Most corpoerations pay quarterly dividens on their common stock rather than annu

Question

Most corpoerations pay quarterly dividens 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 quartlerly installments to its shareholders.

A) suppose a company currently pays an annual dividend of $3.20 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 the company in (a) actually pays it annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $.80 per share, as it has for the previous three quaters. What is your value for the current share price now?

Explanation / Answer

a. using the constant growth model ,the price of the stock paying annual dividends will be:

P=D(1+g)/(R-g)=$3.20(1.06)/(0.12-0.06)=$56.53

B. IF THE COMPANY PAYS quartely dividends instesd of annual dividends, the quartely dividend will be one -forth of annual dividend, or:

quartely dividend:$3.20(1.06)/4=$0.636

to find the equivalent annual dividend we must assume that tha quartely dividends are reinvested at the required return . we can then use this intrest rate to find the equivalent annual dividend .in other words when we recieve the quaterly dividend we reinvest it at the required return on the stock so the effective quartely

effective quartely rate: 1.12^0.25-1=0.0287

the effective annual devidend will be the fva of the quartely dividend payments at the effective quartely required return.int this case the effective annual dividend will be::

effective D1: $0.636(FVIFA2.87%,4)=$2.66

now we can use the constant growth model to find the current stock price as:

PO: $2.66/(0.16-0.06)=$26.6

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