Question

storico co. just paid a dividend of $1.25 per share. the company will increase its dividend by 24 percent next year and will then reduce its dividend growth rate by 6 percentage points per year until it reaches the industry average of 6 percent dividend growth, after which the company will keep a constant growth rate forever. if the stock price is $45.24, what required return must investors be demanding on the company's stock?

Answer 1

To find the required return that investors must be demanding on Storico Co.'s stock, we can use the constant growth stock valuation model. This model calculates the value of a stock based on the dividends it pays and the required return of investors. By iteratively discounting the future dividends and equating it to the stock price, we can find the required return.

Step-by-step explanation:

To find the required return that investors must be demanding on Storico Co.'s stock, we can use the constant growth stock valuation model. This model calculates the value of a stock based on the dividends it pays and the required return of investors. We are given that Storico Co. just paid a dividend of $1.25 per share, and it will increase its dividend by 24 percent next year. Then, the dividend growth rate will reduce by 6 percentage points per year until it reaches the industry average of 6 percent. At this point, the dividend growth rate will remain constant.

First, let's calculate the future dividends, starting with the next year's dividend:

Dividend in year 1 = Dividend in the previous year x (1 + growth rate)

Dividend in year 1 = $1.25 x (1 + 0.24) = $1.55

For the subsequent years until the dividend growth rate reaches 6 percent, we can use the following formula:

Dividend in year n = Dividend in year (n-1) x (1 + growth rate - reduction rate)

We can set up a cash flow timeline to calculate the present value of future dividends:

1. Year 0: $0 (Dividend in the current year is not considered)
2. Year 1: $1.55
3. Year 2: $1.55 x (1 + 0.24 - 0.06)
4. Year 3: $1.55 x (1 + 0.24 - 0.06) x (1 + 0.24 - 0.12)
5. Year n: $1.55 x (1 + 0.24 - 0.06) x (1 + 0.24 - 0.12) x ... x (1 + 0.06) (the growth rate will remain constant at 6 percent)

We are given that the stock price is $45.24. To find the required return, we need to calculate the present value of future dividends and equate it to the stock price:

Stock price = Sum of present value of future dividends

To calculate the present value of future dividends, we discount each year's dividend by the required return. We can start with a reasonable guess for the required return, and then iterate until we reach a value that makes the equation hold true.

Let's go step by step to find the required return:

1. Assume a required return of, say, 8 percent
2. Calculate the present value of future dividends using the assumed required return
3. If the calculated present value equals the stock price, then the assumed required return is the correct answer
4. If the calculated present value is less than the stock price, the required return needs to be higher
5. Repeat steps 2-4 with a higher required return
6. If the calculated present value is greater than the stock price, the required return needs to be lower
7. Repeat steps 2-4 with a lower required return
8. Continue this iterative process until you find the required return that makes the equation hold true with a close approximation

This process helps us find the required return that investors must be demanding on Storico Co.'s stock.