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 $4.00 on its common stock in a single annual installment, and management plans on raising this dividend by 6.25 percent per year indefinitely. If the required return on this stock is 9 percent, what is the current share price? (Do not round intermediate calculations. 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 $1.00 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. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

As per Dividend growth Model,

Market value of Equity(ex-dividend) = Current Dividend(1+ expected continuous dividend growth rate)/(Required Equity return rate or cost - expected continuous dividend growth rate)

Growth rate 6.25%.

Required return 9%

Current dividend = 4

So Current share price = 4(1.0625)/(0.09-0.0625)

=4.25/0.0275=154.54

So current share price is $ 154.54

          Quarterly dividend: $4(1.0625)/4 = $1.0625

               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: 1.090.25 – 1 = .0217

So effective quarterly rate is 2.17%

FV of quarterly dividends of 1.0625 @2.17% interest will be

                  FV= A [ (1+k)n-1/k] where A = quarterly dividend, k=quarterly interest, n=4

FV= 1.0625[(1.0217)4 -1]/0.0217

=4.35

So effective Dividend (1+growth rate )= 4.35

So Price = 4.35/(0.09-0.0625)

=4.35/0.0275=158.18

Therefore , current share price =$158.18

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