Slide #1: Lecture 16 – M&M Proposition I without taxes and Bankruptcy costs
Welcome to Lecture 16: M&M Proposition I without taxes and Bankruptcy costs.
Slide #2: Topics covered
In this lecture, we will cover the following topics:
1. We will first define the variables and terms related to the M&M Proposition I.
2. Next, we will discuss the assumptions of the model.
3. We will then properly introduce the M&M Proposition I, what it says, in words and in
formula.
4. We will then go through the formula associated with the model, and interpret the
meaning of the model and its implication.
5. The meaning and implications will become more apparent as we go through a
numerical example.
6. And, last but never least, you will get a practice problem, with check answers, which
you can work on at your leisure.
Slide #3: Variable definitions
So, let’s start by giving the definitions of the variables and terms we will be using in this
lecture to discuss the M&M proposition.
First, let’s define a couple of important terms.
When we refer to the capital structure decision of a firm, we are talking about the decision
of the firm regarding how much debt and equity to use to finance the assets of the firm.
When we speak of an unlevered firm, what we mean is a firm that has no financial leverage,
i.e., a firm that is financed entirely with equity and zero debt. On the other hand, when we
talk about a levered firm, we are talking about a firm that is financed with a mixture of debt
and equity. So, for an unlevered firm, the debt-equity ratio is equal to 0. For a levered
firm, the debt-equity ratio is greater than 0.
Now, we move on to the definitions of some variables.
EBIT (which stands for Earnings Before Income and Taxes) is a number that measures the
earnings before interest and taxes for a firm. EBIT is usually calculated as Revenues minus
costs.
The letter D is a symbol used to represent the dollar amount borrowed, i.e., owed to a
firm’s Debtors. Usually, this number consists of both long-term debt and current liabilities.
The letter E is a symbol used to represent the market value of the shares in the firm. Its
value is usually calculated as the market value of the firm, less the amount of debt owed to
debtors.
VU represents the value of an unlevered firm, that is, a firm financed completely with equity.
VL represents the value of a levered firm, that is, a firm that is financed with both debt and
equity.
RUE represents the cost of Equity for the Unlevered firm.
We will use these variables almost constantly throughout this lecture, so it is a good idea to
have them memorized at this point. You might want to pause this video right here, take a
breath, and memorize them here and now.
Slide #4: Model assumptions
Before we start going into, or indeed using, the M&M propositions/models, we must keep in
mind the following three key assumptions:
1. The financial market is assumed to be perfect, which means that anyone and any
firm can go to the market to borrow or lend at the same interest rate.
2. There are no taxes, personal or corporate or otherwise.
3. There are no bankruptcy costs, i.e., it costs nothing for a firm or a person to declare
bankruptcy. This assumption does not say that bankruptcy does not occur; it just
says that there are no costs to declaring bankruptcy.
Slide #5: M&M
So, what is M&M?
‘M&M’ actually refers to two finance professors, Dr. Franco Modigliani and Dr. Merton Miller.
They wanted to find the answer to the research question: ‘Will a change in capital structure
cause a subsequent change in the value of the firm? In practice, if the manager of a firm
decides to increase the firm’s financial leverage, will the firm value increase or decrease, or
will it stay the same?’
Slide #6: M&M Proposition I
Modigliani and Miller’s first proposition on the relationship between firm value and capital
structure is as follows:
Given a world without taxes and bankruptcy costs, with perfect market, two firms with the
same EBIT stream where one firm is financed entirely with equity, and the other firm is
financed by a mix of equity and debt. Aside from this difference in capital structure, the two
firms are identical. We call the equity-financed firm an unlevered firm, and the other firm a
levered firm.
Given these conditions, M&M Proposition I states that both firms should have the same
value, and that this value can be calculated simply as the present value of the EBIT stream,
discounted at the unlevered cost of equity:
VU = EBIT/RUE = VL = DL + EL.
Secondly, the value of the levered firm can also be calculated as debt plus equity.
Slide #7: Toaster Arbitrage
Toaster #1
$20
Toaster #2
$30
Modigliani and Miller reached their famous conclusion by using the no-arbitrage argument.
So, what is an arbitrage opportunity? An arbitrage opportunity occurs when we can make
profits without risk or initial cash flow. So, for example, let’s say we have found two lovely
and identical toasters at two different stores. Store #1 sells the toaster at a price of $20,
and Store #2 sells the toaster at $30. What can we do to make arbitrage profits?
We can go to Store #1, buy their toaster at $20, then go wait outside Store #2 and sell
your toaster to that store’s customer for $25. It’s a deal for these customers, and you will
make $5 for each toaster you sell! All you have to do is simply buy and sell toasters to earn
riskless profits! And of course, one will also have to evade the Security people at Store #2.
The trouble with this type of opportunities is that, sooner or later, everyone will see the
existence of these profit opportunities, and then everyone will go buy toasters at Store #1.
After a while, Store #1 will learn that they can raise their toaster price and customers will
still buy from them, as long as the price is lower than that at Store #2. Store #2 will learn
that if they don’t reduce the price, they will lose all their toaster customers. As Store #1
raises toaster price and Store #2 lowers toaster price, there will come a time of
“equilibrium”, where the two stores will charge the same price for the (identical) toasters,
say, $25 per toaster. The free-profit will then disappear for everyone else.
This is the essence of the no-arbitrage argument. In an efficient and perfect market, there
are no arbitrage opportunities, as any profits will be competed away at the equilibrium.
Slide #8: Arbitrage opportunity – VL < VU
So, given that we believe in the existence of an efficient and perfect market, the same noarbitrage argument can be applied to firm value and capital structure.
If two firms have the same EBIT stream and are identical in every way except for their
capital structures, there should not be any difference between their firm values.
If the value of the levered firm is lower than the value of the unlevered firm as indicated in
the pies above, investors will buy low and sell high. They will buy the debt and shares of
the levered firm and sell the shares of the unlevered firm.
Let’s say that the levered firm is financed by 50% debt and 50% equity, with debt valued at
$1,000 and equity valued at $1,000, thus yielding a levered firm value of $2,000.
The unlevered firm’s equity, on the other hand, is valued by the market at $3,000.
Both of these firm values are based on the market’s evaluation of the future income stream
from the two firms.
Since both firms are identical in every respect, they should be worth the same value. The
fact that this is not true will attract investors to buy the levered firm and sell the unlevered
firm.
Let’s say I currently own 10% of the shares in the unlevered firm. I can sell my shares for
0.1 x $3,000 = $300. I then take this $300 and buy $150 worth of debt and $150 worth of
equity in the levered firm. This will give me $150/$1000 = 0.15 = 15% of the debt and
equity in the levered firm. That is, I now own 15% of the levered firm. This gives me 15%
on the same identical cash flow stream as that of the unlevered firm. All I had to do was
switch my allegiance from the unlevered firm to the levered firm. It does not cost me
anything to get an additional 5 percent of the same future cash flow stream. I have just
profited from an arbitrage opportunity without any cash outlay or any additional risk.
Slide #9: Arbitrage opportunity – VL > VU
Similarly, if the value of the levered firm is greater than that of an identical unlevered firm,
we would sell the levered firm’s debt and equity, and use the proceeds to buy the unlevered
firm’s equity. We will gain percentage ownership without any initial cash outlay or any
other risk.
Slide #10: EQUILIBRIUM!
With the no-arbitrage argument, eventually, prices for the two firm’s debt and equity will
balance each other out, in such a way that the value of the levered firm will equal the value
of the unlevered firm. That is, the debt + equity of the levered firm will equate with the
equity value of the unlevered firm.
Slide #11: Equal firm values
We calculate the value of the levered firm as the sum of its equity value and debt value:
Value of the levered firm =VL = EL + DL
The value of the unlevered firm is calculated as the present value of the perpetuity, EBIT,
discounted at the unlevered cost of capital, RUE:
VU = EBIT/RUE.
At the equilibrium point, the value of the levered firm must equal the value of the unlevered
firm:
VL = EL + DL = VU = EBIT/RUE
Slide #12: M&M Proposition I formulae
That is how we arrive at the three M&M Proposition I formulae below:
VU = EBIT/RUE
VL = DL + EL
VL = VU = EBIT/RUE
Take a moment to memorize them, as these are the important formulae relating to this
model.
Slide #13: Numerical example
And now, let’s try out these formulae with this numerical example here.
Two identical firms have identical expected future EBIT-streams of $9,000 per year. Firm U
is financed entirely by issuance of 1,000 shares at a cost of 15%. Firm L is financed by
issuance of 500 shares and $30,000 in debt at an interest rate of 8%.
(a) What
(b) What
(c) What
(d) What
(e) What
is
is
is
is
is
the
the
the
the
the
value of Firm U?
value of Firm L?
value of equity in Firm L?
share price in Firm U?
share price in Firm L?
Slide #14: Numerical example (cont.)
First, we write down the information we have been given:
EBIT = $9,000
Firm U:
# shares = 1,000
Cost of capital = RUE = 0.15
Firm L:
# shares = 500
Debt = $30,000
Debt interest rate = 0.08
To answer part (a) of the problem, we calculate the value of the unlevered firm as:
VU = EBIT/RUE = $9,000 / 0.15 = $60,000
To answer part (b), we calculate the value of the levered firm as:
VL = VU = $60,000
To answer part (c), we calculate the equity value of the levered firm using the formula:
VL = EL + DL
Subtracting DL from both sides, we get
EL = VL – DL = $60,000 - $30,000 = $30,000
Slide #15: Numerical example (cont.)
To answer part (d), which asked for the share price of the unlevered firm, we know that
share price is calculated as the firm’s equity value divided by the number of shares. The
value of the unlevered firm is the same as its equity value (as it is 100% equity-financed).
Therefore, the unlevered firm’s share price, PU, is:
PU = VU / # shares = $60,000 / 1,000 = $60
To answer part (e), which asked for the share price of the levered firm, we again use the
formula:
share price = equity value divided by number of shares
We know that the equity value in Firm L is $30,000 and that there are 500 shares
outstanding. This gives us Firm L’s share price, PL, as:
PL = EL / # shares = $30,000 / 500 = $60
Note that it is not necessarily always true that the share price of the unlevered firm is the
same as the share price of the levered firm. It just works out this way with the numbers in
this numerical example.
Slide #16: Practice problem
They say in academic circles: Publish or Perish. Here, we are fanatical about finance, so,
practice or perish!
Here’s a practice problem for you to test your understanding of M&M Proposition I without
taxes and bankruptcy costs.
We have two companies. Quebec Inc., is an unlevered firm that has 100,000 shares
outstanding. The common stock of this company is currently selling at $15 per share, and
its cost of capital is 20%. Conversely, Ontario Corp. is a levered firm with 60,000 shares
outstanding and $700,000 in debt outstanding. The cost of debt for Ontario Corp. is 10%.
We are then asked two questions:
(a) What is the debt-equity ratio for Ontario Corp., if it has the same expected future
stream of EBIT as the unlevered firm Quebec Inc.?
(b) What is the expected EBIT per year for Quebec Inc.?
You may want to pause here, and take down all the information given. Try to work out the
answers and then continue the video to the next slide to see the check answers.
Slide #17: Check answer for practice problem
Here are the check answers for the practice problem.
Given the following information:
Unlevered firm:
Share price = $15
Number of shares = 100,000
Cost of equity = RUE = 20% = 0.2
(a) D/E ratio for Levered Firm:
Vu = Share price x Number of shares
= $15 x 100,000 = $1,500,000
VL = VU = $1,500,000
VL = DL + EL
 EL = VL – DL
 EL = $1,500,000 - $700,000 = $800,000
DL/EL = 700,000/800,000 = 0.875
(b) Cost of equity for Unlevered Firm:
VU = EBIT/RUE
=> EBIT = VU x RUE = $1,500,000 x 0.2 = $300,000 per year
Slide #18: End of Lecture 16
Here ends Lecture 16 on M&M Proposition I without taxes and bankruptcy costs.