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" ABC " Corporation stock is now selling for $ 48 per share and they have just paid a dividend with an amount equal $2

Finance Jan 24, 2021

" ABC " Corporation stock is now selling for $ 48 per share and they have just paid a dividend with an amount equal $2.00 to per share.
The firm's level of risk is equal to 50% of the market's level of risk.
Moreover, you had been given the following information :
The expected return on the market is 14 %, and the yield on U.S. Treasury bonds is 11 %.
Based on the above-given information, and the market is in equilibrium, what is the expected growth rate?

Expert Solution

Price of Stock = P0 = $48

Dividend on stock = D0 = $2

Expected return on the market = Rm = 14 %

U.S. Treasury bonds = Rf = 11 %

The firm's level of risk is equal to 50% of the market's level of risk

Market's level of risk measured by beta, will be Market beta = 1

The firm's level of risk = Firm beta = 50% of Market beta

Firm beta = 0.5 * 1 = 0.5

Since, market is in equilibrium so;

Expected return of firm = Rf + (Rm - Rf) * Firm beta

Expected return of firm = 11% + (14% - 11%) * 0.5

Expected return of firm = 11% + 3% * 0.5

Expected return of firm = 11% + 1.5%

Expected return of firm = 12.5%

r = 12.5%

Price of " ABC " Corporation stock (P0) = [Dividend (D0) * (1+g)] / (r - g)

P0 = [D0 * (1+g)] / (r-g)

48 = [2 * (1+g)] / (12.5% - g)

48 * (12.5% - g) = 2 + 2g

6 - 48g = 2 + 2g

6 - 2 = 2g + 48g

4 = 50g

g = 4/50

g = 0.08

Therefore, the expected growth rate is 8%

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