A firm's dividends have grown over the last several years. 7 years ago the firm paid a dividend of $2. Yesterday it paid a dividend of $3. What was the average annual growth rate of dividends for this firm?
Solution: | |||
Average annual growth rate of dividends for this firm is 5.96% | |||
Working Notes: | |||
Here we use | |||
Average annual growth rate is the rate at which $2 is compounded to future value in 7 years to $3 , Hence we have to used concept future value of present value of deposit to get the annual rate. | |||
C0 = Present value = $2 the value 7 years ago | |||
FV=Future value of the dividend after 7 years = $3 today dividend amount | |||
r=annual growth rate of dividends = r=?? | |||
n = no. Of periods = 7 year | |||
Using future value formula | |||
FV= C0 x (1+r)^n | |||
3 = 2 (1+ r)^7 | |||
(3/2) = (1+r)^7 | |||
Taking Log on both side | |||
Log(3/2) = Log(1+r)^7 | |||
Log(1.5) = Log(1+r)^7 | |||
using relation loga^b = b x Log a | |||
Log(1.5) = 7 x Log(1+r) | Log(1.5) = 0.176091259 | ||
(0.176091259/7) = Log (1+r) | |||
here we move log to other side and becomes anti log | |||
(1+r) = Antilog (0.176091259/7) | 0.025155894 | ||
(1+r) = Antilog (0.025155894) | We got from online financial calculator | ||
(1+r) = 1.0596340223 | antilog(0.025155894) =1.0596340223 | ||
r=1.0596340223 - 1 | |||
r=0.0596340223 | |||
r= 5.96340223% | |||
r=5.96% in two decimal | |||
r= 5.96340% in 5 decimal | |||
Lets Check is our computed rate is correct. | |||
Using future value formula | |||
FV= C0 x (1+r)^n | |||
3 = 2 (1+ r)^7 | |||
3 = 2 (1+5.96340%)^7 | |||
3 = 2.9999999 | |||
3 = 3 | |||
Hence above computed rate is correct you uses 5 decimal or 2 decimal you will get same answer. | |||
Please feel free to ask if anything about above solution in comment section of the question. |
A firm's dividends have grown over the last several years. 7 years ago the firm paid...
A firm's dividends have grown over the last several years. 3 years ago the firm paid a dividend of $2. Yesterday it paid a dividend of $7. What was the average annual growth rate of dividends for this firm? Round the answer to two decimal places in percentage form.
A firm's dividends have grown over the last several years. 9 years ago the firm paid a dividend of $1. Yesterday it paid a dividend of $6. What was the average annual growth rate of dividends for this form? Round the answer to two decimal places in percentage form. (Write the percentage sign in the "units" box)
A stock you are evaluating just paid an annual dividend of $3.00. Dividends have grown at a constant rate of 1.3 percent over the last 15 years and you expect this to continue. A stock you are evaluating just paid an annual dividend of $3.00. Dividends have grown at a constant rate of 1.3 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 13.1 percent, what...
Four years ago, Bling Diamond, Inc., paid a dividend of $1.85 per share. The company paid a dividend of $2.27 per share yesterday. Dividends will grow over the next five years at the same rate they grew over the last four years. Thereafter, dividends will grow at 7 percent per year. What will the company’s cash dividend be in seven years?
A stock you are evaluating just paid an annual dividend of $2.30. Dividends have grown at a constant rate of 1.6 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 12.4 percent, what is its fair present value?b. If the required rate of return on the stock is 15.4 percent, what should the fair value be four years from today?
A stock you are evaluating just paid an annual dividend of $2.30. Dividends have grown at a constant rate of 1.6 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 12.4 percent, what is its fair present value?b. If the required rate of return on the stock is 15.4 percent, what should the fair value be four years from today?
A stock you are evaluating just paid an annual dividend of $2.70. Dividends have grown at a constant rate of 2.4 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 12.8 percent, what is its fair present value? b. If the required rate of return on the stock is 15.8 percent, what should the fair value be four years from today? (For all requirements, do...
A stock you are evaluating just paid an annual dividend of $2.10. Dividends have grown at a constant rate of 1.2 percent over the last 15 years and you expect this to continue. a. If the required rate of return on the stock is 12.2 percent, what is its fair present value? b. If the required rate of return on the stock is 15.2 percent, what should the fair value be four years from today? For all requirements, do not...
Cost of common stock equity Ross Textiles wishes to measure its cost of common stock equity. The firm's stock is currently selling for S77.77. The firm just recently paid a dividend of $4.11. The firm has been increasing dividends regularly. Five years ago, the dividend was just $3.05. After underpricing and flotation costs, the firm expects to net $71.55 per share on a new issue. a. Determine average annual dividend growth rate over the past 5 years. Using that growth...
The common stock for the Hetterbrand Corporation sells for $59.14, and the last dividend paid was $2.28. Five years ago the firm paid $1.98 per share, and dividends are expected to grow at the same annual rate in the future as they did over the past five years. a. What is the estimated cost of common equity to the firm using the dividend growth model? b. Hetterbrand's CFO has asked his financial analyst to estimate the firm's cost of...