Slide #1: Lecture 17 – M&M Proposition II without taxes and bankruptcy
Welcome to Lecture 17: M&M Proposition II assuming no taxes and no bankruptcy costs.
Slide #2: Topics covered
In this lecture, we will cover six topics.
First, we will lay out what the M&M Proposition II says.
We will then discuss the formula that comes out of the proposition.
Next, we will show the proposition in a graph, which is THE graph to show when explaining
the M&M Proposition II.
Next, we demonstrate the implications of the proposition on the cost of equity and cost of
capital to a firm.
We then go through a numerical example that will make use of the proposition to derive a
firm’s cost of equity and its weighted average cost of capital (WACC).
Last, but never least, we end the lecture with a practice problem for you to try out what you
have learned in the lecture, with the requisite check answers.
Slide #3: M&M Proposition II without taxes and bankruptcy costs
The M&M Propositions are based on three crucial assumptions: One, that the market is
perfect, so that anyone and any firm can go to the market to borrow or lend at the same
rate. Two, that there are no corporate or personal taxes and so there are no tax
advantages to borrowing more debt. Three, that there are no bankruptcy costs, so that
there is nothing preventing a firm from borrowing as much debt as it wishes. That is, there
are no disadvantages to borrowing more.
Keep these assumptions at the back of your mind as we go through the rest of the lecture.
The M&M Proposition II without taxes and bankruptcy costs states that a firm’s cost of
equity depends on three factors only: one, the firm’s weighted cost of capital; two, its cost
of debt; and three, its debt-equity ratio. Another way to express this proposition is that a
firm’s weighted average cost of capital will remain unchanged no matter what its debtequity ratio. That is, the capital structure policy of a firm is irrelevant to its cost of capital.
Slide #4: The Formula
This is the M&M Proposition II formula which is used to calculate a levered firm’s cost of
equity:
RE = RA + [(RA – RD) x (D/E)]
where
RE = required rate of return on equity (cost of equity)
RA = required rate of return on firm’s assets = WACC
RD = required rate of return on debt
D = market value of debt
E = market value of equity
D/E = market value debt-equity ratio
This formula says that the cost of equity (or required rate of return on equity), R E, can be
calculated as the cost of capital on all assets (RA), plus the entirety of the difference
between the cost of capital and the cost of debt (R A - RD), multiplied by the debt-equity
ratio (D/E).
From this formula, we can see that the cost of equity will increase as the cost of capital on
the firm increases, the cost of debt decreases, or the debt-equity ratio increases (i.e., the
debt-level goes up or the equity-level goes down). If we hold the WACC and cost of debt
constant, the cost of equity of a firm will depend only on its D/E ratio, and the higher the
debt-financing in the firm, the higher will be its cost of equity.
Slide #5: The Graph
Required rate of return
RE
RA
WACC
RD
D/E ratio
This graph tells the story of M&M Proposition II without taxes and bankruptcy costs.
The horizontal (x-) axis on this graph represents the debt-equity ratio. As we move from
the left side to the right side on this axis, the debt-equity ratio increases. That is, the level
of debt-financing increases relative to equity-financing.
The vertical (y-) axis represents the required rate of return on the firm’s financing.
higher we move on this axis, the higher is the required rate of return.
The
We see from the rising diagonal line (the top line) on this graph that R E, the required rate of
return on equity, goes up as we increase the debt-equity ratio. That is, the cost of equity
rises as debt-financing is increased.
We also see that the WACC or total cost of capital on assets remains constant no matter
what the debt-equity ratio is. That is why the line for WACC is flat. That is, WACC is
independent of capital structure decisions.
The third line (at the bottom) is RD, the cost of debt. It is assumed to remain constant as
the D/E ratio goes up because of the assumptions from M&M that we listed earlier: that the
market is perfect and that there are no bankruptcy costs. Since anyone can go out there
and borrow or lend at the same rate, the cost of debt will remain unchanged. Further, if
there are no tax advantages to debt-financing, then the cost of debt will not decrease as
debt-financing is increased. Also, if there are no bankruptcy costs, there is no fear of the
cost of debt increasing as a firm borrow more and default risk increases. The cost of debt
will then remain constant as debt-level rises relative to equity-level.
Notice that the cost of debt is lower than the cost of equity.
calculated as:
We know that WACC is
WACC = (E/V)RE + (D/V)RD.
In a world without taxes, as we increase debt-financing, E/V will go down and D/V will go
up, while RE goes up.
M&M Proposition II implies that the increases in R E and D/V are exactly offset by the
decrease in E/V and a lower RD, so that the WACC will remain constant no matter what the
debt-equity split is. That is, the WACC is independent of the capital structure.
Slide #6: The Implications
M&M Proposition II without taxes and bankruptcy costs has three important implications:
1. The cost of equity is determined by only three factors:
- The cost of capital of the firm, denoted by RA, which we already noted is equal
to the WACC of the firm.
- The cost of debt of the firm, denoted by RD
- The debt-equity split of the firm, denoted by D/E
2. A firm’s cost of equity (RE) goes up as its use of debt-financing (D/E) goes up.
3. A firm’s WACC will not change when its capital structure changes, as long as its
future earnings potential does not change, there are no taxes or bankruptcy costs,
and the market is perfect. The cost of equity increases as we increase debtfinancing, but the rise in the cost of equity is exactly offset by the change in the
capital-structure weights and the increase in lower-cost debt-financing, so that the
WACC remains constant. That is, the WACC of the unlevered firm will be the same
as the WACC of the levered firm:
WACCU = WACCL
Slide #7: Numerical Example
Let’s use the M&M Proposition II on a numerical example.
Millets and Multigrain Inc. has a weighted average cost of capital of 15%. It is currently
financed entirely with common stock. Its current share price is $20, with 100,000 shares
outstanding. The company’s managers are contemplating a bond issue of $1.2 million at
10% interest rate. The cash received from the bond issue will be used to repurchase
60,000 of the firm’s common shares. After the repurchase, the share price will remain at
$20. According to M&M Proposition II without taxes and bankruptcy costs, what is the cost
of equity for the firm? What will be its WACC after the debt issue?
Slide #8: Numerical Example (cont.) – Calculation of RE
We first write down the information given:
WACC = RA = 0.15
Share price = $20
# shares = 100,000
(Because this is an unlevered firm, the firm value is equal to its equity value:
VU = E = $20 x 100,000 = $2,000,000.
D = $1,200,000
RD = 0.1
After the debt-issue and share repurchase, we have
DL = $1,200,000
EL = $20 x (100,000 – 60,000) = $20 x 40,000 = $800,000
VL = DL + EL = $1,200,000 + $800,000 = $2,000,000 = VU (from M&M Proposition I without
taxes and bankruptcy costs)
The new D/E ratio will be:
DL/EL = 1,200,000/800,000 = 1.5
We now have all the information we need to calculate the cost of equity based on M&M
Proposition II:
RE = RA + [(RA – RD) x (D/E)]
Plugging in RA = WACC = 0.15, RD = 0.1, and D/E = 1.5, we get
RE = 0.15 + [(0.15 – 0.1) x 1.5]
= 0.15 + 0.075
= 0.225
Therefore, the cost of equity is 22.5%.
Slide #9: Numerical Example (cont.) – Calculation of WACC
With EL of $800,000, DL of $1,200,000, and VL of $2,000,000, the capital structure weights
are:
EL/VL = 800,000 / 2,000,000 = 0.4
DL/VL = 1,200,000 / 2,000,000 = 0.6
We now have enough information to calculate the levered firm’s WACC:
WACC = [(EL/VL) x RE] + [(DL/VL) x RD]
= [0.4 x 0.225] + [0.6 x 0.1]
= 0.09 + 0.06
= 0.15
As you can see, the WACC remains the same after debt-financing, at 15%.
Slide #10: Less talk, more practice
Now, less talk on my part, and more practice on your part. Try the practice problem here on
this slide. The check answer is on the next slide. You may want to pause the video here
and take down all the information given in the problem, and try and solve the problem,
before moving on to the check answer on the next slide.
HST n’ BC Inc. is financed by debt of $2 million and equity of $2 million. The company’s
cost of debt is 8% and its weighted cost of capital is 16%. What is the company’s current
cost of equity? What is the impact on the cost of equity if the company wants to change its
debt-equity ratio to 0? 0.5? 1.5? 2?
Slide #11: Check answer to Practice Problem
We first write out the information given:
D = $2,000,000
E = $2,000,000
RD = 0.08
WACC = RA = 0.16
The debt-equity ratio is:
D/E = 2,000,000 / 2,000,000 = 1
M&M Proposition II without taxes and bankruptcy costs gives us the cost of equity formula:
RE = RA + [(RA – RD) x (D/E)]
Plugging in the numbers for RA, RD, and D/E, we get
RE = 0.16 + [(0.16 – 0.08) x 1]
= 0.16 + 0.08
= 0.24
If the D/E = 0, we have
RE = 0.16 + [(0.16 – 0.08) x 0]
= 0.16 + 0
= 0.16
If the D/E = 0.5, we have
RE = 0.16 + [(0.16 – 0.08) x 0.5]
= 0.16 + 0.04
= 0.2
If the D/E = 1.5, we have
RE = 0.16 + [(0.16 – 0.08) x 1.5]
= 0.16 + 0.12
= 0.28
If the D/E = 2, we have
RE = 0.16 + [(0.16 – 0.08) x 2]
= 0.16 + 0.16
= 0.32
Plotting the rates of return against the D/E ratio, we get the following graph:
0.35
0.3
0.25
0.2
RE
0.15
WACC
0.1
0.05
0
0
0.5
1
1.5
2
2.5
Slide #12:
Here ends Lecture 17 on M&M Proposition II without taxes and bankruptcy costs