27. Most corporations pay quarterly dividends on their common stock rather than
ID: 2681278 • Letter: 2
Question
27.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 $4.20 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 14 percent, what is the current share price?
b.
Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $1.050 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 final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
a.Using the constant growth model, the price of the stock paying annual dividends will be: P0 = D0(1 + g) / (R - g) = $4.20(1.06)/(.14 - .06) = $55.65 b.If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or: Quarterly dividend: $4.20(1.06)/4 = $1.113 To find the equivalent annual dividend, we must assume that the quarterly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock. So, the effective quarterly rate is: Effective quarterly rate: 1.14^.25 - 1 = .0333 The effective annual dividend will be the FVA of the quarterly dividend payments at the effective quarterly required return. In this case, the effective annual dividend will be: Effective D1 = $1.113(FVIFA(3.33%,4)) = $4.64 Now, we can use the constant growth model to find the current stock price as: P0 = $4.64/(.14 - .06) = $58.08
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