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### Chapter 17

Capital Structure Determination

After Studying Chapter 17, you should be able to:

- Define “capital structure.”
- Explain the net operating income (NOI) approach to capital structure and valuation of a firm; and, calculate a firm's value using this approach.
- Explain the traditional approach to capital structure and the valuation of a firm.
- 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.
- Describe various market imperfections and other "real world" factors that tend to dilute M&M’s original position.
- Present a number of reasonable arguments for believing that an optimal capital structure exists in theory.
- Explain how financial structure changes can be used for financial signaling purposes, and give some examples.

Capital Structure Determination

- 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 -- The mix (or proportion) of a firm’s permanent long-term financing represented by debt, preferred stock, and common stock equity.

A Conceptual Look –Relevant Rates of Return

ki = the yield on the company’s debt

I

B

Annual interest on debt

Market value of debt

ki

=

=

- 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 –Relevant Rates of Return

ke = the expected return on the company’s equity

Earnings available to

common shareholders

Market value of common

stock outstanding

E

S

E

S

ke

=

=

- 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

A Conceptual Look –Relevant Rates of Return

ko = an overall capitalization rate for the firm

O

V

Net operating income

Total market value of the firm

O

V

ko

=

=

- Assumptions:
- V = B + S = total market value of the firm
- O = I + E = net operating income = interest paid plus earnings available to common shareholders

Capitalization Rate, ko– The discount rate used to determine the present value of a stream of expected cash flows.

B

B + S

S

B + S

ko

ki

ke

=

+

What happens to ki, ke, and ko

when leverage, B/S, increases?

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 – A theory of capital structure in which the weighted average cost of capital and the total value of the firm remain constant as financial leverage is changed.

Required Rate of Return on Equity

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

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

Required return = E / S on equity* = ($1,350 – $180) / $7,200 = 16.25%

Calculating the required rate of return on equity

Interest payments

= $1,800 × 10%

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

Required Rate of Return on Equity

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

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

Required return = E / S on equity* = ($1,350 - $300) / $6,000 = 17.50%

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

Interest payments

= $3,000 × 10%

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

Required Rate of Return on Equity

B / Skike ko

0.00—15.00% 15%

0.2510%16.25% 15%

0.50 10%17.50% 15%

1.00 10%20.00% 15%

2.00 10%25.00% 15%

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

Calculated in slides 9 and 10

Required Rate of Return on Equity

Capital costs and the NOI approach in a graphical representation.

0.25

ke = 16.25% and

17.5% respectively

0.20

ke (Required return on equity)

0.15

ko (Capitalization rate)

Capital Costs (%)

0.10

ki (Yield on debt)

0.05

0

0 0.25 0.50 0.75 1.0 1.25 1.50 1.75 2.0

Financial Leverage (B/S)

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

- 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 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 – A theory of capital structure in which there exists an optimal capital structure and where management can increase the total value of the firm through the judicious use of financial leverage.

Optimal Capital Structure: Traditional Approach

Traditional Approach

ke

0.25

ko

0.20

0.15

ki

Capital Costs (%)

0.10

Optimal Capital Structure

0.05

0

Financial Leverage (B / S)

Excel and the 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

Summary of the Traditional 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 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).

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

- 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: Modigliani and Miller

- M&M assume an absence of taxes and market imperfections.
- Investors can substitute personal for corporate financial leverage.

Market value

of debt ($65M)

Market value

of equity ($35M)

Total firm market

value ($100M)

Market value

of debt ($35M)

Market value

of equity ($65M)

Total firm market

value ($100M)

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

Arbitrage and Total Market Value of the Firm

Arbitrage – Finding two assets that are essentially the same and buying the cheaper and selling the more expensive.

Two firms that are alike in every respect EXCEPT capital structure MUST have the same market value.

Otherwise, arbitrage is possible.

- Consider two firms that are identical in every respect EXCEPT:
- 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

Valuation of Company NL

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

Market value = E / keof equity = $10,000 / 0 .15 = $66,667

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

Overall capitalization rate = 15%

Debt-to-equity ratio = 0

Valuation of Company L

Earnings available to = E = O – I common shareholders = $10,000 – $3,600 = $6,400

Market value = E / keof equity = $6,400 / 0.16 = $40,000

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

Overall capitalization rate = 14.3%

Debt-to-equity ratio = 0.75

Completing an Arbitrage Transaction

- 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 Arbitrage Transaction

Original return on investment in Company L

$400 × 16% = $64

- Return on investment after the transaction
- $666.67 × 16% = $100 return on Company NL
- $300 × 12% = $36 interest paid
- $64 net return ($100 – $36) AND $33.33 left over.
- This reduces the required net investment to $366.67 to earn $64.

Summary of the Arbitrage 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 acceptable.

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

Market Imperfections and Incentive Issues

- Agency costs (Slide 17–31)
- Debt and the incentive to manage efficiently
- Institutional restrictions
- Transaction costs

- Bankruptcy costs (Slide 17–30)

Required Rate of Return on Equity with Bankruptcy

ke with bankruptcy costs

Premium

for financial

risk

ke with no leverage

Required Rate of Return

on Equity (ke)

ke without bankruptcy costs

Premium

for business

risk

Rf

Risk-free

rate

Financial Leverage (B / S)

- 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 -- Costs associated with monitoring management to ensure that it behaves in ways consistent with the firm’s contractual agreements with creditors and shareholders.

Example of the Effects of Corporate Taxes

Consider two identical firms EXCEPT:

- 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 (i.e., debt) provides a favorable impact on a company’s total valuation.

Corporate Tax Example: Company ND

Valuation of Company ND (Note: has no debt)

Earnings available to = E = O – I common shareholders = $2,000 – $0 = $2,000

Tax Rate (T) = 40%

Income available to= EACS (1 – T) common shareholders = $2,000 (1 – 0.4) = $1,200

Total income available to = EAT+ I all security holders = $1,200 + 0 = $1,200

Corporate Tax Example: Company D

Valuation of Company D(Note: has some debt)

Earnings available to = E = O – I common shareholders = $2,000 – $600 = $1,400

Tax Rate (T) = 40%

Income available to= EACS (1 – T) common shareholders = $1,400 (1 – 0.4) = $840

Total income available to = EAT+ I all security holders = $840 + $600 = $1,440*

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

Tax Shield – A tax-deductible expense. The expense protects (shields) an equivalent dollar amount of revenue from being taxed by reducing taxable income.

Present value of

tax-shield benefits

of debt*

(r) (B) (tc)

=

= (B) (tc)

r

($5,000) (0.4) = $2,000**

=

* 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.

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

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

Value ofValue ofPresent value of

levered = firm if + tax-shield benefits

firmunleveredof debt

* Assuming zero growth and 100% dividend payout

Summary of Corporate Tax Effects

- 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 amount of financial leverage.
- This implies a capital structure of almost 100% debt! Yet, this is notconsistent with actual behavior.

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

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

Bankruptcy Costs, Agency Costs, and Taxes

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

Value of levered firm

= Value offirm ifunlevered

+ Present value of tax-shield benefits of debt

- Present value ofbankruptcy and agency costs

Bankruptcy Costs, Agency Costs, and Taxes

Taxes, bankruptcy, and

agency costs combined

Minimum Cost

of Capital Point

Cost of Capital (%)

Net tax effect

Optimal Financial Leverage

Financial Leverage (B/S)

- 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 undervalued.
- This is a 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.

- Flexibility
- A decision today impacts the options open to the firm for future financing options – thereby reducing flexibility.
- Often referred to unused debt capacity.

- 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.

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 Conceptual Considerations

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