Chapter 19, Problem 19QP

Summary Introduction

To determine: The after-tax cash flow to the shareholders if invested in T-Bills, after-tax cash flow to the shareholders if invested in preferred stock, the future value of T-Bills and the future value of preferred stock investment.

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 19QP

The after-tax cash flow to the shareholders if invested in T-Bills is $4,053,154.23, after-tax cash flow to the shareholders if invested in preferred stock is $4,361,828.43, the future value of T-Bills is $4,067,483.35 and the future value of preferred stock investment is $4,234,702.69.

Explanation of Solution

Option 1: If the company invest money currently

Determine the after-tax yield of corporate investment in T-bills

$\begin{array}{c}AftertaxYiel{d}_{TBill}=\left[YieldonTBills\times \left(1-TaxRate\right)\right]\\ =\left[3\%\times \left(1-35\%\right)\right]\\ =1.95\%\end{array}$

Therefore the after-tax yield of corporate investment in T-bills is 1.95%

Determine the future value of investment of corporate investment in T-bills

$\begin{array}{c}FutureValu{e}_{TBills}=\left[AdditionalCash\times \left({\left(1+AftertaxYield\right)}^{NumberofYears}\right)\right]\\ =\left[\$4,500,000\times \left({\left(1+1.95\%\right)}^3\right)\right]\\ =\left[\$4,500,000\times 1.05964\right]\\ =\$4,768,416.74\end{array}$

Therefore the future value of investment of corporate investment in T-bills is $4,768,416.74

Determine the after-tax cash flow to the shareholders if invested in T-Bills

$\begin{array}{c}AftertaxCashFlowstoShareholder{s}_{TBill}=\left[FutureValu{e}_{TBills}\times \left(1-DividendRate\right)\right]\\ =\left[\$4,768,416.74\times \left(1-15\%\right)\right]\\ =\$4,053,154.23\end{array}$

Therefore the after-tax cash flow to the shareholders if invested in T-Bills is $4,053,154.23

Determine the after-tax corporate dividends if invested in preferred stock

Using a excel spreadsheet we calculate the after-tax coporate dividends as,

Excel Spreadsheet:

Therefore the after-tax corporate dividends if invested in preferred stock is $201,375

Determine the after-tax yield of corporate investment in preferred stock

$\begin{array}{c}AftertaxYiel{d}_{\mathrm{Pr}eferredStock}=\left[\frac{AftertaxCoporateDividends}{AdditionalCash}\right]\\ =\left[\frac{\$201,375}{\$4,500,000}\right]\\ =0.04475or4.48\%\end{array}$

Therefore the after-tax yield of corporate investment in preferred stock is 4.48%

Determine the future value of investment of corporate investment in preferred stock

$\begin{array}{c}FutureValu{e}_{\mathrm{Pr}eferredStock}=\left[AdditionalCash\times \left({\left(1+AftertaxYield\right)}^{NumberofYears}\right)\right]\\ =\left[\$4,500,000\times \left({\left(1+4.48\%\right)}^3\right)\right]\\ =\left[\$4,500,000\times 1.14034\right]\\ =\$5,131,562.86\end{array}$

Therefore the future value of investment of corporate investment in preferred stock is $5,131,562.86

Determine the after-tax cash flow to the shareholders if invested in preferred stock

$\begin{array}{c}AftertaxCashFlowstoShareholder{s}_{\mathrm{Pr}eferredStock}=\left[\begin{array}{l}FutureValu{e}_{\mathrm{Pr}eferredStock}\times \\ \left(1-DividendRate\right)\end{array}\right]\\ =\left[\$5,131,562.86\times \left(1-15\%\right)\right]\\ =\$4,361,828.43\end{array}$

Therefore the after-tax cash flow to the shareholders if invested in preferred stock is $4,361,828.43

Option 2: If the company pay dividend currently

Determine the after-tax payments to shareholders

$\begin{array}{c}AftertaxPayment{s}_{Shareholders}=\left[AdditionalCash\times \left(1-DividendTax\right)\right]\\ =\left[\$4,500,000\times \left(1-15\%\right)\right]\\ =\$3,825,000\end{array}$

Therefore the after-tax payments to shareholders is $3,825,000

Determine the after-tax individual dividend yield on T-Bills

$\begin{array}{c}AftertaxYiel{d}_{T-Bills}=\left[TBillYield\times \left(1-IndividualTax\right)\right]\\ =\left[3\%\times \left(1-31\%\right)\right]\\ =2.07\%\end{array}$

Therefore the after-tax individual dividend yield on T-Bills is 2.07%

Determine the future value if individual invest in T-Bill

$\begin{array}{c}FutureValu{e}_{TBill}=\left[AftertaxPayment\times \left({\left(1+AftertaxYield\right)}^{NumberofYears}\right)\right]\\ =\left[\$3,825,000\times \left({\left(1+2.07\%\right)}^3\right)\right]\\ =\left[\$3,825,000\times 1.06339\right]\\ =\$4,067,483.35\end{array}$

Therefore the future value if individual invest in T-Bill is $4,067,483.35

Determine the after-tax corporate dividends if individual invest in preferred stock

Using a excel spreadsheet we calculate the after-tax coporate dividends as,

Excel Spreadsheet:

Therefore the after-tax corporate dividends if individual in invest preferred stock is $131,962.50

Determine the after-tax yield preferred dividend yield

$\begin{array}{c}Aftertax\mathrm{Pr}eferredYield=\left[\frac{\text{Aftertax Corporate Dividends}}{AftertaxPayments}\right]\\ =\left[\frac{\$131,962.50}{\$3,825,000}\right]\\ =3.45\%\end{array}$

Therefore the after-tax yield preferred dividend yield is 3.45%

Determine the future value if individual invest in preferred stock

$\begin{array}{c}FutureValu{e}_{TBill}=\left[AftertaxPayment\times \left({\left(1+AftertaxYield\right)}^{NumberofYears}\right)\right]\\ =\left[\$3,825,000\times \left({\left(1+3.45\%\right)}^3\right)\right]\\ =\left[\$3,825,000\times 1.10711\right]\\ =\$4,234,702.69\end{array}$

Therefore the future value if individual invest in T-Bill is $4,234,702.69