Slide #1: Lecture 19 M&M Proposition II with Taxes
Welcome to Lecture 19: M&M Proposition II with taxes but no bankruptcy costs.
Slide #2: Topics covered
In this lecture, we will cover the following seven topics:
- We will first discuss the assumptions in M&M Proposition II with taxes.
- We then briefly go through a general interpretation of M&M II with taxes.
- Next, we define the formulae derived from M&M II with taxes.
- We then discuss the implications of the model.
- This will be followed by a graph that will clearly show the implications of the model.
- We then move on to apply the formulae by going through a numerical example.
- And, last but not least, a practice problem is presented for you to try out your newly-learned knowledge, with the requisite check answers.
Slide #3: Assumptions
The three assumptions involved in M&M Proposition II with taxes are:
- A perfect market, in which anyone and any firm can go out into the market and borrow and lend at the same rate. This assumption makes sure that the cost of debt is constant.
- There are no bankruptcy costs. This assumption makes sure that there are no disadvantages to borrowing more and more debt.
- The third assumption is that the firms are going concerns. This assumption allows us to use the PV(perpetuity) to derive the formulae for M&M I and II with taxes.
Slide #4: General Interpretation of M&M II with taxes
Generally speaking, M&M Proposition II with taxes models the cost of equity of a levered firm as being determined by four factors: the cost of unlevered capital (RU), the cost of debt (RD), the firm’s financial leverage (D/E), and the marginal corporate tax rate (TC). The prediction from the model is intimately related to the WACC being reduced by interest tax shields.
Slide #5: Formulae
Two formulae are derived from M&M Proposition II with taxes:
- Cost of equity = RE = RU + [(RU – RD) x (D/E) x (1 - TC)]
- WACC = [(E/V) x RE] + [(D/V) x RD x (1 - TC)]
Slide #6: Variables defined
On this page, we present the variables used in the formulae derived on the previous slide:
RE= Cost of equity
RU= Cost of capital for an unlevered firm
= WACCU = Cost of equity on unlevered firm (REU)
RD= Cost of debt (assumed to be constant)
D = $ amount of debt
E = $ amount of equity
D/E = Debt-equity ratio
TC= Marginal corporate tax rate
V = Total asset value of the firm = D + E
E/V = Weight of equity in the capital structure
D/V = Weight of debt in the capital structure
Slide #7: Implications
The three implications of M&M Proposition II with taxes are:
- The cost of equity will go up as financial leverage (D/E) goes up.
- The risk of equity depends on the firm’s business risk and its financial risk.
- A firm’s WACC will go down as its financial leverage (D/E) goes up.
Slide #8: Graph
On this slide, we have a graph that makes the implications from the M&M Proposition II with taxes clearer.
Cost of capital (R)
RE
WACC
RD (1-TC)
D/E
In the top (diagonal) line, we have the return on equity (cost of equity), which as we can see, goes up as we move to the right of the graph (i.e., as D/E increases).
The second highest (horizontal/flat) line represents the cost of capital of the unlevered firm, which does not change when we increase financial leverage, keeping everything else constant.
The third (curved) line from the top represents the WACC, which decreases at a declining rate as financial leverage (D/E) increases (i.e., as we move towards the right side of the graph).
The bottom (horizontal/flat) line represents the after-tax cost of debt, which does not change as financial leverage (D/E) increases. This is a result of the perfect market assumption of the model.
Slide #9: Numerical example
Now, let’s do a numerical example. We have two companies, ABC and XYZ. ABC Inc. and XYZ Co. are identical except for their financing policy. ABC is financed with all equity, whereas XYZ has $1,000,000 in debt-financing. Both firms have earnings before interest and taxes of $500,000, and both are subject to a 35% corporate tax rate. ABC’s cost of capital is estimated to be 18%. Cost of debt is 9%.
By using M&M I with taxes, we obtain the following values:
Value of unlevered firm: VU = $1,805,555.56
Value of levered firm: VL = $2,155,555.56
Value of levered firm’s equity: EL = $1,155,555.56
a. What is ABC’s cost of equity?
b. What is XYZ’s cost of equity?
c. Compare the two firms’ cost of equity. Which one is higher?
d. What is ABC’s weighted average cost of capital?
e. What is XYZ’s weighted average cost of capital?
f. Compare the two firms’ WACC. Which one is lower?
Slide #10: Numerical example (cont.)
Information given:
D = $1,000,000
EBIT = $500,000
TC = 0.35
RU = 0.18
RD = 0.09
Value of unlevered firm: VU = $1,805,555.56
Value of levered firm: VL = $2,155,555.56
Value of levered firm’s equity: EL = $1,155,555.56
Part a:
ABC’s cost of capital = WACCU = REU = RU = 0.18
Part b:
XYZ’s cost of capital can be calculated using the M&M II formula for cost of equity:
RE = RU + [(RU – RD) x (D/E) x (1 - TC)]
We know RU, RD, and TC. We need to find D/E:
D/E = $1,000,000 / $1,155,555.56 = 0.86538462
XYZ’s RE = 0.18 + [(0.18 - 0.09) x 0.86538462 x (1 – 0.35)] = 0.18 + 0.050625 = 0.230625
Part c:
Comparing the two firms’ cost of equity, we find that the levered firm’s (XYZ) cost of equity is higher. This confirms the first implication of M&M II with taxes.
Slide #11: Numerical example (cont.)
We have the following information:
RE = 0.230625
RD = 0.09
TC = 0.35
D = $1,000,000
Value of unlevered firm: VU = $1,805,555.56
Value of levered firm: VL = $2,155,555.56
Value of levered firm’s equity: EL = $1,155,555.56
We can calculate weight of debt as:
D/VL = $1,000,000 / $2,155,555.56 = 0.46391753
EL/VL = $1,155,555.56 / $2,155,555.56 = 0.53608247
Part d:
ABC’s WACC = RU = 0.18
Part e:
Formula for calculating the levered firm’s WACC:
WACC = [(E/V) x RE] + [(D/V) x RD x (1 - TC)]
Therefore,
XYZ’s WACC = [0.53608247 x 0.230625] + [0.46391753 x 0.09 x (1 - 0.35)] = 0.12363402 + 0.02713918 = 0.1507732
Part f:
Comparing the two firms’ WACC, XYZ has the lower of the two. This confirms the third implication of M&M II with taxes.
Slide #12: Practice problem – The road to finance heaven…
May your road to finance heaven be paved with gold… and practice! Here is a practice problem to get you on your way. Pause the video here, take down the information given, and try to answer the questions before moving on to the next two slides for the check answer. Have fun!
We have two firms, Firm U and Firm L, that are identical in every respect except for their financing policy. Firm U has zero debt, and its assets have an estimated value of $10 million. Firm L is partly financed with debt at an interest rate of 8%, and its assets have an estimated value of $12.5 million. Given that both firms are subject to a corporate tax rate of 40%, and both have an EBIT of $2 million.
Using M&M Proposition I with taxes, we find the cost of capital of Firm U is 12% and debt-equity ratio is 1.
a. What is the cost of equity for Firm U?
b. What is the cost of equity for Firm L?
c. What is the WACC for Firm L?
d. Is the cost of equity higher or lower for Firm L?
e. Is the WACC higher or lower for Firm L?
Slide #13: Check answer
Here is the check answer for the practice problem:
Information given:
VU = $10,000,000
VL = $12,500,000
RD = 0.08
TC = 0.4
EBIT = $2,000,000
RU = 0.12
D/E = 1
Part a:
Firm U’s Cost of equity = RU = 0.12
Part b:
Firm L’s Cost of equity = RE
= RU + [(RU - RD) x (D/E) x (1 - TC)]
= 0.12 + [(0.12 - 0.08) x 1 x (1 – 0.4)]
= 0.12 + 0.024
= 0.144
Slide #14: Check answer (cont.)
Part c:
Information needed to calculate Firm L’s WACC are:
RD = 0.08
TC = 0.4
RU = 0.12
D/E = 1
RE = 0.144
We can use D/E to find the capital structure weights:
D/E = 1
For every dollar of debt, there is one dollar of equity. Therefore, if we imagine the total assets are made up of two parts, then the weight on debt is ½ and the weight on equity is also ½:
D/V = E/V = 0.5
WACC is then calculated as:
WACC = [(E/V) x RE] + [(D/V) x RD x (1 - TC)]
= [0.5 x 0.144] + [0.5 x 0.08 x (1 - 0.4)]
= 0.072 + 0.024
= 0.096
Part d: Cost of equity of 0.144 for Firm L is higher than the cost of equity for Firm U (0.12).
Part e: WACC for Firm L (0.096) is lower than the WACC for Firm U (0.12).
Slide #15: End of Lecture 19
Here ends Lecture 19 on M&M Proposition II with taxes but no bankruptcy costs.