A company paid its annual dividends of $4.40 per share last week. The company expects to grow its dividends at the rate of 5.0 percent per year for four years, after which the dividends are expected to remain constant at the level of $5.68 per share per year in perpetuity. If investors require a rate of return of 11.5 percent on this company's stock, what should be the price of one share of this stock today

$47

Explanation:

Calculation for what should be the price of one share of this stock today

First step is to calculate Year 1 dividend

Year 1 dividend = 4.4 (1 + 5%)

Year 1 dividend= 4.62

Second step is to calculate Year 2 dividend

Year 2 dividend = 4.62 (1 + 5%)

Year 2 dividend= 4.851

Third step is to calculate Year 3 dividend

Year 3 dividend = 4.851 (1 + 5%)

Year 3 dividend= 5.09355

Fourth step is to calculate Year 4 dividend

Year 4 dividend = 5.09355(1 + 5%)

Year 4 dividend= 5.34823

Now let calculate the year 4 value using this formula

Year 4 value = Year 5 dividend / Required rate - Growth rate

Let plug in the formula

Year 4 value = 5.68 / 0.115

Year 4 value=49.3913

Last step is to calculate the Present value using this formula

Present value = Future value / (1 + rate)^time

Let plug in the formula

Price today = 4.62 / (1 + 0.115)^1 + 4.851 / (1 + 0.115)^2 + 5.09355 / (1 + 0.115)^3 + 5.34823 / (1 + 0.115)^4 + 49.3913 / (1 + 0.115)^4

Price today = $47

Therefore what should be the price of one share of this stock today will be $47

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