Lecture 16
M&M Proposition I
Without taxes
And
Bankruptcy costs
Topic covered
1. Definitions of variables
2. Assumptions of the model
3. M&M Proposition I without taxes and
bankruptcy costs.
4. Formula, Meaning and Implication
5. Numerical example
6. Practice problem
Definitions of variables
1.
2.
3.
4.
5.
6.
7.
8.
9.
Capital structure = the mix of debt and equity financing in a firm
Unlevered firm = a firm that is financed entirely with equity, no
debt
Levered firm = a firm that is financed with a mixture of debt and
equity
EBIT
D
E
VU
VL
RUE
= Earnings before interest and taxes
= Dollar amount owed to Debtors
= Market value of all shares in the company
= Value of an unlevered firm
= Value of a levered firm
= Cost of equity for the unlevered firm
Assumptions
1. Perfect financial market
2. No taxes
3. No bankruptcy costs
M&M
• Franco Modigliani
• Merton Miller
• A theoretical model
– Relationship between capital structure and firm value
• Question:
If Debt/Equity mix  or 
=> Firm value  or ?
M&M Proposition I
- No taxes
- No bankruptcy costs
- Perfect market in which everyone and every firm can
borrow and lend at the same rate
- 2 firms with the same EBIT stream
- One firm financed by equity entirely – unlevered
- One firm financed by equity and debt – levered
M&M Proposition:
- Both firms should have the same value
- VU = EBIT/RUE = VL = DL + EL
Arbitrage opportunity
Toaster #1:
$20
Toaster #2:
$30
Arbitrage Opportunity:
VL < V U
50% 50%
Equity Debt
100%
Equity
Arbitrage Opportunity:
VL > VU
50% 50%
Equity Debt
100%
Equity
Equilibrium
50% 50%
Equity Debt
100%
Equity
Equilibrium
VL
= EL +
VU =
DL
EBIT / RUE
M&M I Formula
VU = EBIT/RUE
VL = DL + EL
VL = VU = EBIT/RUE
Numerical Example
Two firms have identical expected future stream of
EBITs 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 is the value of Firm U?
(b) What is the value of Firm L?
(c) What is the value of equity in Firm L?
(d) What is the share price in Firm U?
(e) What is the share price in Firm L?
Numerical Example (cont.)
Numerical Example (cont.)
Practice or perish
Quebec Inc. is an unlevered firm with 100,000 shares
outstanding. Each Quebec share is currently selling at
$15 per share, and the Quebec’s cost of capital is 20%.
Ontario Corp. is a levered firm with 60,000 shares
outstanding and $700,000 in debt. The cost of debt is
10%
(a) What is the debt-equity ratio of Ontario Corp. if it has
the same expected stream of EBIT as Quebec Inc.?
(b) What is the expected EBIT per year for the two
companies?
Check Answer:
Information given:
Unlevered Firm
Levered Firm
Share price = $15
Debt = $700,000
Number of shares = 100,000 Cost of debt = 10%
Cost of equity = 20%
(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
End of Lecture 16
M&M Proposition I
without taxes and bankruptcy costs