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 an annual dividend of $3.60 on its common stock in a single annual installment and management plans on raising this dividend by 2 percent per year, indefinitely. If the required return on this stock is 12 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.

Now suppose that the company actually pays its annual dividend in equal quarterly installments; thus, this company has just paid a dividend of $.900 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.) (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  
   

Answer 1

a. One method of arriving at the stock price is the dividend discount model, which uses the stock's current dividend and its expected dividend growth rate to determine its current stock price. To calculate the price of a stock based on its dividends paid, the most commonly used equation is

Price = Expected next year Dividend/ (Expected rate of return - Growth rate)

= ($3.60*2%)/(0.12-0.02)

= $3.67/0.10

= $36.72. This shall be the price of the stock.

b. Given the dividend being paid quarterly, the sum total of all the dividends paid in the year amounts to $3.60 only. Given the same growth rate, expected rate of return, and the same amount of dividend paid, the stock price based on the quarterly dividends doesn't change. The calculations are same and using the same formula, the stock price is derived as & 36.72.