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.

Suppose a company currently pays an annual dividend of $2.80 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.)

Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $.70 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.)

Suppose a company currently pays an annual dividend of $2.80 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.)

Explanation / Answer

Solution:

a) Calculation of Current share price:

Using the constant growth model, the price of the stock paying annual dividends will be:

P0 = D0 (1 + g) / (R - g)

= 2.80 (1 + 0.02)/ (0.12 - 0.02)

= 2.856/ 0.10

= 28.56

b) Calculation of Current share price:

If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or Quarterly dividend = 2.80(1.02)/4 = 0.714

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: 1.120.25- 1 = .0287

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= 0.714(FVIFA2.87%, 4) = 0.714 * 4.1755 = 2.98

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

P0 = 2.98/ (0.12 - 0.02) = 29.80

Note that we cannot simply find the quarterly effective required return and growth rate to find the value of the stock. This would assume the dividends increased each quarter, not each year.

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