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Capital Structure Decisions

CHAPTER 15

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Topics in Chapter

Overview and preview of capital structure effects

Business versus financial risk

The impact of debt on returns

Capital structure theory, evidence, and implications for managers

Example: Choosing the optimal structure

Determinants of Intrinsic Value: The Capital Structure Choice

Basic Definitions

V = value of firm

FCF = free cash flow

WACC = weighted average cost of capital

rs and rd are costs of stock and debt

ws and wd are percentages of the firm that are financed with stock and debt.

How can capital structure affect value?

A Preview of Capital Structure Effects

The impact of capital structure on value depends upon the effect of debt on:

WACC

FCF

The 2017 Tax Cuts and Jobs Act (TCJA)

Corporate tax rate:

TCJA rate is flat 21%.

Previous rate was graduated, with top rate of 35%.

Limits on interest expense deductions:

Interest/EBITDA < 30% for 2018-2021

Interest/EBIT < 30% for subsequent years

Excess carried forward indefinitely.

Should cause firms to reduce debt.

Business Risk: Uncertainty in EBIT, NOPAT, and ROIC

Uncertainty about demand (unit sales).

Uncertainty about output prices.

Uncertainty about input costs.

Product and other types of liability.

Degree of operating leverage (DOL).

What is operating leverage, and how does it affect a firm’s business risk?

Operating leverage is the change in EBIT caused by a change in quantity sold.

The higher the proportion of fixed costs relative to variable costs, the greater the operating leverage.

Higher operating leverage leads to more business risk: small sales decline causes a larger EBIT decline.

Operating Breakeven

Q is quantity sold, F is fixed cost, V is variable cost, TC is total cost, and P is price per unit.

Operating breakeven = QBE

QBE = F / (P – V)

Example: F=$200, P=$15, and V=$10:

QBE = $200 / ($15 – $10) = 40.

Business Risk versus Financial Risk

Business risk:

Uncertainty in future EBIT, NOPAT, and ROIC.

Depends on business factors such as competition, operating leverage, etc.

Financial risk:

Additional business risk concentrated on common stockholders when financial leverage is used.

Depends on the amount of debt and preferred stock financing.

Consider Two Hypothetical Firms Identical Except for Debt

	Firm U	Firm L
Capital	$20,000	$20,000
EBIT	$2,400	$2,400
Tax Rate	25%	25%
Equity	$20,000	$16,000
Debt	$0	$4,000
rd =		8%

Impact of Leverage on Income Statements

	Firm U	Firm L
EBIT	$2,400	$2,400
Interest	$0	$320
EBT	$2,400	$2,080
Taxes	$600	$520
NI	$1,800	$1,560

NOPAT, ROIC, and ROE

	Firm U	Firm L
EBIT =	$2,400	$2,400
NOPAT = EBIT(1 − T) =	$1,800	$1,800
Operating capital =	$20,000	$20,000
ROIC = NOPAT/Op. Cap. =	9.0%	9.0%
Equity =	$20,000	$16,000
Net income =	$1,800	$1,560
ROE = NI/Equity =	9.0%	9.8%

What does this example illustrate about the impact of financial leverage?

ROIC wasn’t affected by financial leverage.

ROE went up, increasing the expected return to shareholders.

ROEL was greater than ROEU.

Why did leverage increase ROE in this example?

More total dollars paid to L’s investors:

U: NI = $1,800.

L: NI + Int = $1,560 + $320 = $1,880.

Lower taxes paid by L:

U: $600

L: $520.

Less equity tied up in L:

U: $20,000

L: $16,000

Impact of Leverage on Returns if EBIT Falls to $1,600

	Firm U	Firm L
EBIT	$1,600	$1,600
Interest	$0	$320
EBT	$1,600	$1,280
Taxes (40%)	$400	$320
NI	$1,200	$960
ROIC	6.0%	6.0%
ROE	6.0%	6.0%

Impact of Leverage on Returns if EBIT Falls to $1,200

	Firm U	Firm L
EBIT	$1,200	$1,200
Interest	$0	$320
EBT	$1,200	$880
Taxes (40%)	$300	$220
NI	$900	$660
ROIC	4.5%	4.5%
ROE	4.5%	4.1%

Leverage only adds value if ROIC is greater than the after-tax cost of debt.

	EBIT	EBIT	EBIT
	$2,400	$1,600	$1,200
ROIC	9.0%	6.0%	4.5%
rd(1-T)	6.0%	6.0%	6.0%
ROE	9.8%	6.0%	4.1%

Capital Structure Theory

MM theory

Zero taxes

Corporate taxes

Corporate and personal taxes

Trade-off theory

Signaling theory

Pecking order

Debt financing as a managerial constraint

Windows of opportunity

MM Theory: Zero Taxes

	Firm U	Firm L
EBIT	$3,000	$3,000
Interest	0	1,000
NI	$3,000	$2,000
CF to shareholder	$3,000	$2,000
CF to debtholder	0	$1,000
Total CF	$3,000	$3,000

Notice that the total CF are identical for both firms.

MM Results for Zero Taxes: VL = VU

MM assume: (1) no transactions costs; (2) no restrictions or costs to short sales; and (3) individuals can borrow at the same rate as corporations.

MM prove that if the total CF to investors of Firm U and Firm L are equal, then arbitrage is possible unless the total values of Firm U and Firm L are equal:

VL = VU.

Because FCF and values of firms L and U are equal, their WACCs are equal.

Therefore, capital structure is irrelevant.

MM Theory: Corporate Taxes

Corporate tax laws allow interest to be deducted, which reduces taxes paid by levered firms.

Therefore, more CF goes to investors and less to taxes when leverage is used.

In other words, the debt “shields” some of the firm’s CF from taxes.

MM Result for Corporate Taxes: VL = VU + TD

MM show that the total CF to Firm L’s investors is equal to the total CF to Firm U’s investor plus additional amount due to interest deductibility:

CFL = CFU + rdDT.

What is value of these cash flows?

Value of CFU = VU

MM show that the value of rdDT = TD

Therefore, VL = VU + TD.

MM relationship between value and debt when corporate taxes are considered.

Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.

Impact of the TCJA on the MM Result: VL = VU + TD

The TCJA cut the federal corporate tax rate to 21%, reducing the combined federal-plus-state tax rate from about 40% to about 25%.

This significantly reduces the tax shield of TD.

The slope of the graph on the previous slide is lower since the TCJA took effect.

Miller’s Theory: Corporate and Personal Taxes

Personal taxes lessen the advantage of corporate debt:

Corporate taxes favor debt financing since corporations can deduct interest expenses.

Personal taxes favor equity financing, since no gain is reported until stock is sold, and long-term gains are taxed at a lower rate.

Miller’s Model with Corporate and Personal Taxes

Tc = corporate tax rate.

Td = personal tax rate on debt income.

Ts = personal tax rate on stock income.

Tc = 25%, Td = 30%, and Ts = 12%.

Value rises with debt; each $1 increase in debt raises L’s value by about $0.06.

Conclusions with Personal Taxes

Use of debt financing remains advantageous, but benefits are less than under only corporate taxes.

Firms should still use 100% debt.

Note: However, Miller argued that in equilibrium, the tax rates of marginal investors would adjust until there was no advantage to debt.

Impact of the TCJA on the Miller Model (1 of 2)

Cut the combined federal-plus-state Tc from about 40% to about 25%.

Did not significantly affect the personal tax rate on stocks, Ts.

The TCJA cut the top personal rate from 39.6% to 35% (although the changes to the personal rates will revert back to the pre-TCJA values after 2025). The result is relatively small changes in Td.

Impact of the TCJA on the Miller Model (2 of 2)

The TCJA significantly reduced the numerator, (1 − Tc) (1 − Ts), because Tc is much smaller now.

The TCJA made small changes to the denominator, (1 − Td).

The net effect is that the term in brackets is much smaller now.

This means that debt adds much less value than before the TCJA.

Trade-off Theory

MM theory ignores bankruptcy (financial distress) costs, which increase as more leverage is used.

At low leverage levels, tax benefits outweigh bankruptcy costs.

At high levels, bankruptcy costs outweigh tax benefits.

An optimal capital structure exists that balances these costs and benefits.

Tax Shield vs. Cost of Financial Distress

Impact of the TCJA on the Trade-off Theory

The slope of the tax shield line in the previous graph is less steep due to the reduction in corporate taxes.

The TCJA did not affect financial distress costs.

The net affect is that the curved line for VL is much lower and flatter now.

Signaling Theory

MM assumed that investors and managers have the same information.

But, managers often have better information. Thus, they would:

Sell stock if stock is overvalued.

Sell bonds if stock is undervalued.

Investors understand this, so view new stock sales as a negative signal.

Implications for managers?

Pecking Order Theory

Firms use internally generated funds first, because there are no flotation costs or negative signals.

If more funds are needed, firms then issue debt because it has lower flotation costs than equity and not negative signals.

If more funds are needed, firms then issue equity.

Debt Financing and Agency Costs (1 of 2)

One agency problem is that managers can use corporate funds for non-value maximizing purposes.

The use of financial leverage:

Bonds “free cash flow.”

Forces discipline on managers to avoid perks and non-value adding acquisitions.

Debt Financing and Agency Costs (2 of 2)

A second agency problem is the potential for “underinvestment”.

Debt increases risk of financial distress.

Therefore, managers may avoid risky projects even if they have positive NPVs.

Investment Opportunity Set and Reserve Borrowing Capacity

Firms with many investment opportunities should maintain reserve borrowing capacity, especially if they have problems with asymmetric information (which would cause equity issues to be costly).

Market Timing Theory

Managers try to “time the market” when issuing securities.

They issue equity when the market is “high” and after big stock price run ups.

They issue debt when the stock market is “low” and when interest rates are “low.”

The issue short-term debt when the term structure is upward sloping and long-term debt when it is relatively flat.

Empirical Evidence (1 of 4)

Tax benefits are important

At optimal capital structure, $1 debt adds about $0.10 to $0.20 to value on average.

For average firm financed with 25% to 30% debt, this adds about 3% to 6% to the total value.

Warning! These results were for periods before the TCJA and may now overstate the benefits of debt.

Bankruptcies are costly– costs can be up to 10% to 20% of firm value.

Empirical Evidence (2 of 4)

Firms have targets, but don’t make quick corrections when stock price changes cause their debt ratios to change.

Average speed of adjustment from current capital structure is about 30% per year.

Speed is about 50% per year for firms with high cash flow.

Speed is about 70% for firms with high cash flow that are above target.

Empirical Evidence (3 of 4)

Lost value from being above target is bigger than lost value from being below target.

When above target, distress costs rise very rapidly.

Sometimes companies will deliberately increase debt to above target to take advantage of unexpected investment opportunity.

Empirical Evidence (4 of 4)

After big stock price run ups, debt ratio falls, but firms tend to issue equity instead of debt.

Inconsistent with trade-off model.

Inconsistent with pecking order.

Consistent with windows of opportunity.

Many firms, especially those with growth options and asymmetric information problems, tend to maintain excess borrowing capacity.

Implications for Managers (1 of 3)

Take advantage of tax benefits by issuing debt, especially if the firm has:

High tax rate

Stable sales

Low operating leverage

Implications for Managers (2 of 3)

Avoid financial distress costs by maintaining excess borrowing capacity, especially if the firm has:

Volatile sales

High operating leverage

Many potential investment opportunities

Special purpose assets (instead of general purpose assets that make good collateral)

Implications for Managers (3 of 3)

If manager has asymmetric information regarding firm’s future prospects, then avoid issuing equity if actual prospects are better than the market perceives.

Always consider the impact of capital structure choices on lenders’ and rating agencies’ attitudes

Choosing the Optimal Capital Structure: Example

b = 1.0; rRF = 6%; RPM = 6%.

Cost of equity using CAPM:

rs = rRF +b (RPM)= 6% + 1(6%) = 12%

Currently has no debt: wd = 0%.

WACC = rs = 12%.

Tax rate is T = 25%.

Current Value of Operations

Expected FCF = $90 million.

Firm expects zero growth: g = 0.

Vop = [FCF(1+g)]/(WACC − g)

Vop = [$90(1+0)]/(0.12 − 0)

Vop = $750 million.

Other Data for Valuation Analysis

Company has no ST investments.

Company has no preferred stock.

10 million shares outstanding

Current Valuation Analysis

Vop	$750
+ ST Inv.	0
VTotal	$750
− Debt	0
S	$750
÷ n	10
P	$75.00

Investment bankers provided estimates of rd for different capital structures.

wd	0%	20%	30%	40%	50%
rd	0.0%	8.0%	8.5%	10.0%	12.0%

If company recapitalizes, it will use proceeds from debt issuance to repurchase stock.

The Cost of Equity at Different Levels of Debt: Hamada’s Formula

MM theory implies that beta changes with leverage.

bU is the beta of a firm when it has no debt (the unlevered beta)

b = bU [1 + (1 - T)(wd/ws)]

The Cost of Equity for wd = 20%

Use Hamada’s equation to find beta:

b = bU [1 + (1 - T)(wd/ws)]

= 1.0 [1 + (1-0.25) (20% / 80%) ]

= 1.188

Use CAPM to find the cost of equity:

rs= rRF + bL (RPM)

= 6% + 1.188 (6%) = 13.13%

The WACC for wd = 20%

WACC = wd (1-T) rd + ws rs

WACC = 0.2 (1 – 0.25) (8%) + 0.8 (13.13%)

WACC = 11.7%

Repeat this for all capital structures under consideration.

Beta, rs, and WACC

wd	0%	20%	30%	40%	50%
rd	0.0%	8.0%	8.5%	10.0%	12.0%
ws	100%	80%	70%	60%	50%
b	1.00	1.188	1.32	1.50	1.75
rs	12.00%	13.13%	13.93%	15.00%	16.50%
WACC	12.00%	11.70%	11.66%	12.00%	12.75%

The WACC is minimized for wd = 30%. This is the optimal capital structure.

Corporate Value for wd = 20%

Vop = [FCF(1+g)]/(WACC − g)

Vop = [$90(1+0)]/(0.117 − 0)

Vop = $769.23 million.

Debt = DNew = wd Vop

Debt = 0.20($769.23) = $153.85 million.

Equity = S = ws Vop

Equity = 0.80($769.23) = $615.38 million.

Value of Operations, Debt, and Equity

wd	0%	20%	30%	40%	50%
rd	0.0%	8.0%	8.5%	10.0%	12.0%
ws	100%	80%	70%	60%	50%
b	1.00	1.188	1.32	1.50	1.75
rs	12.00%	13.13%	13.93%	15.00%	16.50%
WACC	12.00%	11.70%	11.66%	12.00%	12.75%
Vop	$750.00	$769.23	$771.70	$750.00	$705.88
D	$0.00	$153.85	$231.51	$300.00	$352.94
S	$750.00	$615.38	$540.19	$450.00	$352.94

The WACC is minimized for wd = 30%. This is the optimal capital structure.

Anatomy of a Recap: Before Issuing Debt

	Before Debt
Vop	$750.00
+ ST Inv.	0
VTotal	$750.00
− Debt	0
S	$750.00
÷ n	$10.00
P	$75.00
Total shareholder
wealth: S + Cash	$750

Issue Debt (wd = 20%), But Before Repurchase

WACC decreases to 11.70%.

Vop increases to $771.70.

Firm temporarily has short-term investments of $153.85 (until it uses these funds to repurchase stock).

Debt is now $153.85.

Anatomy of a Recap: After Debt, but Before Repurchase

	Before Debt	After Debt, Before Rep.
Vop	$750.00	$769.23
+ ST Inv.	0	$153.85
VTotal	$750.00	$923.08
− Debt	0	$153.85
S	$750.00	$769.23
÷ n	10.00	10.00
P	$75.00	$76.92
Total shareholder
wealth: S + Cash	$750	$769.23

After Issuing Debt, Before Repurchasing Stock

Stock price increases from $75.00 to $76.92.

Wealth of shareholders (due to ownership of equity) increases from $750 million to $769.23 million.

The Repurchase: No Effect on Stock Price

The announcement of an intended repurchase might send a signal that affects stock price, and the previous change in capital structure affects stock price, but the repurchase itself has no impact on stock price.

If investors thought that the repurchase would increase the stock price, they would all purchase stock the day before, which would drive up its price.

If investors thought that the repurchase would decrease the stock price, they would all sell short the stock the day before, which would drive down the stock price.

Remaining Number of Shares After Repurchase

DOld is amount of debt the firm initially has, DNew is amount after issuing new debt.

If all new debt is used to repurchase shares, then total dollars used equals

(DNew – DOld) = ($153.85 - $0) = $153.85.

nPrior is number of shares before repurchase, nPost is number after. Total shares remaining:

nPost = nPrior – (DNew – DOld)/P

nPost = 10 – ($153.85/$26.60)

nPost = 8 million.

Anatomy of a Recap: After Repurchase

	Before Debt	After Debt, Before Rep.	After Rep.
Vop	$750.00	$769.23	$769.23
+ ST Inv.	0	$153.85	0
VTotal	$750.00	$923.08	$769.23
− Debt	0	$153.85	153.85
S	$750.00	$769.23	$615.38
÷ n	10.00	10.00	8.00
P	$75.00	$76.92	$76.92
Total shareholder
wealth: S + Cash	$750	$769.23	$769.23

Key Points

ST investments fall because they are used to repurchase stock.

Stock price is unchanged.

Value of equity falls from $769.23 to $615.38 because firm no longer owns the ST investments.

Wealth of shareholders remains at $769.23 because shareholders now directly own the funds that were held by firm in ST investments.

Intrinsic Stock Price Maximized at Optimal Capital Structure

wd	0%	20%	30%	40%	50%
rd	0.0%	8.0%	8.5%	10.0%	12.0%
ws	100%	80%	70%	60%	50%
b	1.00	1.188	1.32	1.50	1.75
rs	12.00%	13.13%	13.93%	15.00%	16.50%
WACC	12.00%	11.70%	11.66%	12.00%	12.75%
Vop	$750.00	$769.23	$771.70	$750.00	$705.88
D	$0.00	$153.85	$231.51	$300.00	$352.94
S	$750.00	$615.38	$540.19	$450.00	$352.94
n	10.0	8.0	7.0	6.0	5.0
P	$75.00	$76.92	$77.17	$75.00	$70.59

Shortcuts

The corporate valuation approach will always give the correct answer, but there are some shortcuts for finding S, P, and n.

Shortcuts on next slides.

Calculating S, the Value of Equity after the Recap

S = (1 – wd) Vop

At wd = 20%:

S = (1 – 0.20) $769.23

S = $615.38.

Number of Shares after a Repurchase, nPost

At wd = 20%:

nPost = nPrior(VopNew−DNew)/(VopNew−DOld)

nPost = 10($769.23 −$153.85)/($769.23 −$0)

nPost = 8

Calculating PPost, the Stock Price after a Recap

At wd = 20%:

PPost = (VopNew−DOld)/nPrior

nPost = ($769.23 −$0)/10

nPost = $76.92

Optimal Capital Structure

wd = 30% gives:

Highest corporate value

Lowest WACC

Highest stock price per share

But wd = 40% is close. Optimal range is pretty flat.

Equity as an Option on the Firm’s Value

For highly levered firms there is a relatively high probability of default.

Equity holders make the decision on whether or not to make a required interest or principal payment on the debt.

If they do make the payment, they own the total value of the firm minus the amount due to debtholders.

If they default because the total value of the firm is less than the amount owed to debtholders, then they own nothing.

The equity owners’ position looks like an option to buy the firm with an exercise price equal to the value of the debt.

Example of Equity as an Option: Liu Industries

Liu Industries is a highly levered firm with the following data:

Total Value of Firm	4.00
Face Value of Debt	2.00
Risk Free rate	6.0%
Maturity of debt (years)	1.00
Standard Dev. of Total Value	0.60

Equity as an option

P = underlying value of firm:

P = $4 million

X = exercise price = value of debt:

X = $2 million

t = time to maturity

t = 1 year

rRF = 6%

 = volatility of debt + equity = 0.60

Use Black-Scholes to price this option

Black-Scholes Solution (1 of 2)

Black-Scholes Solution (2 of 2)

N(d1) = N(1.5552) = 0.9401

N(d2) = N(0.9552) = 0.8383

Note: Values obtained from Excel using NORMSDIST function.

V = $4(0.9401) - $2e-0.06(0.8303)

= $3.7604 - $2(0.9418)(0.8303)

= $2.196 Million = Value of Equity

Value of Debt

The value of debt must be what is left over:

Value of debt = Total Value – Equity

= $4 million – 2.196 million

= $1.804 million

This value of debt gives us a yield

Debt yield for 1-year zero coupon debt

= (face value / price) – 1

= ($2 million/ 1.804 million) – 1

= 10.9%

How does  affect an option's value?

Higher volatility  means higher option value.

Managerial Incentives (1 of 2)

When an investor buys a stock option, the riskiness of the stock () is already determined. But a manager can change a firm's  by changing the assets the firm invests in. That means changing  can change the value of the equity, even if it doesn't change the expected cash flows:

Managerial Incentives (2 of 2)

So changing  can transfer wealth from bondholders to stockholders by making the option value of the stock worth more, which makes what is left, the debt value, worth less.

Value of Debt and Equity for Different Volatilities

Bait and Switch

Managers who know this might tell debtholders they are going to invest in one kind of asset, and, instead, invest in riskier assets. This is called bait and switch and bondholders will require higher interest rates for firms that do this, or refuse to do business with them.

How do companies manage the maturity structure of their debt?

Maturity matching

Finance long-term assets with long-term debt

Finance short-term assets with short-term debt.

Information asymmetries: Firms with better future prospects than expected by investors

Issuing long-term debt will lock in a higher interest rate than warranted by company’s prospect.

So issue short-term debt (even though its rate is too high) but refinance at appropriate rate when company’s prospects are revealed

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