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Answer :
Final answer:
The stock price per share for Sweatshirts Unlimited, given a $2.55 annual dividend that is lowering by 20% each year and a required rate of return of 17%, is $5.51.
Explanation:
The value of the shares of Sweatshirts Unlimited can be calculated by using the Gordon Growth Model formula. This formula is used in finance to determine the intrinsic value of a stock. The formula is P = D1/(r - g). P = Stock price, D1 = Dividend at the end of the first year, r = Required return, g = Dividend growth rate.
Given that the dividend is going to decrease by 20% each year, the dividend growth rate is -20% or -0.20. So, D1 is the dividend payment for the first year after the decrease, which is $2.55 * 80% = $2.04. With a required return of 17%, or 0.17, the stock price (P) would be: P = $2.04 / (0.17 - (-0.20)) = $2.04 / 0.37 = $5.51.
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Final Answer:
The shares in Sweatshirts Unlimited are worth $8.64 per share today.
Explanation:
In order to determine the current value of shares in Sweatshirts Unlimited, we'll use the dividend discount model (DDM) to account for the decreasing dividend payments and your required rate of return of 17 percent.
Step 1: Calculate the Dividend for the Next Year
The company plans to decrease the dividend by 20 percent each year. So, the dividend for the next year will be 80 percent of the previous year's dividend:
$2.55 * 0.80 = $2.04
Step 2: Calculate the Present Value of Future Dividends
Since the company will eventually stop paying dividends, this can be treated as a perpetuity that declines by 20 percent annually. The present value of a perpetuity is calculated as:
PV = D / r
Where:
PV = Present Value
D = Dividend in the next year
r = Required rate of return
So, PV = $2.04 / 0.17 = $12
Step 3: Calculate the Value per Share Today
The value per share today is the present value of future dividends. In this case, it's $12.
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