Michael's, Incorporated, just paid $2.45 to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 5.3 percent. If you require a rate of return of 9.5 percent, how much are you willing to pay today to purchase one share of the company's stock?
Question
Michael's, Incorporated, just paid $2.45 to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 5.3 percent. If you require a rate of return of 9.5 percent, how much are you willing to pay today to purchase one share of the company's stock?
Solution
This is a problem of calculating the price of a stock using the Gordon Growth Model. The Gordon Growth Model is a model to determine the intrinsic value of a stock, assuming that the stock's dividends grow at a constant rate. It's formula is:
P = D1 / (r - g)
where: P = price of the stock today D1 = the dividend expected to be received in the next period r = required rate of return g = growth rate of dividends
In this case, we know that: D0 (the dividend just paid) = $2.45 g (growth rate of dividends) = 5.3% = 0.053 r (required rate of return) = 9.5% = 0.095
First, we need to calculate D1, the dividend expected to be received in the next period. Since we know that the dividends are growing at a constant rate, we can calculate D1 as follows:
D1 = D0 * (1 + g) D1 = 2.45 * 1.053 D1 = $2.58 (approximately)
Now we can substitute D1, r, and g into the Gordon Growth Model formula to find the price of the stock:
P = D1 / (r - g) P = 2.58 / 0.042 P = $61.43 (approximately)
So, if you require a rate of return of 9.5 percent, you should be willing to pay approximately $61.43 today to purchase one share of the company's stock.
Similar Questions
Downtown Brothers paid an annual dividend of $1.15 per share this year. Today, the company announced that future dividends will be increasing by 2.6 percent annually. If you require a 12 percent rate of return, how much are you willing to pay to purchase one share of this stock today? Group of answer choices $12.55 $13.70 $9.83 $9.58 $12.23
The CFO of a publicly traded company is expecting to pay a dividend next year of $1.25 and projecting that the price of the company’s stock will be $45 in 1 year. The CFO has determined that the required rate of return for the company is 10%. Based on the data available, what is the value of one share of stock today?
Your firm has a dividend policy that pays constant dividend of $1 per share to ordinary shareholders perpetually. Given your firm’s shareholders’ required rate of return of 5%, calculate the firm’s share price.Group of answer choices$20.00$2.00$200.00$0.05Next
What is the value of a share that has just paid a dividend of $1, growing at 5% and a required rate of return of 10%
The Bell Weather Company is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 18 percent a year for the next 4 years and then decreasing the growth rate to 3 percent per year. The company just paid its annual dividend in the amount of $1.80 per share. What is the current value of one share of this stock if the required rate of return is 7.30 percent?Multiple Choice$83.59$63.06$72.25$85.39$74.05
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.