Chapter 18, Problem 8PS

Tax shields “The trouble with MM’s argument is that it ignores the fact that individuals cannot deduct interest for personal income tax.” Show why this is not an objection if personal tax rates on interest and equity income are the same.

Summary Introduction

To discuss: The reason why it is not an objection if personal tax rates on equity and interest are same.

Explanation of Solution

Given situation:

The argument with MM theory is that it says it ignores the fact that a person cannot deduct the interest for personal income tax.

Reason:

For example, Firm A has a is a levered firm with expected cash flow X and interest on debt as $r_{\text{D}}$. The corporate and personal taxes are considered as ${\text{t}}_{\text{p}}$ and ${\text{t}}_{\text{c}}$.

So, the cash flow to shareholders are as follows:

$\left(\text{X}-{\text{r}}_{\text{D}}\text{D}\right)\left(1-{\text{T}}_{\text{c}}\right)\left(1-{\text{T}}_{\text{p}}\right)$

The value of shareholders position be as follows:

$V_L=\left[\frac{\left(X\right)\left(1-T_c\right)\left(1-T_p\right)}{\left(r\right)\left(1-T_p\right)}\right]-\left[\frac{\left(r_D\right)\left(D\right)\left(1-T_c\right)\left(1-T_p\right)}{\left(r_D\right)\left(1-T_p\right)}\right]$

$V_L=\frac{\left(X\right)\left(1-T_c\right)\left(1-T_p\right)}{\left(r\right)\left(1-T_p\right)}-\left(D\right)\left(1-T_c\right)$

Here, r is the opportunity cost for all equity financed firm. Secondly, if the stockholder borrows D at the rate of same ${\text{r}}_{\text{D}}$ and invest it in the unlevered firm, then their cash flow will be like

$V_L=\left(X\right)\left(1-T_c\right)\left(1-T_p\right)-\left(r_D\right)\left(D\right)\left(1-T_c\right)$

The position of value of stockholder be:

$V_L=\left[\frac{\left(X\right)\left(1-T_c\right)\left(1-T_p\right)}{\left(r\right)\left(1-T_p\right)}\right]-\left[\frac{\left(r_D\right)\left(D\right)\left(1-T_p\right)}{\left(r_D\right)\left(1-T_p\right)}\right]$

Thus, the difference in the wealth of the shareholder for investment in same asset is as follows

${\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}={\text{DT}}_{\text{c}}$

The above is the prediction of MM theory.

Then if a person cannot deduct the interest for personal tax purpose then

$V_{\text{U}}=\left[\frac{\left(X\right)\left(1-T_c\right)\left(1-T_p\right)}{\left(r\right)\left(1-T_p\right)}\right]-\left[\frac{\left(r_D\right)\left(D\right)}{\left(r_D\right)\left(1-T_p\right)}\right]$

$V_L-V_U=\frac{\left(r_D\right)\left(D\right)-\left[\left(r_D\right)\left(D\right)\left(1-T_c\right)\left(1-T_p\right)\right]}{\left(r_D\right)\left(1-T_p\right)}$

${\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}={\text{DT}}_{\text{c}}+\left[\text{D}\frac{{\text{T}}_{\text{p}}}{1-{\text{T}}_{\text{p}}}\right]$

Thus, the shareholders value position in a levered firm is greater when no personal interest deduction is allowed.