Chapter 19, Problem 20QP

a.

Summary Introduction

To determine: The Personal Tax Rate.

Introduction: The term dividends allude to that portion of proceeds of an organization which is circulated by the organization among its investors. It is the remuneration of the investors for investments made by them in the shares of the organization.

Answer to Problem 20QP

The Personal Tax Rate is 35%.

Explanation of Solution

Determine the personal tax rate

If the dividends are not taxed, then the personal tax rate must be equivalent to the corporate tax rate of 35%. Here the total return is identical in both the scenarios of company paying dividends or investing in a treasury bonds. Alternatively we determine the personal tax rate using formula by assuming the personal tax rate as x,

$\begin{array}{c}\left[\begin{array}{l}AdditionalCash\times \left(1-x\right)\\ \left(1+Yiel{d}_{TBill}\times \left(1-x\right)\right)\end{array}\right]=\left[\left(1-x\right)\times \left(\begin{array}{l}AdditionalCash\times \\ \left(1+Yiel{d}_{TBill}\times \left(1-CoporateTax\right)\right)\end{array}\right)\right]\\ \left[\begin{array}{l}\$1,000\times \left(1-x\right)\times \\ \left(1+8\%\times \left(1-x\right)\right)\end{array}\right]=\left[\left(1-x\right)\times \left(\begin{array}{l}\$1,000\times \\ \left(1+8\%\times \left(1-35\%\right)\right)\end{array}\right)\right]\\ \left[1+0.08\times \left(1-x\right)\right]=\left[1+0.08\times \left(1-0.35\right)\right]\\ 0.08\times \left(1-x\right)=0.08\times \left(1-0.35\right)\\ 0.08\times \left(1-x\right)=0.052\\ 1-x=\left[\frac{0.052}{0.08}\right]\\ x=\left[1-0.65\right]\\ =0.35or35\%\end{array}$

Therefore the personal tax rate is 35%

b.

Summary Introduction

To determine: The Respond to the given statement.

Statement: Is the answer in part (a) reasonable?.

Answer to Problem 20QP

Answer: Yes, the answer in part (a) reasonable.

Explanation of Solution

The following reasons suggests that part a asnwer is reasonable,

• It is uninterested if the aftertax incomes from the $1,000 interest in indistinguishable securities are indistinguishable.
• This happens when the tax rates are indistinguishable.

c.

Summary Introduction

To determine: The Personal Tax Rate.

Answer to Problem 20QP

The Personal Tax Rate is 10.5%.

Explanation of Solution

Determine the personal tax rate

$\begin{array}{c}\left[\begin{array}{l}AdditionalCash\times \left(1-x\right)\\ \left(1+Yiel{d}_{\mathrm{Pr}eferredStock}\times \left(1-x\right)\right)\end{array}\right]=\left[\left(1-x\right)\times \left(AdditionalCash\times \left(\begin{array}{l}1+Yiel{d}_{\mathrm{Pr}eferredStock}\times \\ DividendRate+\\ \left(\begin{array}{l}1-\\ DividendRate\end{array}\right)\times \\ \left(1-CorporateTax\right)\end{array}\right)\right)\right]\\ \left[\begin{array}{l}\$1,000\times \left(1-x\right)\times \\ \left(1+12\%\times \left(1-x\right)\right)\end{array}\right]=\left[\left(1-x\right)\times \left(\begin{array}{l}\$1,000\times \\ \left(1+12\%\times \left(1-35\%\right)\times \left(1-70\%\right)\right)\end{array}\right)\right]\\ \left[1+0.12\times \left(1-x\right)\right]=\left[1+0.12\times \left(0.70+\left(1-0.70\right)\times \left(1-0.35\right)\right)\right]\\ \left[0.12\times \left(1-x\right)\right]=\left[0.12\left(0.70+0.30\times 0.65\right)\right]\\ \left[0.12\times \left(1-x\right)\right]=0.12\times 0.895\\ 0.12\times \left(1-x\right)=0.1074\\ 1-x=\left[\frac{0.1074}{0.12}\right]\\ 1-x=0.895\\ -x=-0.105\\ x=0.105or10.5\%\end{array}$

Therefore the personal tax rate is 10.50%

d.

Summary Introduction

To determine: The Respond to the given statement.

Statement: Is this a compelling argument for a low dividend payout ratio.

Answer to Problem 20QP

Answer: No this not a compelling argument for a low dividend payout ratio.

Explanation of Solution

It is a convincing contention, yet there are legitimate imperatives which deflect firms from putting substantial aggregates in stock of different organizations.