Antiques R Us is a mature manufacturing firm. The company just paid a $10.46 dividend, but management expects to reduce the payout by 4% per year indefinitely.
If you require an 11.5% return on this stock, what will you pay for a share today?
Declining Growth Rate:
Under the dividend growth model, the declining growth rate is a constant growth rate at which the dividends of stock keep declining each year until perpetuity. It is not necessary for the growth rate to be declining always, it can even be increasing but it remains constant as per the model.
Answer and Explanation:
The price that will be paid today for Antiques R Us's stock is $64.77.
Antiques R Us has provided the following data:
- Last Dividend, D0 = $10.46
- Declining growth rate, g = -4%
- Required return, Ke = 11.50%
- Current share price, P0 =?
The first step is to determine the next dividend, D1:
- D1 = D0 * (1 + g)
- D1 = $10.46 * (1 - 4%)
- D1 = $10.04
The second step is to determine the current share price:
- P0 = D1 / (Ke - g)
- P0 = $10.04 / (11.50% - (-4%)
- P0 = $10.04 / 15.50%
- P0 = $64.77
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Learn more about this topic:
from Finance 101: Principles of FinanceChapter 14 / Lesson 3