITY (ORDINARY SHARES) IS THE
MOST EXPENSIVE SOURCE OF CAPITAL (REFER
BACK TO WACC).
•   THEREFORE, ACCORDING TO MM, THE OPTIMAL
CAPITAL STRUCTURE IS 100% DEBT.
•   IS THIS ALWAYS PRACTICAL?
•   THE MORE DEBT THAT A COMPANY HAS, THE
CLOSER IT IS TO BANKRUPTCY (FINANCIAL
DISTRESS). THERE ARE ONLY CERTAIN TYPES
OF COMPANIES/INDUSTRIES THAT WE WOULD BE
WILLING TO ACCEPT HIGHER DEBT RATIOS.
•   THESE ARE COMPANIES THAT HAVE A VERY
HEAVY FIXED ASSET BASE, EG, PROPERTY,
MINING.
CAPITAL
STRUCTURE THEORY
(MM)
• LET US ASSUME THAT WE HAVE A
COMPANY THAT HAS 100% EQUITY AND
WOULD LIKE TO TAKE ON DEBT.
• WE KNOW THAT DEBT IS CHEAPER THAN
EQUITY. THEREFORE WHAT DO YOU
EXPECT WILL HAPPEN TO THE COMPANY’S
WACC AS THEY TAKE ON DEBT AND
SUBSTITUTE IT FOR EQUITY?
• THE WACC WILL DECLINE.
• THEREFORE, ACCORDING TO MM, THE
OPTIMAL CAPITAL STRUCTURE IS 100%
DEBT.
• BUT, AS THE COMPANY TAKES ON
INCREASING AMOUNTS OF DEBT, THE RISK
FOR THE LENDER INCREASES. AS A
RESULT, THE COST OF DEBT (Kd) WILL
REACH A POINT WHERE IT WILL START TO
INCREASE AGAIN.
OPTIMAL CAPITAL
STRUCTURE
•   ANY COMPANY SHOULD TRY TO DETERMINE THE
POINT AT WHICH ITS WACC IS AT A MINIMUM.
•   APART FROM THE FACT THAT THE LOWER THE
WACC, THE LESS MONEY IT COSTS THE FIRM TO
MAINTAIN THAT CAPITAL, THE COMPANY WILL
THEN HAVE THE LOWEST DISCOUNT RATE THAT
IT CAN ACHIEVE.
•   WE KNOW THAT THE DISCOUNT RATE IS THE
RATE THAT IS USED TO CALCULATE PROJECT
NPVs. THEREFORE, THE LOWER THE DISCOUNT
RATE, THE MORE LIKELY A PROJECT IS TO BE
ACCEPTABLE (THE SMALLER THE DISCOUNT
RATE, THE HIGHER THE NPV).
•   THE MORE PROJECTS THAT THE FIRM CAN
INVEST IN, THE MORE VALUE THAT WILL BE
OPTIMAL CAPITAL
STRUCTURE
• THE MORE VALUE THAT IT IS ADDED TO THE
FIRM, THE GREATER THE WEALTH OF
SHAREHOLDERS.
• THE GREATER THE WEALTH OF THE
SHAREHOLDERS, THE HIGHER THE SHARE
PRICE.
• THEREFORE, THE FIRM’S OPTIMAL CAPITAL
STRUCTURE WILL BE THE POINT AT WHICH:
– THE WACC IS AT A MINIMUM,
– WHICH WILL CORRESPOND TO THE POINT
WHERE THE SHARE PRICE IS AT A MAXIMUM.
THE COMPANY’S
DECISIONS
• THE COMPANY MUST FIRSTLY
DECIDE UPON ITS CAPITAL
STRUCTURE.
• THE CAPITAL STRUCTURE
THAT THE COMPANY USES
WILL DETERMINE THE
COMPANY’S WACC.
• THE WACC IS THE DISCOUNT
RATE THAT THE COMPANY
USES TO CALCULATE THE NPV
OF NEW PROJECTS THAT IT IS
PLANNING ON INVESTING IN.
DIVIDEND POLICY

1) Relevance:
-Relevant
-Gordon + Lintner – “Bird in the hand”

Main Co
Granny

Trust                   
A Co       B Co       C Co

2) Irrelevance:
- M+M
-Co to invest in +ve NPV projects.
-Any balance to be paid out as a dividend( residual)
RE = ………..        Debt =…………
Project =………      Equity =……….

Under residual theory:

Project =…………..

Debt                     Equity
…….                      ……..
…….                      …….

……..         ……..
RE           New
Shares

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