Topic 7 Capital Structure-1

8/14/2019 Topic 7 Capital Structure-1

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Topic 7 Capital Structure

Overview

This topic is concerned with the issue of whether there exists an Optimal

Capital Structure, one that maximizes the value of the firm.

In order to address the issue, one needs to first examine the effect on equity

holders of introducing Financial Leverage into the firms capital structure

Financial Leverage refers to the extent to which a firm relies on debt.


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Returns

RETURN AVAILABLE TO SHAREHOLDERS

reflects the earning capacity of the firms assets

REQUIRED RATE OF RETURN TO SHAREHOLDERS

the minimum return demanded by shareholders given theinvestment risk

reflects trade- off between risk and return


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Firms Cash Flows

REVENUE

Fixed operating costsVariable operating costs

InterestNET INCOME[NI]

less

equalsNET OPERATING INCOME

[NOI]

less

equals


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Example

Assume that there are 3 identical firms, a , b and c.

Identical in all respects apart from the way in which the firm is financed.

We are initially neglecting the effects of corporate taxation

In each case the firm has total assets of $400,000 and but the mix of debtand equity used to finance these assets differ

We assume that the return that the firm can earn on its assets in each

case is the case, 15%

Therefore, Net Operating Income of all 3 firms is the same at $60,000

The firms that use debt pay 10% interest


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(a)All equity

$

(b)50% debt

50% equity

(c)75% debt

25 % equity

Equity 400,000 200,000 100,000

Debt 200,000 300,000

Total Assets 400,000 400,000 400,000

Debt/Equity ratio 0 1:1 3:1

Net operating Income 60,000 60,000 60,000

Interest (at 10%) 20,000 30,000

Net Income 60,000 40,000 30,000

Return on Assets 15% 15% 15%

(Available) Return on Equity 15% 20% 30%


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The previous analysis can be captured in algebraic form

Let = return available to equity holders

= return provided by the firms assets

aer

afr

E

DrEDrr dafae

E

Drrrrdafafae

aer

Net cash flow - interest

from firms assets payments

equity investments

=


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What happens to the available return to equity holders asresult of the return earned on the firms assets decreasing?

Initially the return on the firms assets of $400,000 was 15%giving a NOI of $60,000. We now assume the return onassets falls to 9% giving a NOI of $36,000

It will be shown that the greater is the D/E ratio the greaterthe drop in the available rate of return to equity holders


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(a)

All equity

$

(b)

50% debt

50% equity

(c)

75% debt

25 % equity

Equity 400,000 200,000 100,000

Debt 200,000 300,000

Total Assets 400,000 400,000 400,000

Debt/Equity ratio 0 1:1 3:1

Net operating Income 36,000 36,000 36,000

Interest (at 10%) 20,000 30,000

Net Income 36,000 16,000 6,000

Return on Assets 9% 9% 9%

Available Return on Equity 9% 8% 6%

Change in available

return on equity-40% -60% -80%


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Financing Structure Different levels of NOI ($000)

0 20 40 60 80

(a) All equity 0% 5% 10% 15% 20%

(b) 50% debt, 50% equity -10% 0% 10% 20% 30%

(c) 75% debt, 25% equity -30% -10% 10% 30% 50%

The below table shows the greater the debt to equity ratio the

greater the change in the available return to equity holders as a

result of a change in the level of Net Operating Income (NOI)


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Effects Of Financial Leverage

The substitution of debt for equity in the capital structure

(1) It increases the availablereturn to equity holders can on theirinvestment. This is due to the firms assets being able to earn a returngreater than the cost of debt.

(2) It increases the risk (variability of the returns)associated with the investment. Thus, the greater the range ofreturns available to shareholders.

Having examined the impact of introducing debt we now turn toexamine how it could impact on the value of the firm through thefirms Capital Structure


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Capital Structure

The long-term sources of finance of the firm

Items found on the right hand side of the Balance Sheet

The combination of debt and equity used to finance the

investment in real assets.

Established by financing decisions

Summarised by the Debt-to-Equity ratio (D/E)

Optimal Capital Structure

The combination of debt & equity that minimises WACC

such that the value of the firm is maximised.

Is there such a combination?


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REAL ASSETS

GENERATE

A STREAM

OF

CASH FLOWS

- inventory

- machinery

- land & buildings

FINANCIAL ASSETS

CLAIMS

UPON THE

CASH FLOW

STREAM

- shares

- term loans

- mortgages

- debentures

Investing

DecisionFinancing

Decision


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Value of the Firm

The firm may be valued by discounting the future cash

flows of the firm by the WACC

V =n

t = 1

NOIt

(1 + r)tV =

n

t = 1

(Revenues - Costs)t

(1 + r)t


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n

i = 1

r = riXi

V =NOI

r

e.g. Equity and debt

r = re ( ) + rd ( )E

V

D

V

SIMPLIFY BY ASSUMING NOI IS CONSTANT

We can now express the equation as a perpetuity.


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Value of the Firm

As NOI increases the value of the firm increases.

NOI reflects the Investment decision of the firm As the Weighted Average Cost of Capital decreases the Value of

the firm increases.

WACC reflects the Financing decision of the firm

Is there a minimum value of the WACC which maximizes thevalue of the firm and how is it achieved?

THE BIG QUESTION

Does substitution of cheaper debt finance for equity reduce theoverall weighted average cost of capital and thereby increase thevalue of the firm?


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Why Is Debt Cheaper Than Equity?

Debt holders have priority over equity holders in their claims on

the firms cash flow stream.

Debt is a contractual claim

Dividends are a residual claim

Lenders therefore face lower risk than equity investors.

Consequently, the return required by debt holders (lenders) isless than the return required by shareholders


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TRADITIONAL APPROACH

The traditional approach to capital structure assumes that there isan optimal capital structure and management can increase thetotal value of the firm through the financing method.

The approach implies that the cost of capital is dependent on thecapital structure of the firm.

This was a practical approach without a theoretical basis.

The determinants of, or path to, the optimal D/E ratio were neverspecified (no formal model)


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The Traditional View Of TheEffect Of Leverage

As the amount of debt increases, this initially reduces the WACC(because debt is cheaper than equity)

However, the cost of debt is not constant but at some point increases.

The required rate of return that shareholders demand, cost of equity,also increases as the level of debt increases and this offsets the initialreduction in WACC.

Traditional view - there is an optimal capital structure.It is where WACC is at a minimum and consequently the value of thefirm is at a maximum


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The Traditional View Of TheEffect Of Leverage

Cost of

Capital

LeverageD/V

0

(a) The Effect on the Cost of Capital

re

rd

r

TotalValue

Leverage0DV

(b) The Effect on Firm Value

V


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Example

r = rd (D/V) + re (E/V)

0.086 = 0.05(10/100) + 0.090 (90/100)

0.084 = 0.05(25/100) + 0.095 (75/100)

0.075 = 0.05(50/100) + 0.10 (50/100)

BUT

0.077 = 0.07(90/100) + 0.14 (10/100)


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Modigliani and Miller (M&M)

questioned the traditional view

examined the relationship between firm value and financing

choice

analysis based on perfect market assumptions

undertook studies of electric utilities and oil companies -evidence supported conclusion that there was norelationship between D/E ratios and cost of capital in theseindustries


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ASSUMPTIONS UNDERLYINGM & M ANALYSIS

1. a perfectly competitive market in which all investors haveperfect knowledge and act rationally;

2. investors are perfectly certain about the future profitabilityof any company;

3. all companies can be divided into homogenous risk classes;

4. no personal or company tax;

5. individuals and companies can raise unlimited debt funds at

the same rate of interest;


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M&M Proposition 1

In perfect capital markets (with no taxes and no bankruptcy costs) thevalue of the firm is independent of its capital structure. i.e. CapitalStructure is irrelevant.

The WACC does not vary with changes in the debt/equity ratio.

A firm cannot change its total value just by dividing its cash flows into

different streams (different classes of investors). The firm's value is determined by its real assets, not by the securities it

issues.

Claims on firms in same business risk class and with same earningsstreams are perfect substitutes and must sell for the same value -

otherwise could make arbitrage profits.

PROVIDED

Personal borrowing is a perfect substitute for corporate borrowing.


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MM Proposition I

Shares40%Debt60%

The size of the pie does not depend on how it is sliced.

The value of the firm is unaffected by its capital structure.

Value of firm Value of firm

Shares60%

Debt

40%


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M&M Proof Of Capital StructureIrrelevance In Perfect Capital Markets

E.g. Firm L and firm U have identical assets capable of generatingidentical cash flows . The only difference is that Firm L is more highlylevered.

If Firm L has the same cost of equity as firm U, and uses cheaper debt, it

will have a lower WACC its value will be higher than Firm U

Investors will sell their shares in Firm L and buy equivalent cash flowstream in Firm U thus making an arbitrage profit. The sale of Firm Lshares will cause Firm Ls price to fall. The increase demand of FirmUs shares will cause Firm Us price to rise.

The process will continue until the value of each firm is the same.


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Assume they own 10% Equity (E) of the Levered Firm, i.e.

$1,500 which provides a 10% claim on NILof $150

The operation

1. Sell E in the levered firm for $1,500

2. Borrow $1,000 at 5%

D/E =1000/1500 =2/3

Same as levered Firm

3. Buy 10% of the E in the un-levered firm for $2,000

The Arbitrager


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M & M Proposition 1

Cost ofCapital

Leverage0

(a) The Effect on th e Cos t of Capital

re

rd

r

TotalValue

Leverage0

(b) The Effect on Firm Value

V


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M&M Proposition 2

The issue to be investigated is how exactly does the required

return on equity in a levered firm change as the degree of

leverage (D/E) changes?

Result: The required rate of return by equity holders can be

shown to be equal to the required rate of return for un-

levered equityplusthe financial risk premium which is afunction of the debt-equity ratio.


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Assume NOIu = NOIL

From M & M Theorem 1 Vu = VL

Vu = NOIu / r*er

r*e is the required return on equity capital in a firm with no debt (pureequity firm)

VL= NOIL / r

Where ris the required rate of return on capital ( both debt andequity) in a levered firm.

r = rd (D/V) + re (E/V)

Since from Modigliani and Miller


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Since from Modigliani and Miller

we know thatVU = VLwe require that

r*e = r = rd(D/V) + re(E/V)

r*e= rd(D/V) + re(E/V)

Solving for re

re = r*e+ (r*erd).D/E

We recognize that in an all equity (un-levered) firm r*e= raf

Therefore re= raf + (rafrd).D/E

This shows that as the degree of leverage (D/E) increases

the required rate of return on equity (re) in a levered

firm increases exactly in line with the increase in the

available rate of return (rae)

E

Drrrr dafafae


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For capital structure to be irrelevant the return equity

holders require on their investment must increase in

line with the return available to them.

As cheaperdebt is substituted for equity in thecapital structure, the return requi red by the equi ty

holders increases in response to the increased r isk

associated with their investment, and thereby

(exactly) offsets the effect on the overall cost ofcapital of the cheaperdebt finance.

Returns to Equity


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Example

Capital structure: equity = 40% debt = 60% rd = 8%

assume business risk re* = 8.8%

re = re* + (re* - rd) D/E

re = 8.8% + (8.8% - 8%) 6/4

re = 10%

WACC= re (E/V) + rd(D/V)

= 10% x 40/100 + 8% x 60/100

= 4% +4.8%

= 8.8%

Example


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Example

If capital structure changes so debt increases to 70%,

M & M argue that this will increase the financial risk to

shareholders and their required rate of return will increase.

re = re* + (re* - rd) D/E

re = 8.8% + (8.8% - 8%) 7/3

re = 10.67%

When capital structure changes

WACC= 10.67% x 30/100 + 8% x 70/100

= 3.2% + 5.6%

= 8.8% no change in WACC


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Type of Risks

NO DEBT: NOI = NI (all variability in net incomecomes from business risk).

DEBT: when the firm borrows, it becomes subjectto financial risk and business risk; interestis subtracted from the NOI, the effect beingan increase in the variability of the NI stream.

= an additional source of risk

= shareholder expected return increases


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BUSINESS RISK:

risk due to nature of the products sold by the company e.g.new competition, technological improvements, etc.

FINANCIAL RISK:

risk due to using debt (directly related to amount of debt inthe capital structure).


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Decomposition Of EquityHolders Required Returns

re = RF + BRP + FRP

Return on a

Risk-free

investment

Premium for

Business Risk

Premium for

Financial Risk

Risk inherent in

firms operations

Risk introduced through the addition of

debt into the capital structure


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Thus, the expected return to equity holders is equal to therequired rate of return for un-levered equity plus thefinancial risk premium which is a function of the debt-equity ratio.

re = return to equity holders

re*= rate of return required by shareholders in a un-levered firm

rd= rate of return required by debt holders

Proposition 2

D

Ere = re* + (re* - rd) x

BusinessRisk

FinancialRisk


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Conclusion from Proposition 2

Increasing leverage does not affect the cost of capital.

The cost of debt is an explicit cost included in the cost of capital.

The financial risk created by leverage is an implicit cost of debt

which increases the cost of capital by increasing the required rate

of return by equity holders.


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Summary

Capital Structure Irrelevance

r

NOIV

WACC

VEr

VDrr

ed

Constant Proportions changing

E

D

rrrr deee**

re varies linearly (and positively) with changes in financial leverage

and offsets the effect on r of the lower cost (rd)


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M&M Proposition 3

The appropriate discount rate for a particular investment

proposal is completely independent of how the investment is

financed. Therefore, the financing decision is irrelevant

from the point-of-view of maximising shareholder wealth.

The appropriate discount rate depends on the features of

the investment proposal, especially risk.

INTRODUCTION TO MARKET


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INTRODUCTION TO MARKETIMPERFECTIONSCapital structure Decision with Corporate

Taxation

M & M introduced corporate taxes conclusion:

interest is tax deductible

thus borrowing represents a tax saving

thus the value of the levered firm is greater than the valueof the un-levered firmby the value of the present value ofthe tax benefits

or VL > VU

where VL = VU + P.V. of the tax savings oninterest


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Imperfect Capital MarketsCorporate Taxes

Levered firms have additional tax deductionsassociated with the interest payments

Value of the levered firm (VL) will be greater thanthe value of the un-levered firm (VU) by the presentvalue of the tax benefits

Implies existence of an optimal capital structure -ALL DEBT

Notation


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Notation

Vu = value of an un-levered firm

VL = value of a levered firm

rd = rate of return required by debt holders

re* = rate of return required by shareholdersin an un-levered firm

re = rate of return required by shareholdersin a levered firm


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Vu =

VL =

VL =

VL =

NOI (1 - tc)

re*

NOI (1 - tc)

re*

NOI (1 - tc)

re*

(rd) (D) tc

rd+

+ D tc

+ D tcVu

Present value of the

interest tax shield


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Modigliani & Miller AnalysisI ntr oduction of Corporate Taxes

V

0D

E

VL

Vu

Present Value of

Interest Tax Shields

(D tc)


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Cost Of Capital

Optimal capital structure will be 100% debt. This willminimise the cost of capital and thereby maximise the value

of the firm.

r

WACC

DE

Why Are All Debt Capital


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Why Are All Debt CapitalStructures Not Observed?

There must be factors that offset the tax advantages of debtfinance when borrowing becomes too high e.g.

1. Personal Taxes2. Financial Distress Costs

3. Conflict of Interest Costs

etc.


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The impact of the introduction of personal taxes is beyond the scope of thiscourse.

A formal analysis of personal taxes is contained in the appendix to this topic.

In Summary

If corporate taxes are introduced to be consistent need to also consider the

impact of personal taxes. Need to consider the way in which the corporate tax system and the personal

tax system are integrated, in particular as regards the treatment of dividends

e.g. are dividends taxed twice?

is there a dividend imputation system in place?

Need to consider whether equity income is treated more favourably than debtincome by the personal tax system.

How are capital gains taxed?


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Depending on the exact nature of the overall tax system can endwith a variety of results.

If the tax system is perfect, in the sense that an individual pays thesame amount of tax whether they receive a dollar of debt incomeor a dollar of equity income, then its back to the originalModigliani Miller result in that the capital structure does not

matter.

If Dividends are taxed twice once at the company level and once atthe individual level ( Classical Tax system) then could be back tothe conclusion the more debt in the capital structure the greaterthe value of the firm.

If debt income is treated more ( less) favourably by the tax systemthan equity income an increase in debt (equity) will increase the

value of the firm


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Direct vs Indirect Bankruptcy Costs

Direct costs

Those costs are directly associated with bankruptcy, e.g. legal

and administrative expenses.

Indirect costsThose costs associated with spending resources to avoid

bankruptcy.

The static theory of capital structure

A firm borrows up to the point where the tax benefit from an

extra dollar in debt is exactly equal to the cost that comes from

the increased probabil i ty of f inancial distress.


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2. Financial Distress Costs

As debt increases to a point where there us a possibility offinancial distress and the F.D.C. increase, there is anoffsetting effect, i.e. the PV of the F.D.C. offset the PV of theinterest tax shields.

where VL= VU +PV of the Tax Saving on Interest

- PV of theFinancial Distress Cost

At the point where this offsetting begins we find the optimalcapital structure for a firm.


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2. Financial Distress CostsValue of the firm

(VL) VL + VU + TC x D

Financial distress costs

Actual firm

value

VU= Value of firm

with no debt

Total debt

(D)D*

Optimal amount

of debt

VU

Maximum

firm value VL*

The gain from the tax shield on debt is offset by financial distress costs. An

optimal capital structure exists which just balances the additional gain from

leverage against the added financial distress cost.


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3. Conflict Of Interest Costs

Debt holders may fear management will transfer wealthfrom themselves to shareholders.

They need to protect themselves from erosion of wealth(increase rdor impose covenants)

this is likely to increase as the D/E ratio increases

these costs are part of financial distress costs


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APPENDIX A . Personal Taxes (Miller 1977)

analysis based on the classical tax system

assumed reequals zero ( rdand tcare important)

investors are risk-neutral and debt is risk-less

there are different clienteles of investors (based on personal tax rate)

Investors face a choice of either a) tax-exempt Govt. bonds or

b) investment in risky firms

To entice investors to invest in debt rather than equity, the firm must offerhigh enough returns (before tax) to offset the disadvantage of higher

personal tax rates.

This counterbalances the interest deductibility of debt (the shareholders oflevered firms end up receiving no benefit from the tax deductibility of intereston corporate debt because the firms are in effect forced to pay debt holderspersonal taxes in the form of higher returns).


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1. Personal Taxes (Miller 1977)

Any gain from leverage on the relationship between two typesof personal taxes and the corporate tax rate.

VL = Vu + D.tc

where (1 - tc) (1- tps) = after-tax return to shareholders

(1 - tpd) = after-tax return to debt holders

= Vu+ [1- ] D(1 - tc) (1 - tps)

(1 - tpd)

D[ ] = GL (gain or leverage)1 - (1 - tc) (1 - tps)

(1 - tpd)


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1. Personal Taxes (Miller 1977)

A point is reached where

(1 - tc) (1- tps) = (1 - tpd)

At this point the gain from leverage is zero and theadvantage of issuing more debt vanishes completely.

At this point a capital structure is optimal

Because this level of debt is optimal for all firms, the D/E isoptimal for the economy as a whole, not for the individual

firm.

Millers Anal sis Corporate &


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Millers Analysis Corporate &Personal Taxes

VL= Vu+ [1- ] D(1 - tc) (1 - tps)

(1 - tpd)

VL

Vu

VL= Vu+ D tc I F tps= tpd

VL> Vu IF (1 - tpd) > (1 - tc) (1 - tps)

VL= Vu IF (1 - tpd) = (1 - tc) (1 - tps)

VL< Vu IF (1 - tpd) < (1 - tc) (1 - tps)

Topic 7 Capital Structure-1

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