Capital Structure Theory & Cost of Capital


II. Cost of capital - general

a) Required return v. cost of capital

b) Risk

c) WACC - general

III. Capital Structure

a) no taxes

b) taxes

c) bankruptcy & other costs

d) trade-off theory

e) pecking order hypothesis

f) Other considerations

IV. Component costs of capital

a) debt

b) preferred

c) equity

1) discounted dividends

2) CAPM (risk adjusted)

d) WACC again

Recall that the goal of management is to maximize the value of the firm. Since the value of the firm is basically a cash flow stream divided by a discount rate (cost of capital), we can maximize value by either maximizing the numerator (CF) or minimizing the denominator (cost of capital).

Optimal capital structure is the mix of debt and equity that minimizes the cost of capital, or equivalently, maximizes the value of the firm. Before discussing the optimal capital structure decision we will need a general concept of the cost of capital.

Introduction to cost of capital

Investors' required return v. Cost of capital

Investors are involved with the corporation through financial markets. They buy the debt and equity which appear on the right-hand-side of our picture. Investors' required returns can in general be written:

==> Rr = r* + + RP ,

where r* = the real rate of return, = expected inflation, and RP is a risk premium. The first two terms should be the same for most financial securities, so that in essence the required return depends on risk. In particular, the security's required return depends on the risk of the security's CF's.

The cost of capital depends on the risk of the firm's CF's. Firm risk and security risk are not necessarily the same. In terms of our picture, firm risk relates to the circle while security risk relates to the two rectangles. We previously discussed the term 'business risk' in conjunction with the circle. An exception is when the firm is an all equity firm, in which case firm risk and security risk are the same. In this special case the cost of capital = the required return on equity, since the cash flows to the firm are precisely the same as cash flows to equity.

When some debt is used the equity return becomes riskier. (why?) The firm's (asset) risk is the same.

Example: (Suppose we have an unlevered firm, U, and a levered firm, L) Also, assume there are two possible outcomes, one good and one bad.

Firm U: Assets 100; Debt 0; Equity 100

  Good: Bad:
Sales 100.00 82.50
Costs 70.00 80.00
EBIT 30.00 2.50
Interest 0.00 0.00
EBT 30.00 2.50
Tax 12.00 1.00
NI 18.00 1.50
ROE 18% 1.5%

Firm L: Assets 100; Debt 50; Equity 50

  Good: Bad:
Sales 100.00 82.50
Costs 70.00 80.00
EBIT 30.00 2.50
Int 5.00 5.00
EBT 25.00 (2.50)
Tax 10.00 (1.00)
NI 15.00 (1.50)
ROE 30% (3%)

Note that CF's to Assets are unchanged (EBIT). Cash flows to Equity are much different however.

Cost of Capital: The cost of capital is a weighted average of the cost of both debt and cost of equity. Why? Because we view capital as a long-run concept, even though at any point in time a firm will only issue either debt or equity. Capital consists of debt and equity, and once the capital enters the firm we can no longer distinguish the debt dollars from the equity dollars. Two analogies are useful. Consider different farmers who deposit their grain in a grain elevator. They do not get back their specific grain, but rather they get back some average of all the grain in the elevator. Closer to home, when you take a bath you use both hot and cold water, but once in the tub the hot water and the cold water are no longer distinguishable. Your bath water is a weighted average of the two. Another way of saying all this is to say that capital is 'fungible.'

More specifically we can write:

WACC = Re[E/(D+E)] + (1-Tc)Rd[D/(D+E)]

More generally: WACC = wi * Ri

Where wi = proportion of capital structure represented by capital source i and Ri = after-tax cost of capital source I. The above is precisely true for the perpetual case and for the finite case works as long as the wi's remain the same.

In theory the weights should be calculated using market values of debt and equity. In practice book values are often used. For debt this is usually not a big deal, but for equity the difference can be significant.

Rewrite as:

Re = Ra + (1-Tc)(Ra - Rd)*D/E

(business risk) ____ (financial risk)

(Ra can be thought of as the required return on equity if the firm had no debt.)

The first term: business risk => risk of asset CF's

a) sales price variability

b) demand variability

c) input price variability

d) high fixed cost (high oper. Leverage)

e) technology

f) competition

g) management depth and breadth

Second term - financial risk => The additional risk imposed on S/H from the use of debt financing. Debt has a prior claim. S/H must stand in line behind B/H.This additional risk on S/H implies a higher required return on equity by investors.

To compute cost of capital:

==> need % debt and % equity

==> optimal capital structure

Optimal capital structure

Recall from introductory finance: There are tax advantages to debt relative to equity. What are disadvantages?

I. Simple case -- no taxes

Ebit: 1,000 forever

Taxes: 0% ==> earnings = 1,000

Shares o/s: 200

EPS: 1,000/200 = $5.00

Ra = Re = 15% (based on risk of firm's CF's)

Value of all equity firm:

1,000/15% = $6,666.67

(Va = Ve)

Per share: = 6,667/200 = $33.33 (=5.00/15%)

Cost of capital = 15%


Now, lets add debt to our capital structure:

Suppose we borrow 2,000 at 10% and buy back equity:

* 140 shares O/S (buy back 60 = 2,000/33.33)

* interest expense = 2,000 * 10% = 200

* Earnings = 1,000 - 200 = 800 forever

* EPS = 800 / 140 = $5.71

*Value of firm (asset): CF's to assets are same, both in their level and their risk

(how CF's are divided between debt and equity differs)

==> Va = 1,000 (CF's to firm) / 15% = 6,666.67

==> Vd = 200/10% = 2,000 ====> Ve = Va - Vd = $4,666.67

(33.33/sh!!) ==> Value per share is unchanged! How can this be if EPS is $5.71 with debt versus $5.00 without it? The answer is that Re is higher as a result of the increased risk. The higher Re exactly offsets the higher EPS so that value is unchanged. We can calculate the new Re from our WACC formula as follows:

WACC = Re(E/[D+E]) + Rd(D/[D+E])

15% = Re(4,666.67/6,666.67) + 10% (2,000/6,666.67)

15% = re*.70 + 10%*30% ==> Re = 17.143%

Check: Ve = 800/17.143% = 4,666.67

Per share: 5.71/17.143% = 33.33

Summary - no taxes

==> WACC doesn't change (nor does Va)

==> M&M Proposition I: The value of the firm is independent of the financing decision. (NOT, 'melts in your mouth, not in your hand.')

The firm risk doesn't change; only % taken by each security holder changes.

==> Re = Ra + (Ra - Rd)*D/E (recall: Ra = Ru)

==> Re increases as D increases (since Ra > Rd)

==> EPS increase is exactly offset by Re increase so that price per share is unchanged.

==> M & M Proposition II: Increased leverage increases Re such that Ra (& WACC) is unchanged.


II. Simple case -- taxes => let taxes = 40%

A. No debt ==> earnings = $600 ==> EPS = $3.00

Value of firm = 600/.15 = 4,000 = $20/sh

(40% is going to government) i.e, 400/.15 = 2,667 to government

Re = Ra = 15% (risk of project CF's is same!!)

B. Debt:

1. Announce debt issue

2. Market computes new value of firm

3. Firm issues debt & purchases stock

Assume the firm issues $2,000 of debt at 10%


  Leveraged All Equity
EBIT 1,000 1,000
Interest 200 0
EBT 800 1,000
Taxes 320 400
Net Income 480 600

If net income were our only concern we might be led to believe that the all equity firm is superior.

Consider cash flows to firm (assets):

Available to all claimholders: 480 + 200 = 680

Before, CF's to assets were: 600

Value of firm = $4,800 = 4,000 + 800 (=Tc*d) (or 80/10%)

Value of levered firm = Value of all equity firm + PV of tax shield.

This says the value of the leveraged firm is equal to the value of the unleveraged firm plus the present value of the tax advantage of debt.

= 600/15% + .4*2,000 = 4,800

Note that all of the tax advantage goes to current S/H:

Shares are repurchased at fair price

Price = $20 + 800/200 = $24

==> Repurchase $2,000/$24 = 83.333 shares

==> 200 - 83.333 = 116.67 shares 0/S

EPS = 480/116.67 = $4.114

==> value per share O/S => 2,800/116.67 = $24

Value of firm: now, the required return for the project's risk is the same, but the actual Cost is less because the government is subsidizing part of it.

Now, since value of debt is $2,000, E = $2,800

Required return on debt: 10%

Cost of debt (1-Tc)*Rd = 6%

WACC = Re(E/V) + (1-Tc)Rd(D/V)


Re = Ru + (Ru - Rd)*(1 - Tc) *D/E

D = 2,000 E = 2,800 V = 4,800

WACC = 12.5% (15% before)

Re = 17.142% (unchanged)

Value of firm = flows to all equity firm/wacc

= 600/12.5% = 4,800

Summary with taxes

* investor required return is same; WACC is lower (why? -- less taxes)

* price per share = $24 (equity gets all tax advantage)

* WACC < Re (all equity) = Ra

So: Why not use all debt????

1. Other tax shields; no taxable income

2. Costs of financial distress - impairs ability of firm to conduct business in efficiently

Note: these costs can be reflected in required rates of return or cash flows (or both)

3. Tradeoff theory - The firm must trade off or balance the tax advantages of debt against the costs of financial distress.

In practice it is not possible to solve for the optimal capital structure very precisely. In fact, the WACC for various levels of debt is like a flat bottom boat. Going from no debt to some debt lowers WACC because of the tax advantage. Then, there is probably a large range over which D/E doesn't matter too much. Eventually too much debt increases risk such that the higher Re and Rd (& thus higher WACC) more than offset the tax advantage.

Handout 1: different D/E levels w/ #'s

- here, CF's do not change; EBIT is same (operating CF's)

- Re & Rd reflect additional risk

- at some point increase in Re and Rd > tax savings

Handout 2: Summary of above and Valuation example

EBIT = 151.52

Tc = 34%

D = 500

Ru = 20% (required asset return, ra)

Rd = 10%

Find V, E, WACC and Re:

Cf's to assets = EBIT * (1-Tc)

Vu = Vl + PV (tax savings)

1. Value of levered firm = Vu + PV(tax savings)

Vl = Vu + Tc*d = 500 + .34 * 500 = $670

E = 670 - 500 = 170

Re = Ra + (Ra - Rd)*(1-Tc)*D/E

Re = .20 + (.20 - .10)* (1-.34)*500/170 = 39.41%

WACC = 39.41%*(170/670) +10%*(1-.34%)*(500/670) = 14.92%

2. Cf's to equity at equity cost of capital

CF's to equity:

EBIT 151.52
Interest 50.00
EBT 101.52
Tax 34.52
Net Income 67.00


E = equity CF's Re = 67 39.41% = $170

3. Cf's to firm at WACC

CF's to firm = EBIT*(1-Tc) = 151.52*.66 = $100

WACC = 14.92% (from above)

Value of firm = $100 14.92% = $670

Equity = value of firm - debt = 670 - 500 = $170

Pecking order hypothesis

This hypothesis further relaxes the 'perfect' markets assumption by assuming that information is not symmetric. In particular, firm management is assumed to have better information about the firm's future prospects than outside investors.

With the pecking order hypothesis, firms use internally generated funds first. Internally generated funds are cheaper because of the costs of issuance of external debt or equity. (Note: Internal funds are not free! What is the cost of internally generated funds?)

If firms must use outside financing, then:

a) first use debt

b) then use equity

The reason firms use debt first, then equity, has to do with the signal which is sent to the market when the firm announces a new issue. In particular, assume management knows more than outside investors about the future prospects of the firm. If the firm is expected to do well, then 1) management will be reluctant to share the success with new equity holders and 2) management expects the firm will have sufficient cash flows to commit to fixed debt payments. If the firm is expected to do poorly, then 1) management would be happy to share this performance with new equity holders and 2) management expects the firm to have trouble with future fixed debt payments. More simply, management would never sell new shares if they thought the shares were undervalued, and they would happily sell new shares if they thought the shares were overvalued. Hence an announcement by management to issue equity must mean that management thinks shares are currently overvalued, or, equivalently, that future firm prospects are not bright. (Management would never issue new equity shares if they thought shares were currently undervalued.) An announcement by management to issue debt must mean that management thinks shares are currently underpriced, or, equivalently, that future firm prospects are bright.

Note that this theory really explains the marginal decision to issue debt or equity and the long-run D/E ratio becomes a cumulative result of the series of short-run decisions.

As discussed in Higgins, empirical evidence supports this signalling story. A public announcement of a new equity issue is accompanied by a significant stock price drop. In the research sample, the stock price drop resulted in a loss averaging 30% of the new issue and 3% of the preannouncement equity. (Conversely, the decision to repurchase shares results in a stock price increase.)

An alternative explanation for the stock price reaction to the issue of new equity is 'dilution.' That is, many managers feel that issuing new shares leads to a lower EPS (more shares O/S) and lower share price. We will examine this issue later.

Why do we observe cross-sectional differences in capital structures across different firms?

Other factors & practical considerations:

1. Cash flow stability

Can the firm commit to the 'fixed' payments required by debt? Cash flow instability can result from volatile revenues or volatile costs.

2.Asset stucture (tangible v. intangible) -

'Assets in place' v. Growth opportunities

3.Profitability- generation of cf's

The more profitable, the more CF's. Closely related to cash flow stability. Also, if the firm is not profitable, then it has no need for the tax advantage afforded to debt.

4.Effects on mgmt behavior - agency problems

Underinvestment problem - if additional funds needed & chance of bankruptcy high, S/H may not be willing to put up additional capital that effectively goes to the benefit of B/H.

Ex: Suppose A = 12 ; D = 15 ; E = (3)

Because of limited liability, we know that equity cannot have a negative value. So the market value of equity will be 0 or higher.

The firm has a project costing $5 with PV of $7. If the firm accepts the project, then:

A = 19

D = 15

E = 4

Risk averse management - management has significant human and financial capital tied to the firm. Consequently, management may be unwilling to accept risky projects with high expected returns because of tmanagement's personal aversion to risk. These projects may nevertheless be beneficial to S/H.

Overinvestment problem - Debt financing creates an incentive for management to invest in risky projects because of the limited liability of S/H. Shareholders share in the upside potential of a risky project, but have limited downside risk.

S&L's in the 80's

5. Current mkt condition: current interest rates & equity prices; explains marginal decision, not L-R D/E.

6. Financial flexibility (slack) - firms like to maintain a 'reserve of borrowing power'. That is, today's financing decision will affect future financing options. If the firm has issued a significant amount of debt in the past it may have reached its debt capacity. If the firm needs more capital, equity will be the only choice. Equity may not be a good choice if current equity market conditions are unfavorable. (If new equity is unavailable at a reasonable price.) Thus the firm may be forced to forgo attractive investment opportunities for lack of cash.

7. Managerial flexibility- debt covenants restrict managerial flexibility for small firms, and particularly venture capital situations in which these covenants are quite restrictive on managment.

Conversely, by committing future corporate cash flows to bondholders in the form of fixed interest and principal payments takes cash flow out of management hands and may help solve the agency problem.


Cost of capital

Now, given the capital structure, how do we determine cost of capital for a project????

Example: Consider two projects having the same risk and assume that: WACC = 12%; Rd = 8% and Re = 16%

  Project A Project B
Financing Debt Equity
IRR 13% 15%

Which project(s) should you accept? Both! Why?

Recall that capital is a pool of both debt and equity, and the cost of capital is weighted average cost of the pool. The decision to issue debt today lowers future debt capacity of the firm, while the decision to issue equity today increases future debt capacity. Both of the above projects should be assigned a cost of capital of 12%. Though Project A uses lower cost debt, the addition of debt increases Re and lowers future debt capacity of the firm.

Risk: remember - the appropriate discount rate depends on the risk of the cash flow stream to which it is applied.

A. If project is a replicate of firm, use firm WACC

B. If project has different risk, should use risk adjusted WACC.

Consider the effect of using WACC for projects having different risk from the firm.


Components of WACC


Return required by investor Rd

1. Capital market for O/S debt of firm.

2. Capital market for similar debt

How do we find practically:

1. If have debt O/S, look at current yield to maturity.

2. Look at S&P or Moody ratings

What do we mean by a 'similar' firm or firms? Having similar business and financial risk. Practically, they should be in the same industry, which controls for business risk, and have similar capital structures.

Cost to firm: = (1 - Tc)*Rd

Preferred stock:

pays dividend forever ==> Pp = D/Rp

==> Rp = D/Pp

==> Dividend yield on preferred

Common stock: (cost of equity)

2 methods:


1) Dividend discount model

Recall: common stock has 2 types of risk:

Systematic (marketwide)

Unsystematic (firm specific)

Because investors can hold diversified portfolios & eliminate unsystematic risk, they are not rewarded for it. Firm specific events tend to offset each other. (ex: strike, invention, competition, etc)

Economy-wide events cannot be eliminated

ex: interest rates, inflation, gnp,etc

According to the capital asset pricing model, we can compute the required return on equity from the following:

Ri = Rf + B(Rm - Rf)

B = firm's beta (or project's beta)

Rf = risk-free rate (Treasury bond)

Use historical average to predict Rm - Rf

What about beta? Use beta of the firm if the firm is publicly traded. If a private firm, then use beta from a portfolio of similar firms, where 'similar' has the same meaning that it did in the above discussion for Rd. Also, financial leverage need not be the same for the firm in question and the portfolio of similar firms, because Beta can be adjusted for different levels of leverage.

Discount dividends

Recall the dividend discount model: P0 = D1/ (Re - g)

We can observe P0, & estimate D1 and g

==> can compute expected return

But, in equilibrium expected return = required (why?)

In order to do this, we make an assumption about dividend path:

A) constant dividends (no growth):

Re = D/Pe

Assumption: either EPS = Dividends /share, or retained earnings have 0 NPV.

B) constant growth in dividends:

Re = D/Pe + g

The trick is to estimate g. Practically we begin by looking at historical growth. Also, recall our previous lecture about growth. If the company is mature and we expect ROE, ROA and leverage to remain the same, then we can use the sustainable growth rate. g = ROE x r.

ex: if payout ratio = 30% & ROE = 20% ==> g = 14%

Risk premium method:

A third way to calculate Re is the risk premium method. This methods adds a risk premium to company's marginal cost of debt. This ad-hoc method typically relies on historical spreads between the company's cost of debt and cost of equity.

Consider two sources of equity: Retained Earnings & new equity:

Cost of retained earnings: Are retained earnings costless? No. S/H will expect to get Re (reinvesting in firm)

New equity issues involve underwriting costs.

==> proceeds to firm are less than the issue price

Rne = D/Pne(1 - c) + g

Where ne designates new equity and c is the % underwriting cost.

Example: suppose D = .40, Pne = 15, g = 14%, c = 8%

Rne = .40/15(1 - .08) + 14%

Rne = 2.9% + 14 = 16.9%


WACC = Ra = Re * [E/(D+E)] + (1 - Tc)*Rd*[D/(D+E)]


We can use CAPM to get levered & unlevered betas to examine the effects of different leverage on Re:

Let Bl = levered beta and Bu = unlevered beta.


Bl = Bu[1 + (1-T)D/E]

Bu = Bl / [1 + (1-T)D/E]

To use:

1. Find unlevered beta with existing D/E

2. Using proposed D/E, find new levered beta.


As an example, suppose you use a portfolio of similar, but publicly traded, firms to calculate beta for a private firm. Also, assume the private firm has different leverage than the portfolio. Take the levered beta of the portfolio and 'unlever' it using the formula above. Then 'relever' it to reflect the leverage of the private firm.

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