Question

C Please show all steps to solve and explain. Do not use excel. Thank you! Marble Corporation's ROE is 17\%. Their dividend payout ratio is 20%. The last dividend, just paid, was $2,58. Dividends are expected to grow by the company's sustainable growth rate indefinitely.

a) What is the current value of Marble common stack if its required return is 18%?
b) If expected dividend is $3, your required rate of return of 18%, you buy the stock at $50, what is the constant dividend growth rate?"

Answer 1

To calculate the current value of Marble Corporation's stock, use the Gordon Growth Model. The current stock price is found to be $66.59, assuming a sustainable growth rate of 13.6%. To find the constant dividend growth rate with a stock price of $50, an expected dividend of $3, and a required return of 18%, the growth rate would be 12%.

Step-by-step explanation:

To calculate the current value of Marble Corporation's common stock using the Gordon Growth Model (Dividend Discount Model), we use the formula:

P = D1 / (r - g)

where:

• P is the current stock price
• D1 is the expected dividend next year
• r is the required rate of return
• g is the dividend growth rate

a) Given that the dividend payout ratio is 20% and the ROE is 17%, we can determine the sustainable growth rate (g) as:

g = ROE × (1 - Dividend Payout Ratio) = 0.17 × (1 - 0.20) = 0.17 × 0.80 = 0.136 or 13.6%

The expected dividend next year (D1) will be:
D1 = D0 × (1 + g) = $2.58 × (1 + 0.136) = $2.58 × 1.136 = $2.93

Now, we can find the current stock price (P):
P = D1 / (r - g) = $2.93 / (0.18 - 0.136) = $2.93 / 0.044 = $66.59

b) To find the constant dividend growth rate when the stock price is $50, the expected dividend is $3, and the required return is 18%, we rearrange the formula to solve for g:

g = r - (D1 / P) = 0.18 - ($3 / $50) = 0.18 - 0.06 = 0.12 or 12%