Final answer:
To value a stock with declining dividends, the dividend discount model is used. For the given company Antiques R Us, with a dividend of $9 decreasing by 4% annually and an 11% required return, the stock is valued at $128.57 per share today.
Step-by-step explanation:
The student's question pertains to the valuation of a stock with declining dividends in a mature manufacturing firm, specifically Antiques R Us. To find this valuation, we must use the dividend discount model for stocks with declining dividends. The formula for this valuation when dividends are expected to decrease indefinitely is:
P = D / (r - g)
where:
- P is the price of the stock today
- D is the dividend just paid
- r is the required rate of return
- g is the decline rate (as a positive number) applied to the dividend
Given that Antiques R Us just paid a dividend of $9, expects to reduce this payout by 4 percent per year indefinitely, and the required return is 11 percent, we can calculate the price:
P = $9 / (0.11 - 0.04)
P = $9 / 0.07
P = $128.57
Therefore, if you require an 11 percent return on Antiques R Us stock and the dividends are decreasing by 4 percent per year, you would be willing to pay $128.57 for a share today.