Question

Assume that Katy Co. is a constant growth company whose last dividend (D0), which was paid yesterday) was $2.00, and whose dividend is expected to grow indefinitely at a 7 percent rate. Assume the required rate of return for Katy is 13%

A. What is the firm’s expected dividend in year 2?
B. What is the firm’s current stock price?
C. What is the stock's expected price 1 year from now?
D. What is the expected dividend yield, the capital gains yield, and the total return during the first year?
E. Now assume that the stock is currently selling at $32.29, with no other changes. What is the expected rate of return on the stock?
F. What would the stock price be if its dividends were expected to have zero growth, with no other changes?

Answer 1

A. The firm's expected dividend in year 2 is $2.14. B. The firm's current stock price is $35.67. C. The stock's expected price 1 year from now is $35.67. D. The expected dividend yield is 5.6%, the capital gains yield is 10.5%, and the total return is 16.1%. E. The expected rate of return on the stock is 13.63%. F. The stock price would be $2.00 if its dividends were expected to have zero growth.

Step-by-step explanation:

A. To calculate the expected dividend in year 2, we can use the constant growth formula. The constant growth formula is D1 = D0 * (1 + g), where D1 is the expected dividend in year 2, D0 is the last dividend, and g is the growth rate. Plugging in the values, D0 = $2.00 and g = 7%, we get:

D1 = $2.00 * (1 + 0.07) = $2.14

Therefore, the firm's expected dividend in year 2 is $2.14.

B. To calculate the firm's current stock price, we can use the dividend discount model. The dividend discount model is P0 = D1 / (r - g), where P0 is the stock price, D1 is the expected dividend in year 2, r is the required rate of return, and g is the growth rate. Plugging in the values, D1 = $2.14, r = 13%, and g = 7%, we get:

P0 = $2.14 / (0.13 - 0.07) = $35.67

Therefore, the firm's current stock price is $35.67.

C. To calculate the stock's expected price 1 year from now, we can use the constant growth formula. Plugging in the values, D0 = $2.00, g = 7%, and r = 13%, we get:

P1 = D1 / (r - g) = $2.14 / (0.13 - 0.07) = $35.67

Therefore, the stock's expected price 1 year from now is $35.67.

D. The expected dividend yield is the expected dividend in year 1 divided by the stock price. The capital gains yield is the change in the stock price divided by the stock price. The total return is the sum of the dividend yield and the capital gains yield.

Using the values from above, the expected dividend in year 1 is $2.00 and the stock price is $35.67, so the expected dividend yield is $2.00 / $35.67 = 0.056 or 5.6%. The change in the stock price is $35.67 - $32.29 = $3.38, so the capital gains yield is $3.38 / $32.29 = 0.105 or 10.5%. The total return is 5.6% + 10.5% = 16.1%.

E. To calculate the expected rate of return on the stock, we can use the dividend discount model. Plugging in the values, D1 = $2.14, P0 = $32.29, and g = 7%, we get:

r = (D1 / P0) + g = ($2.14 / $32.29) + 0.07 = 0.0663 + 0.07 = 0.1363 or 13.63%

Therefore, the expected rate of return on the stock is 13.63%.

F. When dividends are expected to have zero growth, the constant growth formula becomes D1 = D0, where D1 is the expected dividend in year 2 and D0 is the last dividend. Plugging in the value D0 = $2.00, we get:

D1 = $2.00

Therefore, the stock price would be $2.00 if its dividends were expected to have zero growth.