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 $2.80 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 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.) |
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 $.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.) |
Solution :-
(A)
Dividend Per Share = $2.80
Growth Rate = 6%
Next Year Dividend = $2.80 * ( 1 + 0.06 ) = $2.968
Required Return ( ke ) = 12%
Now Share Price = Next Year Dividend / ( Ke - Growth ) = $2.968 / ( 0.12 - 0.06 ) = $49.47
(B)
Quarterly Dividend = $2.80 / 4 = $0.70
Quarterly ke = ( 1 + 0.12 )4 - 1 = 1.02874 - 1 = 0.02874 = 2.874%
Equivalent Annual Dividend = $0.70 * FVAF ( 2.874% , 4 )
= $0.70 * 4.17577
= $2.92304
Now Share Price = Next Year Dividend / ( Ke - Growth ) = $2.923 * ( 1 + 0.06 ) / ( 0.12 - 0.06 ) = $51.64
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