Antiques R Us is a mature manufacturing firm. The company just paid a dividend o

Question

Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $12.15, but management expects to reduce the payout by 6 percent per year indefinitely. If you require a return of 10 percent on this stock, what will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $12.15, but management expects to reduce the payout by 6 percent per year indefinitely. If you require a return of 10 percent on this stock, what will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Recent Dividend paid D0 = $ 12.15

Expected reduction in payout g = 6.1% per annum indefinitely or g = - 0.061 (-6.1/100)

Required rate of return = 10% or 0.10

The formula for arriving at the value of a stock with a constant dividend growth is

PV = D0 (1+g) / (r - g)

The same formula can be used with a modification of using -g in place of g

Hence, the formula gets modified as

PV = D0 (1+ (-g))/ (r - (-g)) --> PV = D0 (1-g) / (r+g)

Substituting the values

PV = 12.15 * (1-0.061) / (0.10 + 0.061)

PV = 12.15 * 0.939 / 0.161

PV = 11.40885 / 0.161 = 70.86

Hence the price at which the stock can be purchsed today is $ 70.86

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