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17.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chapter 17Chapter 17

Capital Structure Capital Structure DeterminationDetermination



After Studying Chapter 17, After Studying Chapter 17, you should be able to:you should be able to:

1. Define “capital structure.”

2. Explain the net operating income (NOI) approach to capital structure and valuation of a firm; and, calculate a firm's value using this approach.

3. Explain the traditional approach to capital structure and the valuation of a firm.

4. Discuss the relationship between financial leverage and the cost of capital as originally set forth by Modigliani and Miller (M&M) and evaluate their arguments.

5. Describe various market imperfections and other "real world" factors that tend to dilute M&M’s original position.

6. Present a number of reasonable arguments for believing that an optimal capital structure exists in theory.

7. Explain how financial structure changes can be used for financial signaling purposes, and give some examples.


• A Conceptual Look• The Total-Value Principle• Presence of Market Imperfections and

Incentive Issues• The Effect of Taxes• Taxes and Market Imperfections

Combined• Financial Signaling



• Concerned with the effect of capital market decisions on security prices.

• Assume: (1) investment and asset management decisions are held constant and (2) consider only debt-versus-equity financing.

Capital Structure Capital Structure -- The mix (or proportion) of -- The mix (or proportion) of a firm’s permanent long-term financing a firm’s permanent long-term financing

represented by debt, preferred stock, and represented by debt, preferred stock, and common stock equity.common stock equity.

Capital StructureCapital Structure


kkii = the yield on the company’s debt = the yield on the company’s debt

Annual interest on debt

Market value of debt

I

B==kkii

Assumptions:• Interest paid each and every year• Bond life is infinite• Results in the valuation of a perpetual

bond• No taxes (Note: allows us to focus on just

capital structure issues.)

A Conceptual Look –A Conceptual Look –Relevant Rates of ReturnRelevant Rates of Return


E

S==

kkee = the expected return on the company’s equity = the expected return on the company’s equityEarnings available to Earnings available to common shareholderscommon shareholders

Market value of common Market value of common stock outstandingstock outstanding

kkee

Assumptions:• Earnings are not expected to grow• 100% dividend payout• Results in the valuation of a perpetuity• Appropriate in this case for illustrating the

theory of the firm

E

S



O

V==

kkoo = an overall capitalization rate for the firm = an overall capitalization rate for the firm

Net operating incomeTotal market value of the firmkkoo

Assumptions:

• V = B + S = total market value of the firm• O = I + E = net operating income = interest

paid plus earnings available to common shareholders

O

V



Capitalization Rate, kCapitalization Rate, koo – The discount rate used to determine the present value of a

stream of expected cash flows.

kkoo kkeekkii

BB + S

SB + S

= +

What happens to kkii, kkee, and kkoo when leverage, B/S, increases?

Capitalization RateCapitalization Rate


Assume:

• Net operating income equals $1,350

• Market value of debt is $1,800 at 10% interest

• Overall capitalization rate is 15%

Net Operating Income Approach Net Operating Income Approach – A theory of – A theory of capital structure in which the weighted average capital structure in which the weighted average

cost of capital and the total value of the firm cost of capital and the total value of the firm remain constant as financial leverage is changed.remain constant as financial leverage is changed.

Net Operating Net Operating Income ApproachIncome Approach


Total firm valueTotal firm value = O / ko = $1,350$1,350 / 0.15= $9,000$9,000

Market value = V – B = $9,000$9,000 – $1,800$1,800 of equity = $7,200$7,200

Required returnRequired return = E / S on on equityequity* = ($1,350$1,350 – $180$180) / $7,200$7,200

= 16.25%16.25%

Calculating the required rate of return on equityCalculating the required rate of return on equity

* B / S = $1,800 / $7,200 = 0.25

Interest paymentsInterest payments = $1,800 × 10%= $1,800 × 10%

Required Rate of Required Rate of Return on EquityReturn on Equity


Total firm valueTotal firm value = O / ko = $1,350$1,350 / 0.15= $9,000$9,000

Market value = V – B = $9,000$9,000 – $3,000$3,000 of equity = $6,000$6,000

Required returnRequired return = E / S on on equityequity* = ($1,350$1,350 - $300$300) / $6,000$6,000

= 17.50%17.50%

What is the rate of return on equity if B=$3,000?What is the rate of return on equity if B=$3,000?

* B / S = $3,000 / $6,000 = 0.50

Interest paymentsInterest payments = $3,000 × 10%= $3,000 × 10%



B / S kkii kkee k ko o

0.00 —— 15.00%15.00% 15% 15% 0.25 10%10% 16.25%16.25% 15% 15% 0.50 10%10% 17.50%17.50% 15% 15% 1.00 10%10% 20.00%20.00% 15% 15% 2.00 10%10% 25.00%25.00% 15% 15%

Examine a variety of different debt-to-equity Examine a variety of different debt-to-equity ratios and the resulting required rate of ratios and the resulting required rate of

return on equity.return on equity.

Calculated in slides 9 and 10



Capital costs and the NOI approach in a Capital costs and the NOI approach in a graphical representation.graphical representation.

0 0.25 0.50 0.75 1.0 1.25 1.50 1.75 2.0Financial Leverage (B/S)

0.25

0.20

0.150.15

0.100.10

0.05

0

Cap

ital

Co

sts

(%)

kkee = 16.25% and = 16.25% and

17.5% respectively17.5% respectively

kkii (Yield on debt) (Yield on debt)

kko o (Capitalization rate)(Capitalization rate)

kke e (Required return on equity)(Required return on equity)



NOI Approach

You can create this type of analysis in Excel also. You can use some modeling experience to write formulas to calculate the required rates.

Refer to “VW13E-17.xlsx” on the ‘NOI Approach’ tab

Excel & the NOI ApproachExcel & the NOI Approach


• Critical assumption is ko remains constant.

• An increase in cheaper debt funds is exactly offset by an increase in the required rate of return on equity.

• As long as ki is constant, ke is a linear function of the debt-to-equity ratio.

• Thus, there is no one optimal capital no one optimal capital structurestructure.

Summary of NOI ApproachSummary of NOI Approach


Optimal Capital Structure Optimal Capital Structure – The capital structure that minimizes the firm’s cost of capital and thereby maximizes the value of the firm.

Traditional Approach Traditional Approach – A theory of capital structure in which there exists an optimal capital optimal capital structure structure and where management can increase the total value of the firm through the judicious

use of financial leverage.

Traditional ApproachTraditional Approach


Traditional ApproachTraditional Approach

Financial Leverage (B / S)

0.25

0.20

0.150.15

0.100.10

0.05

0

Cap

ital

Co

sts

(%)

kkii

kkoo

kkee

Optimal Capital StructureOptimal Capital Structure

Optimal Capital Structure: Optimal Capital Structure: Traditional Approach Traditional Approach


Traditional Approach

You can create this type of analysis in Excel also. We use some assumptions in this model built into the formulas.

Refer to “VW13E-17.xlsx” on the ‘Traditional Approach’ tab

Excel and the Excel and the Traditional ApproachTraditional Approach


• The cost of capital is dependent on the capital structure of the firm.

• Initially, low-cost debt is not rising and replaces more expensive equity financing and ko declines.

• Then, increasing financial leverage and theassociated increase in ke and ki more than offsetsthe benefits of lower cost debt financing.

• Thus, there is one optimal capital structureone optimal capital structure where ko is at its lowest point.

• This is also the point where the firm’s totalvalue will be the largest (discounting at ko).

Summary of the Summary of the Traditional ApproachTraditional Approach


• Advocate that the relationship betweenfinancial leverage and the cost of capital is explained by the NOI approach.

• Provide behavioral justification for a constantko over the entire range of financial leverage possibilities.

• Total risk for all security holders of the firm isnot altered by the capital structure.

• Therefore, the total value of the firm is notaltered by the firm’s financing mix.

Total Value Principle: Total Value Principle: Modigliani and Miller (M&M)Modigliani and Miller (M&M)


Market value of debt ($65M)

Market value of equity ($35M)

Total firm marketvalue ($100M)

• M&M assume an absence of taxes and market imperfections.

• Investors can substitute personal for corporate financial leverage.

Market value of debt ($35M)

Market value of equity ($65M)

Total firm marketvalue ($100M)

• Total market value is not altered by the capital structure (the total size of the pies are the same).

Total Value Principle: Total Value Principle: Modigliani and MillerModigliani and Miller


Arbitrage Arbitrage – Finding two assets that are – Finding two assets that are essentially the same and buying the essentially the same and buying the

cheaper and selling the more expensive.cheaper and selling the more expensive.

Two firms that are alike in every respect EXCEPTEXCEPT capital structure MUSTMUST have

the same market value.

Otherwise, arbitragearbitrage is possible.

Arbitrage and Total Arbitrage and Total Market Value of the FirmMarket Value of the Firm


Consider two firms that are identical in every respect EXCEPTEXCEPT:

• Company NL – no financial leverage• Company L – $30,000 of 12% debt• Market value of debt for Company L equals its

par value• Required return on equity

– Company NL is 15%– Company L is 16%

• NOI for each firm is $10,000

Arbitrage ExampleArbitrage Example


Earnings available to Earnings available to = EE = O – I common shareholderscommon shareholders = $10,000$10,000 - $0

= $10,000$10,000

Market valueMarket value = E / ke of of

equityequity = $10,000$10,000 / 0 .15 = $66,667$66,667

Total market valueTotal market value = $66,667$66,667 + $0= $66,667$66,667

Overall capitalization rateOverall capitalization rate = 15%15%Debt-to-equity ratio = 0

Valuation of Company NLValuation of Company NL

Arbitrage Example: Arbitrage Example: Company NLCompany NL


Earnings available to Earnings available to = EE = O – I common shareholderscommon shareholders = $10,000$10,000 – $3,600

= $6,400$6,400

Market valueMarket value = E / ke of of

equityequity = $6,400$6,400 / 0.16 = $40,000$40,000

Total market valueTotal market value = $40,000$40,000 + $30,000= $70,000$70,000

Overall capitalization rateOverall capitalization rate = 14.3%14.3%Debt-to-equity ratio = 0.75

Valuation of Company LValuation of Company L

Arbitrage Example: Arbitrage Example: Company LCompany L


Assume you own 1% of the stock of Company L (equity value = $400).

You should:

• 1. Sell the stock in Company L for $400.

• 2. Borrow $300 at 12% interest (equals 1% of debt for Company L).

• 3. Buy 1% of the stock in Company NL for $666.67. This leaves you with $33.33 for other investments ($400 + $300 - $666.67).

Completing an Completing an Arbitrage TransactionArbitrage Transaction


Original return on investment in Company LOriginal return on investment in Company L

$400 × 16% = $64

Return on investment after the transaction• $666.67 × 16% = $100 return on Company NL$100 return on Company NL• $300 × 12% = $36 interest paid$36 interest paid• $64 net return $64 net return ($100$100 – $36$36) AND $33.33 left over$33.33 left over.

This reduces the required net investment to $366.67 to earn $64.

Completing an Completing an Arbitrage TransactionArbitrage Transaction


• The equity share price in Company NL rises based on increased share demand.

• The equity share price in Company L falls based on selling pressures.

• Arbitrage continues until total firm values are identical for companies NL and L.

• Therefore, all capital structures are equally as Therefore, all capital structures are equally as acceptable.acceptable.

• The investor uses “personal” rather than corporate financial leverage.

Summary of the Summary of the Arbitrage TransactionArbitrage Transaction


• Agency costs (Slide 17–31)

• Debt and the incentive to manage efficiently

• Institutional restrictions

• Transaction costs

• Bankruptcy costs (Slide 17–30)

Market Imperfections Market Imperfections and Incentive Issuesand Incentive Issues


Financial Leverage (B / S)

RRffReq

uir

ed R

ate

of

Ret

urn

on

Eq

uit

y (k

e) kke e with no leveragewith no leverage

kkee without bankruptcy costs without bankruptcy costs

kkee with bankruptcy costs with bankruptcy costs

PremiumPremiumfor financialfor financial

riskrisk

PremiumPremiumfor businessfor business

riskrisk

Risk-freeRisk-freeraterate

Required Rate of Return Required Rate of Return on Equity with Bankruptcyon Equity with Bankruptcy


• Monitoring includes bonding of agents, auditing financial statements, and explicitly restricting management decisions or actions.

• Costs are borne by shareholders (Jensen & Meckling).

• Monitoring costs, like bankruptcy costs, tend to rise at an increasing rate with financial leverage.

Agency Costs Agency Costs -- Costs associated with monitoring -- Costs associated with monitoring management to ensure that it behaves in ways management to ensure that it behaves in ways

consistent with the firm’s contractual agreements consistent with the firm’s contractual agreements with creditors and shareholders.with creditors and shareholders.

Agency CostsAgency Costs


Consider two identical firms EXCEPTEXCEPT:

• Company ND – no debt, 16% required return• Company D – $5,000 of 12% debt• Corporate tax rate is 40% for each company• NOI for each firm is $10,000

The judicious use of financial leverage financial leverage (i.e., debt) (i.e., debt) provides a favorable impact

on a company’s total valuation.

Example of the Effects Example of the Effects of Corporate Taxesof Corporate Taxes


Earnings available to Earnings available to = EE = OO – Icommon shareholderscommon shareholders = $2,000$2,000 –

$0 = $2,000$2,000

Tax Rate Tax Rate (TT) = 40%40%

Income available toIncome available to = EACSEACS (1 – TT)common shareholderscommon shareholders = $2,000$2,000 (1 – 0.40.4)

= $1,200$1,200

Total income available toTotal income available to = EATEAT + I all all security holderssecurity holders = $1,200$1,200 + 0

= $1,200$1,200

Valuation of Company NDValuation of Company ND (Note: has no debt)

Corporate Tax Example: Corporate Tax Example: Company NDCompany ND


Earnings available to Earnings available to = EE = OO – Icommon shareholderscommon shareholders = $2,000$2,000 –

$600 = $1,400$1,400

Tax Rate Tax Rate (TT) = 40%40%

Income available toIncome available to = EACSEACS (1 – TT)common shareholderscommon shareholders = $1,400$1,400 (1 – 0.40.4)

= $840$840

Total income available toTotal income available to = EATEAT + I all all security holderssecurity holders = $840$840 + $600

= $1,440$1,440*

Valuation of Company DValuation of Company D (Note: has some debt)

* $240 annual tax-shield benefit of debt (i.e., $1,440 - $1,200)

Corporate Tax Example: Corporate Tax Example: Company DCompany D


Tax Shield Tax Shield – A tax-deductible expense. The – A tax-deductible expense. The expense protects (shields) an equivalent dollar expense protects (shields) an equivalent dollar

amount of revenue from being taxed by reducing amount of revenue from being taxed by reducing taxable income.taxable income.

Present value ofPresent value oftax-shield benefitstax-shield benefits

of debtof debt*= (rr) (BB) (ttcc)

rr= (BB) (ttcc)

* Permanent debt, so treated as a perpetuity** Alternatively, $240 annual tax shield / 0.12 = $2,000, where

$240=$600 Interest expense × 0.40 tax rate.

= ($5,000$5,000) (0.40.4) = $2,000$2,000**

Tax-Shield BenefitsTax-Shield Benefits


Value of unlevered firm Value of unlevered firm = $1,200 / 0.16(Company ND)(Company ND) = $7,500$7,500*

Value of levered firm Value of levered firm = $7,500$7,500 + $2,000$2,000 (Company D)(Company D) = $9,500$9,500

Value ofValue of Value ofValue of Present value Present value ofof

leveredlevered = firm iffirm if + tax-shield tax-shield benefitsbenefits

firmfirm unleveredunlevered of debtof debt

* Assuming zero growth and 100% dividend payout

Value of the Levered FirmValue of the Levered Firm


• The greater the financial leverage, the lower the cost of capital of the firm.

• The adjusted M&M proposition suggests an optimal strategy is to take on the maximum take on the maximum amount of financial leverageamount of financial leverage.

• This implies a capital structure of almost 100% This implies a capital structure of almost 100% debt! debt! Yet, this is notnot consistent with actual behavior.

• The greater the amount of debt, the greater the tax-shield benefits and the greater the value of the firm.

Summary of Summary of Corporate Tax EffectsCorporate Tax Effects


• Corporate plus personal taxesCorporate plus personal taxes

Personal taxes reduce the corporate tax advantage associated with debt.

Only a small portion of the explanation why corporate debt usage is not near 100%.

• Uncertainty of tax-shield benefitsUncertainty of tax-shield benefits

Uncertainty increases the possibility of bankruptcy and liquidation, which reduces the value of the tax shield.

Other Tax IssuesOther Tax Issues


As financial leverage increases, tax-shield tax-shield benefits benefits increase as do bankruptcy and bankruptcy and agency costsagency costs.

Value of levered firmValue of levered firm= Value ofValue of firm iffirm if unlevered unlevered + Present value of tax-shield benefits Present value of tax-shield benefits of debt of debt - Present value ofPresent value of bankruptcy and bankruptcy and agency costs agency costs

Bankruptcy Costs, Bankruptcy Costs, Agency Costs, and TaxesAgency Costs, and Taxes


Optimal Financial LeverageOptimal Financial Leverage

Taxes, bankruptcy, andTaxes, bankruptcy, andagency costs combinedagency costs combined

Net tax effectNet tax effect

Financial Leverage (B/S)

Co

st o

f C

apit

al (

%)

Minimum Costof Capital Point

Bankruptcy Costs, Bankruptcy Costs, Agency Costs, and TaxesAgency Costs, and Taxes


• Informational Asymmetry is based on the idea that insiders (managers) know something about the firm that outsiders (security holders) do not.

• Changing the capital structure to include more debt conveys that the firm’s stock price is undervaluedconveys that the firm’s stock price is undervalued.

• This is a valid signal valid signal because of the possibility of bankruptcy.

• A manager may use capital structure changes to convey information about the profitability and risk of the firm.

Financial SignalingFinancial Signaling


2. Flexibility• A decision today impacts the options open to the firm for

future financing options – thereby reducing flexibility.• Often referred to unused debt capacity.

1. Timing• After appropriate capital structure determined it is still

difficult to decide when to issue debt or equity and in what order

• Factors considered include the current and expected health of the firm and market conditions.

Timing and FlexibilityTiming and Flexibility


• Taxes

• Explicit cost

• Cash-flow ability to service debt

• Agency costs and incentive issues

• Financial signaling

• EBIT-EPS analysis

• Capital structure ratios

• Security rating

• Timing

• Flexibility

Checklist of Practical and Checklist of Practical and Conceptual ConsiderationsConceptual Considerations

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