Question

An investor buys 100 shares of a $40 stock that pays an annual cash dividend of $2 a share (a 5 percent dividend yield) and signs up for the dividend reinvestment plan.

a. If neither the dividend nor the price changes, how many shares will the investor have at the end of ten years? How much will the position in the stock be worth?
b. if the price of the stock rises by 6% annually, but the dividend remains at $2, how many total shares does the investor end up with at the end of year 10?
c. If the price of the stock rises by 6 percent annually but the dividend rises by only 3 percent annually, how many shares are purchased each year for the next ten years? How much is the total position worth at the end of ten years? Since dividend plans credit fractional shares, use three decimal places in parts (b) and (c)

Answer 1

Answer:

a= 163 shares worth 6,515.58 dollars

b= It purchase 43.5 shares

giving a total of 143.5 shares worth 71.634 each giving a net worth of $10,280.33861

c=  It purchase 50.3 shares

giving a total of 150.3 shares worth 71.634 each giving a net worth of $10.766.88

Explanation:

We increase at 5% rate each year.

$Principal \: (1+ r)^{time} = Amount$

Principal 4,000.00 (100 shares x $40 each

time 10.00

rate 0.05000

$4000 \: (1+ 0.05)^{10} = Amount$

Amount 6,515.58

Total shares after 10 years

6,515.58 / 40 = 162.8894627 = 163

If the price rise at 6% but dividends remains constant

Shares Dividends  // Price // Shares purchased

1 100         200     42.4         4.717

2 104.717 209.434     44.944 4.66

3 109.377 218.754     47.641   4.592

4 113.969 227.938     50.5      4.514

5 118.483 236.966     53.53   4.427

6 122.91 245.82     56.741         4.333

7 127.243 254.486     60.146 4.232

8 131.475 262.95     63.754 4.125

9 135.6 271.2     67.58   4.014

10 139.614 279.228     71.634  3.898

TOTAL143.512                                 43.512

c)

$\left[\begin{array}{ccccc} Years& Shares& Dividends& Price& Shares purchased\\1&100&200&42.4&4.717\\2&104.717&215.718&44.944&4.8\\3&109.517&232.374&47.641&4.878\\4&114.395&250.006&50.5&4.951\\5&119.346&268.65&53.53&5.019\\6&124.365&288.347&56.741&5.082\\7&129.447&309.133&60.146&5.14\\8&134.587&331.051&63.754&5.193\\9&139.78&354.139&67.58&5.241\\10&145.021&378.44&71.634&5.283\\TOTAL&150.304\\\end{array}\right]$

150.304 x 71.634 = 10766.87674