4. An investor buys 500 shares of stock at $50 and the stock pays a 4% annual di

Question

4. An investor buys 500 shares of stock at $50 and the stock pays a 4% annual dividend. a. If the investor holds the stock for 10 years and the neither the price nor the dividend change and the investor chooses to reinvest the dividends into stock what will be the value of the stock holdings and how many shares will the investor have? b. If the investor holds the stock for 10 year and the stock price increases by 5% per year and the dividend remains the same, what will be the value of the holdings if the investor reinvests the dividends in additional stock holdings and how many shares of stock will the investor have? c. If the investor holds the stock for 10 year and the stock price increases by 5% per year and the dividend remains the same, what will be the value of the holdings if the investor does not reinvest the dividends how many shares of stock will the investor have and how much will they be worth? d. What is the difference between a, b, c and how significant are the additions from reinvesting?

Explanation / Answer

Total investment = 500 * 50 = 25,000

value of stock holdings would be 25,000 * (1+i)^n

here i = 4% and n = 10

25,000 + 1000* ((1+4%)^10-1)/4%

= 25,000 + 1000* 12.01

= 37,006.11

b)

valu of the holdings would 500 * 50*1.05^10 + 2* ((1+4%)^10-1)/4%

= 500 * 81.44 + 12,006.11

= 52,728.47

c)

If dividend is not reinvested the stock value would be

500 * 50*1.05^10

= 40,722.37

Reinvesting shows the power of compounding, if the dividend is reinvested the money multiplies faster

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