# Impact of the corporate tax rate on the cost of equity (Modigliani & Miller Proposition II)

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?

• What is the question? It looks like a statement
– 1muflon1
Oct 31, 2022 at 16:13
• @1muflon1, the last sentence says "I find it counterintuitive". I am looking for some explanation for why this is (or is not) the case. Oct 31, 2022 at 16:14
• A bit related: economics.stackexchange.com/questions/52465 Oct 31, 2022 at 16:23

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.

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.

• 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. Apr 2 at 18:41