A firm's stock is selling for $85, Dividend yield=5%. A 7% growth rate is expected for the common stock. The firm's tax rate is 32%. (question) What is the firm's cost of retained earnings?
a)8.16%
b)12.00%
c)12.35%
d)cannot be determined
12%
To calculate the firm's cost of retained earnings, we need to use the dividend growth model, also known as the Gordon Growth Model. This model calculates the required return on equity (cost of retained earnings) using the formula:
Cost of Retained Earnings = (Dividend per Share / Stock Price) + Growth Rate
Given information:
Stock Price = $85
Dividend Yield = 5% (0.05)
Growth Rate = 7% (0.07)
Tax Rate = 32% (0.32)
First, let's calculate the Dividend per Share using the Dividend Yield:
Dividend per Share = Dividend Yield * Stock Price
Dividend per Share = 0.05 * $85
Dividend per Share = $4.25
Now, let's calculate the cost of retained earnings using the formula:
Cost of Retained Earnings = ($4.25 / $85) + 0.07
Cost of Retained Earnings = 0.05 + 0.07
Cost of Retained Earnings = 0.12
However, we need to adjust the cost of retained earnings for the taxes, as the firm's tax rate is 32%. The tax-adjusted cost of retained earnings is calculated by multiplying the cost of retained earnings by (1 - Tax Rate):
Tax-Adjusted Cost of Retained Earnings = Cost of Retained Earnings * (1 - Tax Rate)
Tax-Adjusted Cost of Retained Earnings = 0.12 * (1 - 0.32)
Tax-Adjusted Cost of Retained Earnings = 0.12 * 0.68
Tax-Adjusted Cost of Retained Earnings = 0.0816
Therefore, the firm's cost of retained earnings is 8.16%.
The correct answer is (a) 8.16%.
To calculate the cost of retained earnings, we can use the Dividend Growth Model (also known as Gordon Model) formula:
Cost of Retained Earnings = (Dividend / Current Stock Price) + Growth Rate
First, we need to find the dividend by multiplying the dividend yield (5%) by the current stock price ($85):
Dividend = Dividend Yield x Current Stock Price
Dividend = 0.05 x $85
Dividend = $4.25
Next, we can plug this value and the growth rate (7%) into the formula:
Cost of Retained Earnings = ($4.25 / $85) + 0.07
Cost of Retained Earnings = 0.05 + 0.07
Cost of Retained Earnings = 0.12 or 12%
Therefore, the firm's cost of retained earnings is 12%.
The correct answer is b) 12.00%.