Question

As you know, any individual's view of opportunity cost is likely to be different from others'. Prices in the market - whether bonds or stocks - communicate something about what market participants overall see as opportunity cost. Or, in more market specific terms, required returns.

So say you see that Fake Company Zeta closed today at $25.46. You also know that the company just announced its most recent annual dividend of $2.52. Plus, the company has a history of increasing dividends about 1.5% each year. Given this information, what is the market communicating about a required return on this stock?

Because you should be accustomed to working with four decimals, enter your answer as a decimal and rounded to the nearest fourth decimal. Do not enter as a percent. Do not use percent signs, dollar signs, or commas.

For example, if you calculated 0.1147, you would enter 0.1147. If you are working with more than four decimals and calculated 0.09286, then enter 0.0929.

With the explanation and examples above, no credit is given for answers entered incorrectly. Answers are considered correct + or - 0.0050.

Answer 1

The required return for Fake Company Zeta's stock is calculated using the dividend growth model, which combines the expected dividend payout, the current share price, and the dividend growth rate. Based on the provided information, the required return, when rounded to four decimal places, is 0.1154.

Step-by-step explanation:

When assessing the required return on a stock, investors look at the current share price, the dividend paid, and the growth rate of the dividends. For Fake Company Zeta, which closed at $25.46 with an annual dividend of $2.52 that grows annually by 1.5%, the market is communicating information about the expected return through the stock's pricing. To calculate the required return, also known as the discount rate, we need to consider the dividend growth model (Gordon Growth Model).

The formula to calculate the required return (r) considering the Dividend Growth Model is:

r = (D1/P0) + g

Where:
D1 = expected dividend payout next year ($2.52 * 1.015 = $2.5583)
P0 = current share price ($25.46)
g = dividend growth rate (1.5% or 0.015)

Using these figures, the calculation would be as follows:

r = ($2.5583 / $25.46) + 0.015

r = 0.1004424603 + 0.015

r = 0.1154424603

Therefore, when rounded to the nearest fourth decimal, the required return is 0.1154.