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

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 $$R_D$$.)

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.

• Interesting. I thought the government reimburses the interest expenses from the taxes that are collected from the lenders, so that the net contribution of the government is zero. But now it seems the government is a net payer when it comes to interest expenses from corporate borrowing. Hmm... Commented Oct 19, 2022 at 14:29
• @RichardHardy ? What do you mean by net payer? Government is net payee since they get money out of the tax, the tax shield is not explicit subsidy only implicit one, government still collects its taxes just the fact that you can deduct interest from income makes your taxes lower but that does not mean government sends you money
– 1muflon1
Commented Oct 19, 2022 at 14:35
• I meant it in the narrow sense with regards to corporate borrowing (and lending) alone. Anyway, the interest the lender earns is most likely taxed in some form in the end, whether thought corporate tax (if the lender is a firm), personal income tax (if the lender is a private person) or otherwise. So in that sense the government probably does not end up being a net sponsor of corporate borrowing. Commented Oct 19, 2022 at 16:06
• @RichardHardy i am not sure I understand what happens is that firm first has some EBIT let’s say EBIT is 10000 then company pays interest 5000 so EBT is 5000 and then if corporate tax rate is 50% company pays 2500 and net profit is 2500 and government revenue is 2500 so government only gets income does not pay anything to anyone
– 1muflon1
Commented Oct 19, 2022 at 16:41
• I do not disagree with that. I was trying to make a parallel point, but nevermind. Thank you for a good discussion and explanation! (I will wait before accepting you answer as usually, but I will eventually return and do that.) Commented Oct 19, 2022 at 16:47

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).