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Royal Hills Corporation pays 30% of its earnings to stockholders and retains 70% to finance growth. The firm recently paid a $3.20 common stock dividend. Investors require a return of 14% on Royal Hills common stock. If the firm earns a return on equity of 10%, what should be the value of Royal Hills common stock?

Answer :

Final answer:

The calculation of the value of Royal Hills common stock, using the Gordon Growth Model formula and given figures, results in a stock value of $45.71.

Explanation:

To calculate the value of Royal Hills common stock, we can use the Gordon Growth Model formula: P = D / (k - g), where 'P' is the price of the stock, 'D' is the dividend, 'k' is the required rate of return, and 'g' is the growth rate of the dividends.

In this case, 'D' has already been given as $3.20. The required rate of return 'k' is 14%, or 0.14. The growth rate 'g' of the dividends can be calculated as follows: the firm retains 70% of its earnings for growth, and the firm's return on equity is 10%, or 0.10, so the growth rate is 0.70 * 0.10 = 0.07, or 7%.

Plugging these numbers into the formula, we find: P = 3.20 / (0.14 - 0.07) = $45.71. Therefore, the value of Royal Hills common stock should be $45.71.

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Rewritten by : Barada

Answer:

$48.91

Explanation:

The computation of the value of the common stock is shown below:

As we know that

Growth rate = Return on equity × retention ratio

= 10% × 0.7

= 7%

So,

The Value of the common stock = Dividend next year ÷ (Required return - growth rate)

= $3.2 × 1.07 ÷ (0.14-0.07)

= $48.91

Basically we applied the above formula so that the value of the common stock could come