Chapter 7, Problem 1PROB

Summary Introduction

Stock was purchased for $20, one year ago and today it is trading at $19. Four dividend payments of $0.20 has been made during the period of 1 year.

Stock’s rate of return is the total return which the investors are getting, considering both the dividends received and capital appreciation. Dividend yield plus capital gains yield is the rate of return which the investors get on selling the stock.

Dividend yield is calculated as the expected dividend for a year divided by the price of the stock at the beginning of the period.

$\begin{array}{l}\text{Dividend yield = }\widehat{\frac{{\text{D}}_1}{{\text{P}}_0}}\\ where,\\ \widehat{{\text{D}}_1}=\text{Next expected dividend}\\ {\text{P}}_0\text{= Price of the stock at the beginning of the period }\end{array}$

Capital gains yield is the change in stock value represented as a percentage change.

$\begin{array}{l}\text{Capital Gain yield}=\frac{\widehat{P_1}-P_0}{P_0}\\ where,\\ \widehat{P_1}=\text{Price of the stock at the end of the period}\\ {\text{P}}_0=\text{ Price of the stock at the beginning of the period}\end{array}$

Rate of return on the stock is the sum of the dividend yield and capital gains yield.

${\text{Rate of return(r}}_s\text{)=}\widehat{\frac{D_1}{P_0}}+\frac{\left(\widehat{P_1}-P_0\right)}{P_0}$

Explanation of Solution

1. Rate of return on the stock is calculated as below:

   $\begin{array}{ll}{r}_s& =\widehat{\frac{D_1}{P_0}}+\frac{\left(\widehat{P_1}-P_0\right)}{P_0}\hfill \\ & where,\\ \widehat{D_1}& =0.2\times 4\hfill \\ & =0.80\hfill \\ P_0& =20\hfill \\ \widehat{P_1}& =19\hfill \end{array}$

   Putting the values in the above equation

   $\begin{array}{rr}{r}_s& =\frac{0.80}{20}+\frac{\left(19-20\right)}{20}\hfill \\ & =0.04+(-0.05)\hfill \\ & =-0.01\hfill \\ & =\boxed{-1.00\%}\hfill \end{array}$

   Rate of return on the stock is $\boxed{-1.00\%}$

2. 1. Dividend yield is calculated as the dividend received for the year divided by the price of the stock at the time of buying

      $\begin{array}{rr}\text{Dividend yield }& =\widehat{\frac{{\text{D}}_{\text{1}}}{{\text{P}}_{\text{0}}}}\hfill \\ & where,\\ \widehat{{\text{D}}_1}& =\text{0}\text{.80}\hfill \\ {\text{P}}_0& =\text{ 20}\hfill \\ \text{Dividend yield }& =\frac{\text{0}\text{.80}}{20}\hfill \\ & =0.04\hfill \\ & =\boxed{4\%}\hfill \end{array}$

      Dividend yield on the stock DC is $\boxed{4.00\%}$

3. Capital gains yield is calculated as the percentage return on the stock based on the stock’s appreciation value

   $\begin{array}{rr}\text{Capital Gain yield}& =\frac{\widehat{P_1}-P_0}{P_0}\hfill \\ where,\\ \widehat{P_1}& =\text{19}\hfill \\ {\text{P}}_0& =\text{20}\hfill \\ \end{array}$

   $\begin{array}{rr}\text{Capital gains yield }& =\frac{19-20}{20}\hfill \\ & =\frac{-1}{20}\hfill \\ & =-0.05\hfill \\ & =\boxed{-5.00\%}\hfill \end{array}$

   Capital gains yield on the stock of DC is $\boxed{-5.00\%}$