Consider a no-growth stock paying $10 dividends a year. The next dividend will b

Question

Consider a no-growth stock paying $10 dividends a year. The next dividend will be paid in one year. We require a 12% annual return (annual compounding) on this stock.
a. Assuming the dividends continue forever, what is the value of the stock today?
b. What is the value (or approximate value) of the stock (today) if we assume the company will vanish (without a trace – no more dividends, no salvage value) after 100 years?

Explanation / Answer

a) Value of the bond for perpetual annual dividend D of $10 each year with annual return k of 12% (= 0.12), = D/k = 10/0.12 = $83.33 (ANSWER) b) for n = 100 years, NO SALVAGE VALUE and other data unchanged. Value of bond = D((1+k)^100 -1)/(k(1+k)^100) => = 10(1.12^100-1)/(0.12*1.12^100) => = 83.33 + approx. 0 = = 83.33 ($) (ANSWER)

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