Most corporations pay quarterly dividends on their common stock rather than annu

Question

Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders.

a. Suppose a company currently pays a $2.80 annual dividend on its common stock in a single annual installment, and management plans on raising this dividend by 6 percent per year, indefinitely. If the required return on this stock is 12 percent, what is the current share price?

b. Now suppose that the company in (a) actually pays its annual dividend in equal quarterly installments; thus, this company has just paid a $.70 dividend per share, as it has for the previous three quarters. What is your value for the current share price now? (Hint: Find the equivalent annual end-of-year dividend for each year.) Comment on whether or not you think that this model of stock valuation is appropriate.

Explanation / Answer

a) Using Dividend Discount model

P = D(1+g)/(k-g) = 5*1.06/(0.12-0.06) = $88.33

b) Equivalent Dividend at the year's beginning = 1.25*( 1.12^-1 + 1.12^-.75 + 1.12^-.5 +1.12^-.25)

= 1.25 *(1-1.12^-1)/(1.12^0.25 -1) = $4.66

Therefore the required P = 4.66*1.06/(.12-.06) = $82.33

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