Effect of tax on required return on debt (and equity)

Question

Debt financing has a tax advantage over equity financing, as the borrower gets reimbursed the tax on interest payments and other debt-servicing costs. Thus $$ R_{\text{WACC}}=\frac{E}{E+D}R_E+(1-T_C)\frac{D}{E+D}R_D $$ where $R_{\text{WACC}}$ is the weighted average cost of capital for the borrower (a firm), $E$ is the market value of equity, $D$ is the market value of debt, $R_E$ is the cost of equity, $R_D$ is the cost of debt and $T_C$ is the corporate tax rate.

On the other hand, the lender does not get $R_D$ but only $(1-T_C)R_D$ after tax. So if the lender actually wants to get $R_D$ after tax, they need to charge $\frac{R_D}{1-T_C}$. Question 1: Is that a useful way of thinking about how the lender actually sets the required rate of return?

Question 2: Consequently, if the corporate tax were abolished, would we have $$ R_{\text{WACC, no tax}}=\frac{E}{E+D}\tilde R_E+\frac{D}{E+D}\tilde R_D $$ with $\tilde R_E=R_E$ and $\tilde R_D=\frac{R_D}{1-T_C}$?

(I guess not, as the equity holders also pay corporate tax. If they were to follow the same logic as the lenders, then they would also set their required return to $\frac{R_E}{1-T_C}$. This way the effect of tax would not change the ratio between $R_E$ to $R_D$.)

Answer 1

Question 1: Is that a useful way of thinking about how the lender actually sets the required rate of return?

No lender actually gets $R_D$, a bond holder does not pay corporate rate on their interest income (there of course could be capital income taxes but you don’t specify that).

Also the equation is written from the point of the view of firm. The original $ (1-T_c)$ is there to represent the tax shield the firm gets.

R then is just treated as exogenously given. In real life it’s of course determined by nominal and real factors including any tax people have to pay for their interest income. However, it’s not correct to put there corporate tax rate since individual bond holder won’t pay that. Moreover, interest rate is not determined to satisfy the equation above. It is determined independently on money markets (and the equilibrium interest rate on money market already takes into account any taxes).

So the $R_D$ there is already $R_D(\pi,r,t_g)$ where $\pi$ is inflation, $r$ real rate, $t_g$ any capital taxes the bond holder has to pay.

Also in real life it could also be function of how much debt company has since more debt financing means more risk but I don’t want to overcomplicate it. However, this simple model does not include that explicitly.

Question 2: Consequently, if the corporate tax were abolished, would we have $$ R_{WACC, \text{ no tax}}=\frac{E}{E+D}\tilde R_E+\frac{D}{E+D}\tilde R_D $$ with $\tilde R_E=R_E$ and $\tilde R_D=\frac{R_D}{1-T_C}$?

No as explained above.

Answer 2

This is not a direct answer but some supplementary material to the helpful answer of @1muflon1. Section 15.4 of Berk & DeMarzo "Corporate Finance" (5th global ed., 2019) contains the following:

Personal taxes have the potential to offset some of the corporate tax benefits of leverage that we have described. In particular, in the United States and many other countries, interest income has historically been taxed more heavily than capital gains from equity.

They further derive the effective tax advantage of debt to be $$ T^* = 1 - \frac{ (1-T_C)\cdot (1-T_e) }{ (1-T_i) } $$ where $T_e$ is the personal tax on equity income and $T_e$ is the personal tax on interest income. $T^*$ itself is interpreted in the following way:

if the corporation paid $(1-T^*)$ in interest, debt holders would receive the same amount after taxes as equity holders would receive if the firm paid \$1 in profits to equity holders. That is, $(1-T^*)(1-T_i)=(1-T_C)(1-T_e)$.

They also provide a realistic (as far as I can tell) example for an investor in the highest tax bracket of the tax advantage of debt falling from $21\%$ to $-0.3\%$ according to the tax code from 2018. That is, there is basically no tax advantage to debt (actually, there is a slight disadvantage).