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 $4.10 on its common stock in a single annual installment and management plans on raising this dividend by 4 percent per year indefinitely. If the required return on this stock is 14 percent. What is the current share price?
b) Now suppose the company is (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $1.025 per share, as it has for the previous three quarters. What is your value for the current share price now??
Dividend Growth Model:
As per the dividend growth model, the present value of all the dividends, considering growth, is the price of the stock. It follows the concept of present value of perpetuity to give us the value of the stock.
Answer and Explanation:
As per Dividend growth model,
Share price = Next dividend / (Return - Growth)
Next dividend = Current dividend x (1 + Growth) = 4 x 1.04 = $4.16
Return = 14% = 0.14
Growth = 4% = 0.04
Stock price = 4.16 / 0.10 = $41.60
Since the dividend is paid out quarterly but the growth is annually we would consider the same formula except for the fact that the return would be effective annual rate for quarterly compounded dividends.
Effective annual rate
= (1 + Quarterly rate)^4 - 1
= (1 + 0.14/4)^4 - 1
The stock price would be
= 4.16 / (0.1475 - 0.04)
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from Finance 101: Principles of FinanceChapter 14 / Lesson 3