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 $5.00 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 and round your answer to 2 decimal places, e.g., 32.16.)
  
Current share price            $

b. Now suppose the company in part (a) actually pays its annual dividend in equal quarterly installments; thus, the company has just paid a dividend of $1.25 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.)
  
Current share price            $

Answer 1

Answer (a):

Current share price = $69.44

Working:

Current share price = Perpetual annual dividend / required return = $6.25 /9% = $69.44

Answer (B):

Current share price = $71.75

Working:

Quarterly dividend payment = 6.25 / 4 = $1.5625

As required rate of return = 9%, when we calculate and apply quarterly required rate, we have to first calculate quarterly discount rate taking annual effective rate = 9%

Quarterly discount rate = (1 + 9%) ^(1/4) - 1 = 2.177818%

Hence:

End of the year value of quarter 1 dividend = 1.5625 * (1 + 2.177818%) ³ = $1.666825

End of the year value of quarter 2 dividend = 1.5625 * (1 + 2.177818%) ² = $1.631298

End of the year value of quarter 3 dividend = 1.5625 * (1 + 2.177818%) = $1.596528

End of the year value of quarter 4 dividend = 1.5625

Equivalent annual end-of-year dividend for each year = $1.666825 + $1.631298 + $1.596528 + 1.5625 = $6.457151

Current share price = $6.457151 /9% = $71.75