Chapter 17, Problem 15QP

Summary Introduction

To determine: Whether the cash can be paid today or at the end of 3 years and the best alternative which generates a high after-tax income for the shareholders.

Introduction:

Dividends and reinvestments: The Company has 3 millions extra cash either reinvested or used for dividend payments. Extra cash can be used as dividends for the shareholders or it can be a reinvestment made in any financial asset.

Answer to Problem 15QP

The extra cash that can be reinvested in financial assets is known as preferred stock.

Explanation of Solution

Given information:

When the company has 3 millions in extra cash, it opts for two alternatives:

• One is to pay dividends at the end of the three years to the shareholders
• Another is to reinvest in financial assets’ treasury bills or preferred stock

The firm can reinvest in T bills yielding 3% or 5% in the preferred stock and as per IRS regulations, the company can exclude a taxable income of 70% of the dividend received from investing in tax of another company.

The reinvesting income will pay a special dividend at the end of 3 years.

The dividend tax rate is 15%, the individual personal tax is 31%, and the corporate tax rate is 35%.

Formula:

The formula to calculate the after-tax cash flow:

$\text{After tax cash flow}=\text{Future value of investments}\times \left(1-\text{tax rate}\right)$

The formula to calculate the future value of preferred stock:

$\text{Future value of investment in preferred stock}=\text{Extra cash}{\left(\text{1+After corporate dividend yield}\right)}^n$

The formula to calculate the future value of treasury bills:

$\text{Future value of investment in T- bills}=\text{ Extra cash}{\left(\text{1+Percentage yieldof T bills}\right)}^n$

Note: n is the number of years; and since the company has $3 million after-tax, the full amount can be reinvested.

The reinvestment can opt for 2 alternatives:

• Investing in treasury bills and paying a special dividend at the end of 3 years.
• Another alternative is to pay the dividends today to the individuals and to invest on their own in the treasury bills or preferred stocks

Alternative: 1

The investment in treasury bills

Compute the after-tax of t-bills:

$\begin{array}{c}\text{Aftertax corporate yeild}=\text{ Percentage yield of T bills}\left(1-\text{Corporate tax rate}\right)\\ =0.03\left(1-0.35\right)\\ =0.03\left(0.65\right)\\ =0.0195\end{array}$

Hence, the after-tax of T-bill is 1.95%.

Compute the future value of investing in Treasury bill:

$\begin{array}{c}\text{Future value of investment in T- bills}=\text{ Extra cash}{\left(\text{1+Percentage yieldof T bills}\right)}^n\\ =\text{\$3,000,000}{\left(1+0.0195\right)}^3\\ =\$3,000,000{\left(1.0915\right)}^3\\ =\$3,000,000\times 1.0596\\ =\$3,178,944\end{array}$

Hence, the future value of investment in T-bills is $3,178,944.

Compute the after-tax cash flow:

Note: These future values of investments will be paid to the shareholders as dividends.

The after-tax cash flow is as follows:

$\begin{array}{c}\text{After tax cash flow}=\text{Future value of investments}\times \left(1-\text{tax rate}\right)\\ =\$3,178,944.49\left(1-0.15\right)\\ =\$3,178,944.49\left(0.85\right)\\ =\$2,702,102.82\end{array}$

Hence, the after-tax cash flow is $2,702,102.82.

The investment in preferred stocks

In the case of preferred stocks, the dividends received will be again reinvested in the same preferred stocks and 70% of the incomes are excluded from tax.

Compute the dividend from the preferred stocks and taxable preferred dividend:

$\begin{array}{c}\text{Preferred dividend}=\text{Percentage of prefered stocks}\times \text{Extra cash}\\ =\text{0}\text{.5}\left(\$3,000,000\right)\\ =150,000\\ \text{Taxable preferred dividends}=\left(1-0.70\right)\left(\$150,000\right)\\ =\left(0.30\right)\left(\$150,000\right)\\ =\$45,000\end{array}$

Hence, the preferred dividend is $150,000 and taxable preferred dividend is $45,000.

Compute the taxes, which the company pays:

$\begin{array}{c}\text{Taxes}=\text{0}\text{.35}\left(\$45,000\right)\\ =\$15,750\end{array}$

Hence, the company pays $15,750 as taxes on the preferred stocks dividends.

Compute the after-tax corporate dividend and the after-tax dividend yield for the corporation:

$\begin{array}{c}\text{After tax corporate dividend}=\text{Taxable preferred dividend}-Taxes\text{on preferred dividend}\\ =\$150,000-\$15,750\\ =\$134,250\end{array}$

Hence, the after-tax dividend yield is $134,250.

$\begin{array}{c}\text{After tax corporate dividend yeild}=\frac{\text{After corporate dividend}}{\text{Extra cash}}\\ =\frac{\$134,250}{3,000,000}\\ =0.04475\text{ or 4}\text{.475\%}\end{array}$

Hence, the after-tax corporate dividend yield is 4.475%.

Compute the future value of investing in the preferred stock:

$\begin{array}{c}\text{Future value of investment in preferred stock}=\text{Extra cash}{\left(\text{1+After corporate dividend yield}\right)}^n\\ =\$3,000,000{\left(1+0.04475\right)}^3\\ =\$3,421,041\end{array}$

Hence, the future value of the investment of the preferred stock is $3,421,041.

Compute the after-tax cash flow:

Note: These future values of investments will be paid to the shareholders as dividend.

The after-tax cash flow is as follows:

$\begin{array}{c}\text{After tax cash flow}=\text{Future value of investments}\times \left(1-\text{personal dividend tax rate}\right)\\ =\$3,421,041\left(1-0.15\right)\\ =\$3,421,041\left(0.85\right)\\ =\$2,907,886\end{array}$

Hence, the after- tax cash flow of the shareholders is $2,907,886.

Alternative: 2

Another alternative is to pay the dividends today to the individuals and to invest on their own in the treasury bills or preferred stocks.

The individual investment in treasury bills:

Compute the after-tax cash received today by the shareholders:

$\begin{array}{c}\text{After tax cash}=\text{Extra cash}\left(1-\text{personal dividend tax rate}\right)\\ =\$3,000,000\left(1-0.15\right)\\ =\$3,000,000\left(0.85\right)\\ =\$2,550,000\end{array}$

Hence, the after-tax received today by the shareholders is $2,550,000.

If this cash is invested in the Treasury bill, the yield will be as follows:

Compute the after-tax individual yield on T-bills:

$\begin{array}{c}\text{Aftertax individual yield}=\left(\text{Percentage of treasury bill yield}\right)\left(\text{1}-\text{Personal IT rate}\right)\\ =0.03\left(1-0.31\right)\\ =0.03\left(0.69\right)\\ =0.0207\text{ or 2}\text{.07\%}\end{array}$

Hence, the after-tax individual yield is 2.07%.

Compute future value of individual investment in T-bills:

$\begin{array}{c}\text{Future value of investments}=\text{Aftertax cash received today}\left(1+\text{After tax individual yield}\right)\\ =\$2,550,000{\left(1+0.0207\right)}^3\\ =\$2,550,000{\left(1.0207\right)}^3\\ =\$2,550,000\left(1.06339\right)\\ =\$2,711,655.57\end{array}$

Hence, the future value of individual investment in T-bills is $2,711,655.57.

The individual investment in preferred stocks

When the individual invests in preferred stocks, the dividend earned from these stocks will be reinvested in the same stocks.

Compute the dividend earned from the preferred stocks:

$\begin{array}{c}\text{Preferred dividend}=\text{Preferrd stock yield}\left(\text{Aftertax cash received today}\right)\\ =0.05\left(\$2,550,000\right)\\ =\$127,500\end{array}$

Hence, the dividend earned from the preferred stocks is $127,500.

Compute the taxes, which the individual pays on preferred stocks:

$\begin{array}{c}\text{Taxes}=\left(\text{Personal tax rate}\right)\left(\text{Preferred dividend}\right)\\ =\text{0}\text{.31}\left(\$127,500\right)\\ =\$15,750\end{array}$

Hence, the taxes on the preferred dividend are $15,750.

Compute the individual after-tax preferred dividend and yield on the after-tax preferred dividend:

$\begin{array}{c}\text{After tax preferred dividend}=\text{Preferred dividend}\times \text{Taxes on preferred dividend}\\ =\$127,500-\$39,525\\ =\$87,975\end{array}$

$\begin{array}{c}\text{After tax preferred dividend yield}=\frac{\text{After tax preferred dividend}}{\text{After tax cash received today}}\\ =\frac{\$89,975}{\$2,550,000}\\ =0.0352\text{ or }3.52\%\end{array}$

Hence, the after-tax preferred dividend is $87,975 and the after-tax preferred dividend yield is 3.52%.

Compute the future value of the individual investment in the preferred stock:

$\begin{array}{c}\text{Future value in preferred stock}=\text{After tax cash received today}{\left(1+\text{Aftertax individual dividend yield}\right)}^n\\ =\$2,550,000{\left(1+0.0345\right)}^3\\ =\$2,550,000{\left(1.0345\right)}^3\\ =\$2,550,000\left(1.107111\right)\\ =\$2,823,135\end{array}$

Hence, the future value of the individual investment in the preferred stock is $2,823,135.

The best alternative, which generates the highest after-tax income for the shareholders:

Alternative: 1

Investment in treasury bills:

The after-tax cash flow to the shareholders is $2,702,102.82.

Investment in preferred stocks

The after-tax cash flow to the shareholders is $2,907,886.

The alternative: 1 with preferred stock: Investing the cash in the preferred stock gives the maximized after-tax cash flow to the shareholders which can be paid as a special dividend at the end of three years.

Conclusion

Thus, the dividends can be paid at the end of 3 years and the best alternative to invest the cash is in preferred stocks.