1. Corporate Financial Policy 2004-2005 Introduction
Professor André Farber
Solvay Business School
Université Libre de Bruxelles
The format of these lecture notes is based on an idea of Mark Rubinstein. In 1998, he published Derivatives, the first PowerPlus Picture Book. The idea is to combine the slides used in classes with text. This is done in Power by taking advantage of space available in the Notes .

2. How to finance a company?
Corporate Financial Policy Introduction
How to finance a company?
Should a firm pay its earnings as a dividends?
When should it repurchase some of its shares?
If money is needed, should a firm issue stock or borrow?
Should it borrow short-term or long-term?
When should it issue convertible bonds?
In this course, we will analyze financing decision by corporation.
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3. Corporate Financial Policy 1. Introduction
Some data – Benelux 2004
In order to give to feeling on what we will study, here are summary statistics for Benelux companies.
Source of data: Petercam – Benelux Stock Guide – December 2004
Market Capitalization: the market value of all shares (number share * stock price)
Free Float: the percentage of shares held by the general public
Net Debt: Financial Debt – Cash
Net Debt / Book Equity: a measure of the accounting leverage ratio
Net Debt /(Net Debt + Market Cap): a measure of leverage based on market values
Dividend Yield: Dividend / Stock price
Payout ratio: Dividend per share / Earnings per share
Note that a substantial fraction (30%) of the companies have negative net debt (cash > financial debt). To concentrate on companies with positive net debt, the next column calculates the debt ratio for companies with positive net debts.
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4. Divide and conquer: the separation principle
Corporate Financial Policy Introduction
Divide and conquer: the separation principle
Assumes that capital budgeting and financing decision are independent.
Calculate present values assuming all-equity financing
Rational: in perfect capital markets, NPV(Financing) = 0
2 key irrelevance results:
Modigliani-Miller 1958 (MM 58) on capital structure
The value of a firm is independent of its financing
The cost of capital of a firm is independent of its financing
Miller-Modigliani 1961 (MM 61) on dividend policy
The value of a firm is determined by its free cash flows
Dividend policy doesn’t matter.
The classic articles of Modigliani and Miller are the inescapable starting point of any analysis of the financial policy of a firm. They show that, in a perfect capital market, the financing decisions of a firm are of no consequence: neither the capital structure (the debt/equity ratio) nor the dividend policy (the payout ratio) modify the value of the firm.
It took some time to understand the exact meaning of “perfect capital markets” and many controversies took place around this issue.
The conditions required for Modigliani Miller’s Proposition I were summarized by Fama in 1978 (20 years after the publication of the MM paper)
1. Perfect capital market: no transactions costs, costless bankruptcy, no taxes, no agency costs
2. Equal Access: individual and firms have equal access to the capital market.
3. Homogeneous Expectations: costless access to information, all agents can correctly assess this information.
4. Only Wealth Count: the effect of a firm’s financial decision can be equated with effects on security holder wealth.
5. Given Investment Strategy: the investment strategies of firm are given.
6. Me-first rule: the payoffs on the firm’s outstanding bonds are unaffected by changes in capital structure.
Reference Fama, E., The Effects of a Firm’s Investment and Financing Decisions on the Welfare of its Security Holders, American Economic Review 68, 3 (June 1978)
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5. Corporate Financial Policy 1. Introduction
Market imperfections
Issuing securities is costly
Taxes might have an impact on the financial policy of a company
Tax rates on dividends are higher than on capital gains
Interest expenses are tax deductible
Agency problems
Conflicts of interest between
Managers and stockholders
Stockholders and bondholders
Information asymmetries
The Modigliani Miller proposition provides the list of factors which might explain why financial policies matter. As Merton Miller noted: “Looking back now, perhaps we should have put more emphasis on the other, upbeat side of the “nothing matters” coin: showing what doesn’t matter can also show, by implication, what does” (Miller 1988).
For a superb recent review of capital structure, read Myers 2000
Reference Miller, M., The Modigliani-Miller Proposition After Thirty Years, Journal of Economic Perspectives, 2, 4 (Autumn 1988) Myers, S., Capital Structure, Journal of Economic Perspectives, 15, 2 (Spring 2001)
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6. Corporate Financial Policy 1. Introduction
Course outline
09/02/ Introduction – MM 1958, 1961
16/02/ Debt and taxes
23/02/ Adjusted present value
02/03/ WACC
09/03/ Case study
16/03/ Option valuation: Black-Scholes
23/03/ Capital structure and options: Merton’s model
13/04/ Optimal Capital Structure Calculation: Leland
20/04/ Convertible bonds and warrants
27/04/ IPO/Seasoned Equity Issue
04/05/ Dividend policy
11/05/ Unfinished business/Review
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7. Practice of corporate finance: evidence from the field
Corporate Financial Policy Introduction
Practice of corporate finance: evidence from the field
Graham & Harvey (2001) : survey of 392 CFOs about cost of capital, capital budgeting, capital structure.
« ..executives use the mainline techniques that business schools have taught for years, NPV and CAPM to value projects and to estimate the cost of equity. Interestingly, financial executives are much less likely to follows the academically proscribed factor and theories when determining capital structure »
Are theories valid? Are CFOs ignorant?
Are business schools better at teaching capital budgeting and the cost of capital than at teaching capital structure?
Graham and Harvey Journal of Financial Economics 60 (2001)
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8. Corporate Financial Policy 1. Introduction
Finance 101 – A review
Objective: Value creation – increase market value of company
Net Present Value (NPV): a measure of the change in the market value of the company
NPV = V
Market Value of Company = present value of future free cash flows
Free Cash Flow = CF from operation + CF from investment
CFop = Net Income + Depreciation - Working Capital Requirement
We begin with a brief review of the foundations of finance.
Financial decisions should create value. The standard measure of value creation is the Net Present Value (NPV) NPV = Σ(Ct × DFt)
The value of a company is equal to the expected free cash flows discounted at a risk adjusted discounted.
The framework that links together the various cash flows of a company is the statement of cash flow
For an unlevered company:
FCF = CFoperation + CFinvestment
FCF = DIV –ΔK+ ΔCASH
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9. The message from CFOs: Capital budgeting
Corporate Financial Policy Introduction
The message from CFOs: Capital budgeting
The origin of present value calculation is not known. Some authors trace its roots to the early days of financial economics in the 15th century (Poitras 2000). Others look for the origin even further in time (see Goetzman 2003 who argues that one of the early formulations of the net present value rule was presented by Leonardo of Pisa – better known as Fibonacci – around year 1200).
Up to the advent of computers, present value was a topic for mathematicians and engineers. As far as I remember, I was exposed to this formula for the first time in the early 1960s in a course on insurances taught by a mathematician. I loved the mathematics of it but working the result with a slide rule was a real challenge.
This of course explains the low rate of penetration of the DCF method at that time (a survey in the US published in 1959 indicates that 19% of the respondents were using the method).
The penetration rate of DCF techniques increased rapidly after the mid 1950’s (Callahan and Haka, 2002). Two reasons explain this evolution.
First, the calculation of present value was facilitated by the diffusion of tables of present value factors and the apparition of handheld calculators. Anthony, a professor at Harvard Business School, has played a critical role through his popular textbook published in These tables could now be produced on computers. In an article published in 1955, Charles Christenson, of Harvard, describes how the tables were calculated on the Mark IV Calculator of Harvard University Computation Laboratory. Some year later, calculators appeared. In 1972, HP launched the HP35, the first handheld scientific calculator
A second reason explains the diffusion of DCF techniques. From 1950 on, economics entered business schools. The economic foundation of the present value rule had been laid down by Irving Fisher in 1930 in his famous treaty on interest but the practical implication of his work had not been fully grasped. In 1950, Joel Dean, a professor at Columbia University published Capital Budgeting, the book that made DCF techniques accessible to business managers. During the following years, problems related to the techniques were clarified and solved by academics (James Lorie, Leonard Savage, Harry Roberts, Jack Hirshleifer, all at the University of Chicago – note that Lorie, Savage and Roberts were professors of statistics, finance was not yet recognized as a discipline).
By the end of the 1950s, the battle for the present value had been won (the paper by Jack Hirshleifer published in 1958 is still a classic)
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10. Corporate Financial Policy 1. Introduction
From Markowitz to CAPM
Expected Return
Expected Return
Security Market Line P
20% P M
rM 14%
14% M
rf 8% 8%
Here is a quick review of the foundations of modern finance.
The figure on the left hand side is a review of the contribution of Harry Markowitz. In his seminal paper published in 1952, Markowitz showed how to calculate the composition of an optimal portfolio based on two parameters: the expected return and the standard deviation of return (Sigma), a measure of risk. His key result was to show that only efficient portfolios should be considered: those that maximize the expected return of a level of risk. Some years later (in 1958), James Tobin introduced borrowing and lending. He showed that there exist one and only one optimal risky portfolio (portfolio M). The investor’s job can be separated into two stages: first find the optimal risky portfolio, then choose the optimal combination of this risky portfolio with the risk-free asset. This depends on the investor’s risk aversion. The (risk -expected return) combinations that can be achieved are located on the straight line rfM. Point P illustrates an asset allocation with money invested in the risk-free asset. Point Q shows what happens if money is borrowed to invest in M more than the initial amount.
In , Sharpe and Lintner introduced the Capital Asset Pricing Model. In this model, the optimal risky portfolio M is the market portfolio and the expected return on a security is positively (and linearly) related to the security’ s beta.
The beta can be interpreted as the responsiveness of a security’s return to the return of the market.
The covariance of the security’s return with the market’s return measures the contribution of the security to the risk of the market portfolio.
The beta (or the covariance) are measures of the systematic risk of a security: the risk than can not be eliminated through diversification.
The CAPM states that, in equilibrium, the excess return (rj - rf) per unit of systematic is is the same for all securities:
(rj – rf) / βj = rM – rf for all j 2
Sigma 1
Beta
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11. The message from CFOs : cost of equity
Corporate Financial Policy Introduction
The message from CFOs : cost of equity
The CAPM has been widely adopted by companies to calculate their cost of capital.
Academics still debate the validity of the CAPM.
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12. CAPM – an other formulation
Corporate Financial Policy Introduction
CAPM – an other formulation
Consider a future uncertain cash flow C to be received in 1 year.
PV calculation based on CAPM:
with:
The standard approach to calculate the present value of a risky future cash flow is to discount the expected cash flow at a risk-adjusted discount rate.
But that there another method. The expected cash flows are adjusted to obtain certainty equivalents. These certainty equivalent cash flows are discounted at the risk-free interest rate.
Here is an example.
You want to calculate the present value of an expected cash flow of 100 to be received in one year. The standard deviation of this cash flow is 20. The correlation with the market portfolio is 0.5. The risk-free interest rate is 5%, the risk premium on the market portfolio is 8% and the standard deviation of the market is 20%. Lambda, the price of covariance risk is .08 / (.20)² = 2
cov(C,rM) = Correlation(C,rM) σC σM = (0.5)(20)(.20) = 2
The certainty equivalent cash flow is CEQ = E(C) – λ cov(C,rM) = 100 – 2 × 2 = 96
V = 96 / 1.05 = 91.43
See Brealey and Myers 9.6 for additional details.
See Brealey and Myers Chap 9
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13. Binomial option pricing model
Corporate Financial Policy Introduction
Binomial option pricing model
Used to value derivative securities: PV=f(S)
Evolution of underlying asset: binomial model
u and d capture the volatility of the underlying asset
Replicating portfolio: Delta × S + M
Law of one price: f = Delta × S + M uS fu S dS fd Δt
M is the cash position M>0 for investment M<0 for borrowing
Consider the following example. You want to value a call option with three months to maturity. The strike price of the option is 20 and the spot price of the underlying asset is 20. The risk-free interest rate (with continuous compounding) is 5%. The volatility of the underlying asset is 30%.
You want to use the binomial option pricing model with Δt=3/12=0.25
The up and down factors are: u = and d = The two possible stock prices three months later are uS = and dS = 17.21
The values of the call option at the end of the period are: fu = Max(0, )=3.24 and fd = Max(0, )=0
The composition of the replicating portfolio is: Delta = and M = You should buy shares and borrow
As a consequence, the value of the call option is: f = ×20 – = 1.61.
As an exercise, you can verify that similar calculations for a put option would lead to the following results:
fu = 0, fd = 2.79
Delta = , M =
f = 1.36
r is the risk-free interest rate with continuous compounding
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14. Corporate Financial Policy 1. Introduction
Risk neutral pricing
The value of a derivative security is equal to risk-neutral expected value discounted at the risk-free interest rate
p is the risk-neutral probability of an up movement
Risk-neutral pricing is a very powerful technique to price derivative securities. The difficulty is to be able to calculate the risk neutral probabilities. This calculation is straightforward in the binomial model. It requires more advanced mathematical techniques in more general model.
To continue the example in the previous slide, the risk neutral probability of an up movement is:
p = (e.05×0.25 – 0.861)/( ) = 0.504
The value of the call and the put options are:
Call f = (0.504 × 3.24)/ e.05×0.25 = 1.61
Put f = (0.504 × 2.79)/ e.05×0.25 = 1.36
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15. State prices – Digital options
Corporate Financial Policy Introduction
State prices – Digital options
Consider digital options with the following payoffs:
Using the binomial option pricing equation: uS dS
Up: vu 1
Down: vd
Calculation of present values using state prices:
In corporate finance, academics and practitioners tend to favor the mean-variance approach introduced by Markowitz, Sharpe and Lintner. There is, however, another way to model uncertainty introduced by Arrow (a Nobel price in economics) in 1953 and later used with Debreu (another Nobel price) to model general equilibrium. In this approach, uncertainty is captured by a list of possible future states of the economy. Arrow introduced the concept of a contingent contract: « a contract for the delivery of goods or money contingent on the occurrence of a state of affairs ». For many years, this approach was considered as too abstract and too theoretical for practical purposes.
We now understand that the contingent contracts imagined by Arrow are digital options. A unit digital option is a security that pays one euro if and only if a certain state occurs. The prices of these digital options can be calculated using option pricing models. Using the binomial option pricing model, two general results emerge:
Any security can be decomposed into a portfolio of digital options(or of Arrow securities). By the law of one price, the value of the security is equal to the value of the portfolio of Arrow securities.
The price of unit digital option is equal to the risk neutral probability discounted at the risk-free interest rate.
As digital options seems to be the smallest particles of which securities are composed, Sharpe suggests (with a bit of hyperbole) to name the approach nuclear financial economics.
For a full development of the approach, see Cohrane (2001) or Lengwiler (2004)
References:
Cochrane, J., Asset Pricing, Princeton University Press 2001
Lengwiler, Y., Microfoundations of Financial Economics, Princeton University Press, 2004
Sharpe, W., Nuclear Financial Economics in Beaver et all. Risk Management: Problems & Solutions, McGraw-Hill 1995
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16. Corporate Financial Policy 1. Introduction
Using state prices
Calculation of present values using state prices:
Back to previous example. (S = 20, σ = 30%, Δt = 0.25, r = 5%)
Current price Future prices
Up Down
Stock S = uS = dS = 17.21
Bond e-rΔt =
The risk-neutral probability of an up movement is p = (see
The state prices are vu = × = and vd = ( ) × = 0.490
Call option (K = 20): f = × 3.24 = 1.61
Put option (K= 20): f = × 2.79 = 1.36
Note the state prices could be calculated directly by solving the following system of equations:
= vu × vd × 17.21
0.987 = vu + vd
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17. Cost of capital with debt
Corporate Financial Policy Introduction
Cost of capital with debt
CAPM holds – Risk-free rate = 5%, Market risk premium = 6%
Consider an all-equity firm:
Market value V 100
Beta 1
Cost of capital 11% (=5% + 6% * 1)
Now consider borrowing 20 to buy back shares.
Why such a move?
Debt is cheaper than equity
Replacing equity with debt should reduce the average cost of financing
What will be the final impact
On the value of the company? (Equity + Debt)?
On the weighted average cost of capital (WACC)?
We now move to the impact of financing. If a company is partly financed by debt, does the value change?
This is not an obvious problem.
Debt is cheaper than equity and we might expect that the average cost of financing will be lower is debt is used.
But we also know that the risk of the equity of a levered company is higher. This should make remaining equity more costly.
What is result of the combination of this two effects?
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18. Corporate Financial Policy 1. Introduction
Modigliani Miller (1958)
Assume perfect capital markets: not taxes, no transaction costs
Proposition I:
The market value of any firm is independent of its capital structure:
V = E+D = VU
Proposition II:
The weighted average cost of capital is independent of its capital structure
WACC = rAsset
rAsset is the cost of capital of an all equity firm
Modigliani and Miller theorem were not the first to state that the Modigliani-Miller proposition of the irrelevancy of capital structure. They had been preceded by John Burr William. In his book The Theory of Investment Value (1938), he wrote:
“If the investment value of an enterprise as a whole is by definition the present worth of all its future distributions to security holders, whether on interest or dividend account, then this value in no wise depends on what the company’s capitalization is. Clearly, if a single individual or a single institutional investor owned all of the bonds, stocks and warrants issued by the corporation, it would not matter to this investor what the company’s capitalization was (except for details concerning the income tax). Any earnings collected as interest could not be collected as dividends. To such an individual it would be perfectly obvious that total interest- and dividend-paying power was in no wise dependent on the kind of securities issued to the company’s owner. Furthermore no change in the investment value of the enterprise as a whole would result from a change in its capitalization. Bonds could be retired with stock issues, or two classes of junior securities could be combined into one, without changing the investment value of the company as a whole. Such constancy of investment value is analogous to the indestructibility of matter or energy: it leads us to speak of the Law of the Conservation of Investment Value, just as physicists speak of the Law of the Conservation of Matter, or the Law of the Conservation of Energy.” (pp )
Reference
Rubinstein, M., Great Moments in Financial Economics: II Modigliani-Miller Theorem, Journal of Investment Management (Second Quarter 2003) (available at
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19. Corporate Financial Policy 1. Introduction
MM 58: Proof by arbitrage
Consider two firms (U and L) with identical operating cash flows X
VU = EU VL = EL + DL
Current cost Future payoff
Buy α% shares of U αEU = αVU αX
______________________________
Buy α% bonds of L αDL αrDL
Buy α% shares of L αEL α(X – rDL)
Total αDL + αEL = αVL αX
As the future payoffs are identical, the initial cost should be the same. Otherwise, there would exist an arbitrage opportunity
In 1958, when MM published their paper, the Capital Asset Pricing Model did not exist. Modigliani and Miller were among the first authors to base their result on the absence of arbitrage opportunities in competitive markets.
When asked to explain the theorem of American TV viewers, Miller presented the proposition as follow “Think of the firm as a gigantic pizza, divided into quarter. If now you cut each quarter in half into eights, the M and M proposition says that you will have more pieces but not more pizza”
Or, as Yogi Berra, the famous basket ball player, would put it: “You better cut the pizza in four pieces because I’m not hungry enough to eat six”
References:
Miller, M., The history of finance, Journal of Portfolio Management, Summer 1999
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20. Corporate Financial Policy 1. Introduction
MM 58: Proof using CAPM
1-period company
C = future cash flow, a random variable
Unlevered company:
Levered (assume riskless debt):
So: E + D = VU
The CAPM can be used to prove MM Proposition I. Remember, however, that the proposition does not require the CAPM.
Reference:
Rubinstein, M., A Mean-Variance Synthesis of Corporate Financial Policy
=VU
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21. MM 58: Proof using state prices
Corporate Financial Policy Introduction
MM 58: Proof using state prices
1-period company, risky debt: Vu>F but Vd<F
If Vd < F, the company goes bankrupt
Current value Up
Down
Cash flows
VUnlevered Vu Vd
Equity E
Vu – F
Debt D F
Example.
Consider an unlevered company with a market value equal to 100. Suppose that the length of one period is 1 year. The continuously compounded risk-free interest rate is 5%. The volatility of the unlevered company is 69.31%. During the period, the value of the company will either double (u = 2) or be divided by 2 (d = 0.5).
Based on these parameters, the state prices are vu = and vd = 0.602
The company decides to borrow and to use the proceed to buy back some of its shares. It issues a one-year zero-coupon with a face value F = 60.
In the up state: Vu = 200
The company repays its debt
The market value of the equity is equal to 200 – 60 = 140
The market value of the debt is equal to 60
If the down state: Vd = 50
The company is unable to repay its debt: it goes bankrupt
Stockholders lose everything. The market value of equity is 0
Bondholder take over the company. The market value of the debt is 50
Using the state prices, we can calculate the initial value of the equity and of the debt:
E = × 140 = 48.94
D = × × 50 = 51.06
Notice that the value of the risky debt is lower than the value of the riskless debt (60 × e-5% = 57.07)
More on this later in the course.
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22. Weighted average cost of capital
Corporate Financial Policy Introduction
Weighted average cost of capital
V (=VU ) = E + D
Value of equity
rEquity
Value of all-equity firm
rAsset
rDebt
Value of debt
We now want the understand the implication of MM Proposition I on the weighted average cost of capital of a company.
Consider the balance sheet (using market values) of a company. It can be viewed either from the asset side or from the liability side.
When viewed from the liability side, the weighted average cost of capital is the expected return on a portfolio of both equity and debt.
Consider someone owning a portfolio of all firm’s securities (debt and equity) with XEquity = E/V and XDebt = D/V
Expected return on portfolio = rEquity * XEquity + rDebt * XDebt
This is equal to the WACC (see definition):
rPortoflio = WACC
But she/he would, in fact, own a fraction of the company. The expected return would be equal to the expected return of the unlevered (all equity) firm
rPortoflio = rAsset
The weighted average cost of capital is thus equal to the cost of capital of an all equity firm
WACC = rAsset
WACC
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23. Corporate Financial Policy 1. Introduction
Using MM 58
Value of company: V = 100
Initial Final
Equity
Debt
Total MM I
WACC = rA 11% 11% MM II
Cost of debt - 5% (assuming risk-free debt)
D/V
Cost of equity 11% % (to obtain WACC = 11%)
E/V 100% 80%
Please note how the solution is built.
We first use MM Proposition I: the value of the company does not change.
As a consequence, the value of the equity of the levered company is E = VU – D = 100 – 20 = 80
We then use MM Proposition II: the WACC does not change WACC = rAsset = 11%
We then work out the cost of equity
11% = rEquity × % × 0.20
We make the assumption that the debt is riskless because we don’t know, at this stage, the impact of leverage on the cost of debt. This will be analyzed later in the course using option pricing models.
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24. Why are MM I and MM II related?
Corporate Financial Policy Introduction
Why are MM I and MM II related?
Assumption: perpetuities (to simplify the presentation)
For a levered companies, earnings before interest and taxes will be split between interest payments and dividends payments
EBIT = Int + Div
Market value of equity: present value of future dividends discounted at the cost of equity
E = Div / rEquity
Market value of debt: present value of future interest discounted at the cost of debt
D = Int / rDebt
Practitioners calculate present value by discounting expected unlevered cash flows at the weighted average cost of capital. We illustrate this approach in a simplified setting. It will be generalized later.
Suppose:
Expected EBIT is constant
No taxes
Replacement investment = Depreciation
Debt is a constant
The free cash flow of the unlevered company is:
FCFU = EBIT + Depreciation – Replacement investment = EBIT
and
FCFU = DivU
For the levered company:
FCFL = EBIT – Int + Depreciation – Replacement investment = EBIT – Int
FCFL = Div
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25. Relationship between the value of company and the WACC
Corporate Financial Policy Introduction
Relationship between the value of company and the WACC
From the definition of the WACC:
WACC * V = rEquity * E + rDebt * D
As rEquity * E = Div and rDebt * D = Int
WACC * V = EBIT
V = EBIT / WACC
Market value of levered firm
If value of company varies with leverage, so does WACC in opposite direction
EBIT is independent of leverage
The value of the levered company is calculated by discounting the free cash flow of the unlevered company (FCFU = EBIT) at the WACC.
Of course, we know from MM Proposition II that WACC = rAsset
As a consequence:
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26. MM II: another presentation
Corporate Financial Policy Introduction
MM II: another presentation
The equality WACC = rAsset can be written as:
Expected return on equity is an increasing function of leverage:
rEquity
12.5%
Additional cost due to leverage
11% rA
WACC
This is another presentation of the equality: WACC = rAsset
This presentation shows that the cost of equity increases with leverage.
If a company replace equity with debt, two things happens:
The company saves money because the cost of debt is lower than the cost of equity
On the other hand, the remaining equity becomes more costly.
In the MM 58 framework, the two effects offset each other. 5%
rDebt
D/E
0.25
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27. Why does rEquity increases with leverage?
Corporate Financial Policy Introduction
Why does rEquity increases with leverage?
Because leverage increases the risk of equity.
To see this, back to the portfolio with both debt and equity.
Beta of portfolio: Portfolio = Equity * XEquity + Debt * XDebt
But also: Portfolio = Asset
So: or
The reason why the cost of equity increases with leverage is because the risk is higher.
Remember that the beta of a portfolio is equal to the weighted average of the betas of the individual securities in the portfolio.
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28. Corporate Financial Policy 1. Introduction
Back to example
Assume debt is riskless:
Beta asset = 1
Beta equity = 1(1+20/80) = 1.25
Cost of equity = 5% + 6%  1.25 = 12.50
If we make the assumption that the debt is riskless, beta equity is a linear function of the debt-to-equity ratio.
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29. Summary: the Beta-CAPM diagram
Corporate Financial Policy Introduction
Summary: the Beta-CAPM diagram  
Beta L
βEquity U
βAsset r
rEquity
rAsset
rDebt=rf
D/E
The IS-LM diagram used by economist is the source of inspiration for this figure. For many years, I have tried to create a figure which would look as impressive as the IS-LM diagram. Here is the result.
The figure in the first quadrant shows the relationship between the debt-equity ratio and the beta equity. The figure is based on the assumption that the debt is riskless. In that case, the relationship is linear.
The security market line in illustrated in the second quadrant.
 The relationship between the debt-equity ratio and the cost of equity, the cost of debt and the WACC is in the third quadrant
 This is simply a -45% line.
This diagram can be used to show that investors can choose the level of leverage that they wish by rebalancing their portfolios.
If the company has no debt (point U), an investor can create leverage by borrowing at the risk-free interest to reach L, the risk and expected returns of a levered company.
If, on the hand, the company is levered (point L), an investor can allocate his money between the stock of the levered company and the risk free asset to undo the leverage and reach point U.  
rEquity
rDebt
D/E
WACC
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