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.
Required:
(a)
Suppose a company currently pays an annual dividend of $3.20 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.
Current share price $
(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 $.80 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.
Current share price $
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To answer these questions, we need to use the formula for the present value of a growing perpetuity. The formula is:
PV = D / (r - g)
Where:
PV = Present value of the perpetuity
D = Dividend payment
r = Required return (or discount rate)
g = Growth rate of dividends
(a) Let's calculate the current share price using the formula and the given information:
D = $3.20 (annual dividend)
r = 12% (required return)
g = 6% (growth rate of dividends)
PV = $3.20 / (0.12 - 0.06)
= $3.20 / 0.06
= $53.33
So, the current share price is $53.33.
(b) In this case, we need to find the equivalent annual end-of-year dividend for each year, assuming the payment is made in equal quarterly installments.
Quarterly dividend paid = $0.80
Annual dividend paid = $0.80 * 4 = $3.20 (equivalent annual dividend)
Now, we can use the same formula to calculate the current share price with the new dividend payment:
D = $3.20 (annual dividend)
r = 12% (required return)
g = 6% (growth rate of dividends)
PV = $3.20 / (0.12 - 0.06)
= $3.20 / 0.06
= $53.33
So, the current share price remains $53.33, even if the dividend is paid in equal quarterly installments.