<p>You say that when <span class="math-container">$T_C$</span> is close to 100%,</p>
<blockquote>
<p>the shareholders are getting close to nothing, as the government takes almost everything what is left after the bondholders have taken their share of EBIT.</p>
</blockquote>
<p>This suggests you think <span class="math-container">$R_E$</span> and <span class="math-container">$R_U$</span> are pre-tax returns. However, they are actually after-tax returns. By noting that, the puzzle goes away.</p>

CC BY-SA 4.0
2022-11-03T11:00:37.677Z
2022-11-03T11:00:37.677Z
Richard Hardy
<p>Your statement “the equity holders get nothing” doesn’t seem clear to me and I don’t think it follows from the equation. The equity holders still get <span class="math-container">$R_E$</span>.</p>
<p>The equation and theorem follow from a simple no-arbitrage condition between debt and equity.</p>
<p>With taxes, debt provides the advantage of a tax shield, which means debt becomes better (cheaper) than equity. The higher the tax rate, the higher the tax shield.</p>
<p>To satisfy no-arbitrage, the return on (cost of) equity then also has to come down, because the effective cost of debt is coming down with the tax rate. Otherwise the firm would just have all debt and no equity.</p>
<p>All your other concerns should be resolved from there.</p>

CC BY-SA 4.0
2023-04-02T18:41:38.830Z
Thanks! What solves the puzzle is the realization that $R_E$ and $R_U$ are after-tax returns. Without that, the puzzle would remain. Fortunately, I have already noted that in my answer.
Richard Hardy
CC BY-SA 4.0
2023-04-02T15:18:08.560Z
2023-04-02T15:18:08.560Z
BB King
<p>Consider Modigliani &amp; Miller Proposition II with corporate taxes. The cost of equity is
<span class="math-container">$$
R_E=R_U+(R_U-R_D)\cdot \frac{D}{E}\cdot (1-T_C) \tag{1}
$$</span>
where <span class="math-container">$R_E$</span> is the cost of equity, <span class="math-container">$R_U$</span> is the cost of capital a firm would have if it had no debt (unlevered cost of capital), <span class="math-container">$R_D$</span> is the cost of debt, <span class="math-container">$D$</span> is debt, <span class="math-container">$E$</span> is equity and <span class="math-container">$T_C$</span> is the corporate tax rate.</p>
<p><span class="math-container">$R_U$</span> has to be equal to return on assets, <span class="math-container">$R_A=R_U$</span>. Otherwise (if <span class="math-container">$R_A&lt;R_U$</span>), the shareholders would not be willing to hold the shares.</p>
<p>Now by equation <span class="math-container">$(1)$</span>, <span class="math-container">$R_E$</span> falls as <span class="math-container">$T_C$</span> increases. If <span class="math-container">$T_C$</span> is incredibly high, say close to 100%, we get <span class="math-container">$R_E\approx R_U$</span>. So the shareholders are getting close to nothing, as the government takes almost everything what is left after the bondholders have taken their share of EBIT. Yet the shareholders' <em>required</em> return <span class="math-container">$R_E$</span> is lower than in the case of no tax where the shareholders reap all the profit after the bondholders have taken their share of EBIT. I find that counterintuitive. Could anyone help me clarify why this is (or is not) so?</p>

CC BY-SA 4.0
2022-10-31T16:13:46.283Z
What is the question? It looks like a statement
1muflon1
CC BY-SA 4.0
2022-10-31T16:14:34.140Z
@1muflon1, the last sentence says "I find it counterintuitive". I am looking for some explanation for why this is (or is not) the case.
Richard Hardy
CC BY-SA 4.0
2022-10-31T16:23:13.857Z
A bit related: https://economics.stackexchange.com/questions/52465
Richard Hardy
<taxation><corporate-finance>
Impact of the corporate tax rate on the cost of equity (Modigliani & Miller Proposition II)
Richard Hardy
# Impact of the corporate tax rate on the cost of equity (Modigliani & Miller Proposition II)

(Asked by: username_0 on 2022-10-31)

Consider Modigliani & Miller Proposition II with corporate taxes. The cost of equity is
$$
R\_E=R\_U+(R\_U-R\_D)\cdot \frac{D}{E}\cdot (1-T\_C) \tag{1}
$$
where $R\_E$ is the cost of equity, $R\_U$ is the cost of capital a firm would have if it had no debt (unlevered cost of capital), $R\_D$ is the cost of debt, $D$ is debt, $E$ is equity and $T\_C$ is the corporate tax rate.

$R\_U$ has to be equal to return on assets, $R\_A=R\_U$. Otherwise (if $R\_A), the shareholders would not be willing to hold the shares.

Now by equation $(1)$, $R\_E$ falls as $T\_C$ increases. If $T\_C$ is incredibly high, say close to 100%, we get $R\_E\approx R\_U$. So the shareholders are getting close to nothing, as the government takes almost everything what is left after the bondholders have taken their share of EBIT. Yet the shareholders' *required* return $R\_E$ is lower than in the case of no tax where the shareholders reap all the profit after the bondholders have taken their share of EBIT. I find that counterintuitive. Could anyone help me clarify why this is (or is not) so?

**Tags:** taxation, corporate-finance

> **Comments:**
> **username_1**: What is the question? It looks like a statement  
> **username_0**: @username_1, the last sentence says "I find it counterintuitive". I am looking for some explanation for why this is (or is not) the case.  
> **username_0**: A bit related: https://economics.stackexchange.com/questions/52465  

---

## 2 answers

### Answer by username_0 on 2022-11-03. Score: 1

You say that when $T\_C$ is close to 100%,

> the shareholders are getting close to nothing, as the government takes almost everything what is left after the bondholders have taken their share of EBIT.

This suggests you think $R\_E$ and $R\_U$ are pre-tax returns. However, they are actually after-tax returns. By noting that, the puzzle goes away.


---

### Answer by username_2 on 2023-04-02. Score: 1

Your statement “the equity holders get nothing” doesn’t seem clear to me and I don’t think it follows from the equation. The equity holders still get $R\_E$.

The equation and theorem follow from a simple no-arbitrage condition between debt and equity.

With taxes, debt provides the advantage of a tax shield, which means debt becomes better (cheaper) than equity. The higher the tax rate, the higher the tax shield.

To satisfy no-arbitrage, the return on (cost of) equity then also has to come down, because the effective cost of debt is coming down with the tax rate. Otherwise the firm would just have all debt and no equity.

All your other concerns should be resolved from there.

> **Comments:**
> **username_0**: Thanks! What solves the puzzle is the realization that $R_E$ and $R_U$ are after-tax returns. Without that, the puzzle would remain. Fortunately, I have already noted that in my answer.  

---

