Chapter 17, Problem 16QP

Dividends versus Reinvestment [LO2] After completing its capital spending for the year, Carlson Manufacturing has $1,000 extra cash. Carlson’s managers must choose between investing the cash in Treasury bonds that yield 3 percent or paying the cash out to investors who would invest in the bonds themselves.

a. If the corporate tax rate is 35 percent, what personal tax rate would make the investors equally willing to receive the dividend or to let Carlson invest the money?

b. Is the answer to (a) reasonable? Why or why not?

c. Suppose the only investment choice is a preferred stock that yields 6 percent. The corporate dividend exclusion of 70 percent applies. What personal tax rate will make the stockholders indifferent to the outcome of Carlson’s dividend decision?

Summary Introduction

To determine: The personal tax rate.

Introduction:

C manufacturing company has 1000 extra cash. The managers decide to invest the cash in treasury bills that yield 3% or to pay the cash out to the investors.

Answer to Problem 16QP

The personal tax rate is 35%.

Explanation of Solution

Given information:

The corporate tax rate is 35%.

Determine the personal tax rate:

Note: Consider the tax rate as ‘ $x$’and the individual receives the after-tax dividend by the company.

Compute the individual after-tax dividend:

$\begin{array}{c}\text{Aftertax dividend}=\text{Extra cash}\left(1-x\right)\\ =\$1,000\left(1-x\right)\end{array}$

Therefore, the after-tax dividend can be invested in treasury bonds.

Compute the after-tax cash flow from treasury bonds:

$\begin{array}{c}\text{After tax cash flow from treasury bonds}=\left[\begin{array}{l}\text{Extra cash}\left(1-x\right)\\ \left[\begin{array}{l}1+\text{Percentage of }\\ \text{treasury bonds yield}\left(1-x\right)\end{array}\right]\end{array}\right]\\ =\$1,000\left(1-x\right)\left[1+0.03\left(1-x\right)\right]\end{array}$

Note: Let this be equation 1.

Compute the proceeds if the firm invests the money:

$\text{Firms proceeds}=\text{\$1000}\left[1+0.03\left(1-0.35\right)\right]$

Compute the proceeds if the firm pays dividend:

$\text{Proceeds}=\left(1-x\right)\left\{\text{\$1000}\left[1+0.03\left(1-0.35\right)\right]\right\}$

Note: Let this be equation 2.

Whether the investors invest the after-tax dividend or receive the proceeds from the firm’s investment, the investors’ proceeds will be the same.

Solve these two equations to find the rate of indifference.

$\begin{array}{l}\$1,000\left(1-x\right)\left[1+0.03\left(1-x\right)\right]=\left(1-x\right)\left\{\text{\$1000}\left[1+0.03\left(1-0.35\right)\right]\right\}\\ 1+0.03\left(1-x\right)=1+0.03\left(1-0.35\right)\\ 1+\left(0.03-0.03x\right)=1+0.03-0.0105\\ 1+0.03-0.03x=1.0195\\ \end{array}$

$\begin{array}{l}0.03x=0.0105\\ x=0.35\text{ or 35\%}\end{array}$

Therefore, the personal tax rate that makes the investors equally and fairly willing to obtain the dividend or C to invest money is 35%

Summary Introduction

To discuss: Whether the above solution is reasonable or not.

Explanation of Solution

Yes, the above solution is reasonable.

Person C is indifferent if the after-tax proceeds from the $1,000 investments in the securities are identical. The above indifference occurs only when the tax rates are identical.

Summary Introduction

To determine: The personal tax rate.

Answer to Problem 16QP

The personal tax rate is 10.50%.

Explanation of Solution

Given information:

The preferred stocks yield at 6%, seventy percentage of income is exempted from the corporate taxes, and person C gets more benefits by investing in stocks.

Compute the personal tax rate:

The same answer in part (a) will apply to this, as the pretax returns are the same.

The seventy percentage of income is exempted from the corporate taxes and Person C gets more benefits by investing in stocks.

The rate of tax on income, which includes indifference, is lower.

Solve the equations to get the value of personal tax rate.

Derived equation: 1

$\$1,000\left(1-x\right)\left[1+0.06\left(1-x\right)\right]$

Derived equation: 2

$\left(1-x\right)\left\{\text{\$1000}\left(1+0.06\left[0.70+\left(1-0.70\right)\left(1-0.35\right)\right]\right)\right\}$

Note:

$\text{Exempt from tax}=1-0.70$

Corporate tax percentage is 35%

Find $x$ by solving the above 2 equations:

$\begin{array}{l}\$1,000\left(1-x\right)\left[1+0.06\left(1-x\right)\right]=\left(1-x\right)\left\{\text{\$1000}\left(1+0.06\left[0.70+\left(1-0.70\right)\left(1-0.35\right)\right]\right)\right\}\\ 1+0.06\left(1-x\right)=1+0.06\left[0.70+\left(1-0.70\right)\left(1-0.35\right)\right]\\ 1+0.06-0.06x=1+0.06\left[0.70+\left(0.3\times 0.65\right)\right]\\ 1.06-0.06x=1+0.06\left(0.70+0.195\right)\end{array}$

$\begin{array}{l}1.06-0.06x=1+.06\left(0.895\right)\\ 1.06-0.06x=1.0537\\ 0.06x=0.0063\\ x=0.1050,or10.50\%\end{array}$

Hence, the rate of personal tax is 10.50%.

Summary Introduction

To discuss: The reason whether a low dividend payout ratio has a compelling argument or not

Explanation of Solution

Yes, the low dividend payout ratio has a compelling argument and it has some legal constraints, which restricts the firms from investing their money in the stocks of other companies.