John Molson School of Business at Concordia University
Lecture Notes on
Theory of Finance II
Topic V
Peiran Cheng
Winter 2019
Capital Structure
Table of Contents
I.
II.
III.
IV.
V.
VI.
Financial Leverage and Firm Value ...…………….P2
The Modigliani and Miller Proposition……..…......P4
Proving MM with No Taxes ……………...………...P6
MM with Corporate Taxes.....…………….…….......P7
An Illustration for MM with No Taxes…….……...P10
An Example for MM with Corporate Taxes …......P13
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Capital Structure
What is Capital Structure? What are differences between capital structure, capital allocation, and capital
budgeting?
Value of Firm (Pie Model – the sum of the financial claims of the firm – market values of debt and equity)
Obviously, shareholders will want to choose the capital structure that produces the highest firm value.
Financial Leverage and Firm Value
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Take a look at the numbers in the above forms, pay special attention to EPSs, what does financial
leverage mean based on your findings?
Financial Leverage and EPS
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Is Debt Better?
Leverage creates risk. A risk-averse investor might prefer the all-equity firm, while a risk-neutral (or less
risk-averse) investor might prefer leverage. Does a risk-loving investor simply love risk? How should we
define risk-hating, risk-neutral, and risk-loving?
MM (Modigliani and Miller) Proposition (famous) – argument that compares a simple strategy A
… with a two-part strategy (B) – Homemade Leverage
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Important Result (Rather Pessimistic)
Where does competition come into play? Let us discuss it with an analogy from Zootopia :D in class.
Must individuals borrow at higher rates than corporations? Let us discuss in class.
MM Propositions
For Proposition I, let us recall that the value of the firm is the present value of its future cash flows.
For Proposition II, mathematically, what is the condition on which the expected return on equity is
positively related to leverage? 𝑟0 is the cost of capital for an all-equity firm. It must always equal to
WACC in a world without corporate taxes, and it should normally exceed 𝑟𝐵 (why?).
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Proving MM Proposition I (No Taxes)
MM Proposition II (No Taxes)
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M&M Proposition II (1958)
This can be an interesting graph to talk about.
The MM Proposition I (Corp. Taxes) – adding an additional claim on the value of the firm – CRA
It feels like the Canadian Tax Law actually subsidizes debt financing, right? And why is the PV T C B?
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M&M Proposition I (1963)
The MM Proposition II (Corp. Taxes)
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The Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate Taxes
Financial Leverage adds risk to the firm’s equity. As compensation, the cost of equity rises with the
firm’s risk.
Note that the cost of debt capital is after-tax because interest is tax deductible at the corporate level.
However, the cost of equity is not because dividends are not deductible. In the no-tax case, WACC is not
affected by leverage. However, since debt is tax advantaged relative to equity, it can be shown that
WACC declines with leverage in a world with corporate taxes.
Always remember: higher returns have to come with higher risks.
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Proposition I & II: An Illustration
Solution
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Firm Issues Equity
Equity Issue: Balance Sheet on Completion of the Project
You may wonder where the 11 million is from on this page and the next page. The 10 million is the
expected yearly cash flow on old assets and the 1 million is the expected yearly cash flow on new assets.
Your knowledge of accounting comes handy in this topic.
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Debt Financing
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Total Cash Flow to Investors under Each Capital Structure with Corporate Taxes
Taxes and MM: An Example
Why is the interest payment 400,000?
… the MM Proposition provides a short cut to calculate the tax saving.
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An Example: Dividend Airline
Value of the Firm
Note in the calculation, the value of the firm is the present value of its perpetual cash flows.
E=S.
Check:
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Reflection on Debt
Old Polonius counsels his hotheaded son Laertes, who is about to embark for Paris for his gentleman's
education. While he still has the chance, Polonius wholesales a stockroom of aphorisms, the most famous
of which is "Neither a borrower nor a lender be." On Polonius's terms, there is little to argue with in his
perhaps ungenerous advice. His logic is thus: lending money to friends is risky, because hitching debt
onto personal relationships can cause resentment and, in the case of default, loses the lender both his
money and his friend. Borrowing invites more private dangers: it supplants domestic thrift
("husbandry")—in Polonius's eyes, an important gentlemanly value. Incidentally, in the days when
Hamlet was first staged, borrowing was epidemic among the gentry, who sometimes neglected husbandry
to the point where they were selling off their estates piece by piece to maintain an ostentatious lifestyle in
London. (Hamlet Act 1, scene 3, 75-77)
Nassim Nicholas Taleb is a great writer on the subject of risk, and I recommend you to read all his books.
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