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.

a.  

Suppose a company currently pays an annual dividend of $3.70 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? (Round your answer to 2 decimal places. (e.g., 32.16))

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 $0.925 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)

P = D*(1+g)/(R-g) = 3.7*(1.04)/(.14-.04) = $38.48

b)

if the company pays quarterly dividend,

the quarterly dividend will be, 3.7*1.04/4 = $.962

to find equa; annual dividen assume that quarterly dividend are reinvested at required return. we can use this interest rate to find equavalent annual dividend

Effective quarter rate = (1.14^.25)-1 = .03329

the effective annual dividend will be FVA of the quarterly dividend payment of quarterly dividend payment at effective quarter rate

Effective, D1 = .962*FVIFA(3.33%,4) = .962*4.2043 = $4.0445

Now, we can use the constant growth model to find correct stock price,

P = 4.0445/(.14-.04) = $40.45

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