BEEM117Economics of Corporate Finance

Lecture 1

Some announcements

• Course information (slides, homework, etc.)– http://people.exeter.ac.uk/maf206/ecf.htm– Office hours: 13:30-15:30 on Mondays

• “Main” textbook:– Tirole, J. The Theory of Corporate Finance, 2006– Available in the library and bookstore.

• Other references will be in week’s handout

Some announcements

• Warning:– Basing your study on lecture slides alone is a fatal mistake!– These slides will NOT contain all relevant information for the

exam.– You must do the required readings/homework every week!

• Assessment:– 100% exam; – Exam will consist of 6 questions, of which you must answer

any 3.

Some announcements

• Each week we will meet for two hours:– 1st hour will cover new material;– 2nd hour will cover homework and questions.

• The purpose of the 2nd hour is to review old material and address any questions you have.– If you haven’t done the work, it’s usefulness will be

limited.– Also it is a good opportunity to provide feedback

regarding the class.

Corporate Finance

• We will start by recognising there are two different ways a firm can finance itself:– It can issue stocks (Equity);– It can borrow money from investors (Debt).

• Debt can be thought as simply a claim on the income generated by the firm.

• Equity holders receive any remaining profit– They are “residual claimants”.

Corporate Finance

• Claims to the firm’s revenues can be stratified further, depending on type of debt/equity:– 1. Secured Debt: – 2. Ordinary Debt:

• Senior• Junior/Subordinated

– 3. Preferred Stock:– 4. Common Stock:

Debt vs. Equity

• Why pay attention to whether firms issue debt or equity?

• Does this decision impact the value of a firm?

• Modigliani and Miller devoted their attention to this question in the late 1950’s and had a striking (and Nobel prize-winning) answer:– Under some conditions, the value of the firm is

unaffected by the combination of debt and equity.

The Value of a Firm:Definitions and simplifying assumptions

• ‘The firm’ is an incorporated limited liability company.

• Firm’s equity is tradable and is of only one type – common stock, denoted as S.

• Firm’s can also raise capital by issuing bonds, B, which are also marketable.

The Value of a Firm:Definitions and simplifying assumptions

• V is the total market value of the firm:– V = B + S.

• Leverage ratio = B/S.

• Firm must make financial outlays at certain dates to bond holders.

• Failure to do so (i.e. revenues < debt repayments) results in bankruptcy.

The Value of a Firm

• A traditional approach to finance argued that market value of the firm is inversely related to its cost of capital.

• Suppose a firm has zero debt:

• Issuing debt in exchange for its equity reduces its cost of capital (why?)

• Equity is related to profitability of firm, while debt repayments are pre-determined.

The Value of a Firm

• Hence equity is a riskier investment than debt.

• Also if debt levels are low, risk of bankruptcy is negligible.

• As debt levels rise the possibility of default goes up and that increases the cost of capital.

The Value of a Firm

WACC

• Assume firms maximise their market value;

• Let:– B/S express a firm’s leverage;– ρ denote a firms WACC;– i denote the rate of return on equity;– r denote the rate of return on bonds.

• Then: rV

Bi

V

S

WACC

• Because V = S + B, we can re-write S/V and B/V as functions of leverage.

• We can re-express WACC as:

)/(1

/,)/(1

1

SB

SB

V

B

SBV

S

rSB

SBi

SB )/(1

/

)/(1

1

WACC

• Take an example of a firm which has 60% of its financing through equity and 40% via bonds.– The leverage of the firm is therefore 0.6/0.4 = 2/3.

• The interest rate on its debt is 10% and the expected rate of return to equity holders is 15%.– ρ = 0.6 x 0.15 + 0.4 x 0.1 = 0.13

• As B/S goes up, so does the risk of bankruptcy: – Bondholders demand higher returns on their investment,

making debt less attractive, – Hence the U-shape of the WACC

Modigliani-Miller (MM)

• MM’s work in the late 1950’s completely changed the way economists perceive this question.

• They argued that under certain conditions, the value of the firm is independent of its leverage. (MM-1)

• That is, the shape of the ρ function is a flat line

• This means the cost of equity must be a function of leverage. (MM-2)

MM-1 Assumptions

• Existence of risk classes– A risk class is a set of firms with identical earnings across

different states of the world.

• Taxes are neutral– The tax rate is the same for all firms and the same for all

types of earnings.

• Frictionless capital markets– Zero transaction costs– No restrictions on asset trades

MM-1 Assumptions

• Investors can borrow on the same terms as firms

• Firms’ financial policy convey no information about earnings across states of the world

• No Bankruptcy– Earnings are assumed to be higher than debt

payments across all states of the world.

MM-1

• There are k states of the world, each of whom occurs with probability pk.

• The value of the firm’s assets (or it’s revenue) in state k is Xk.– Therefore firm’s earnings are also uncertain.

• Once the true state of the world is revealed, so are firm’s earnings.

MM-1

• Bond holders are promised a payment equal to Z, which is assumed to be constant across k.– By assumption Xk > Z

• Equity holders’ payment is a function of Xk.– In particular, it is equal to max(Xk – Z,0).

• So, does the mix of equity and debt matter for the value of the firm?

MM-1

• Consider two different firms, U and L.– U is unlevered– L has issued bonds with market value BL

– U and L are exactly identity in all other regards

• Suppose firm L sets Z=600 on its bonds and also that BL is equal to 500.

• There are two states of the world such that:– X1 = 1500 and X2 = 700

• Finally, suppose the market value of both firms is 1000

MM-1

MM-1

• If both firms’ value is the same, a 1% investment in either firm yields the same payoff in every state of the world.

• If this is not true, an investor could construct an arbitrage portfolio:– With a zero capital outlay, generate non-negative

payoffs in all states and strictly positive in at least one state.

MM-2

• The second MM theorem states that the firm’s cost of equity capital is a linear function of its debt-to-equity ratio.

• To show this we must state some definitions:– Cost of equity capital:

– Cost of bond finance:

– Cost of capital (WACC): V

XEB

Zr

S

ZXEi

)(1

1

)(1

MM-2

• MM-2 states that the following linear relationship holds:

• As the cost of bond finance goes up, the smaller the effect the leverage ratio has on the cost of equity.

• Conversely, the higher the leverage ratio, the higher the cost of equity.

• Note, however, that ρ is invariant wrt B/S as per the last slide.

S

Bri )(