Richard, Inc., will pay a quarterly dividend per share of $1.15 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1.7 percent forever. The appropriate rate of return on the stock is 12 percent, compounded quarterly. What is the current stock price?
Question
Richard, Inc., will pay a quarterly dividend per share of $1.15 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1.7 percent forever. The appropriate rate of return on the stock is 12 percent, compounded quarterly. What is the current stock price?
Solution
To calculate the current stock price, we need to calculate the present value of the dividends for the first 12 quarters and the present value of the dividends from the 13th quarter onwards.
Step 1: Calculate the present value of the dividends for the first 12 quarters.
The formula for the present value of a series of future payments is:
PV = D / (1 + r)^t
where:
- PV is the present value
- D is the dividend
- r is the rate of return
- t is the time period
We need to calculate this for each of the first 12 quarters and sum them up.
Step 2: Calculate the present value of the dividends from the 13th quarter onwards.
From the 13th quarter onwards, the dividends grow at a rate of 1.7% per quarter forever. This is a growing perpetuity. The formula for the present value of a growing perpetuity is:
PV = D / (r - g)
where:
- PV is the present value
- D is the dividend in the first period of the perpetuity
- r is the rate of return
- g is the growth rate
In this case, D is the dividend in the 13th quarter, which is $1.15 * (1 + 0.017)^12.
Step 3: Add the present values from step 1 and step 2 to get the current stock price.
Please note that the rate of return and the growth rate need to be in the same terms (i.e., both should be quarterly rates). The annual rate of return of 12% compounded quarterly is equivalent to a quarterly rate of 3% (12% / 4).
Similar Questions
Each quarter, A company pays a dividend on its perpetual preference shares. Today, the share is selling at $83.45（P0）. If the required rate of return for such shares is 10.5%, what is the quarterly dividend paid by this company?
The Co. just paid a dividend of $1 per share. Analysts expect its dividend to grow at 25 percent per year for the next three years and then 5 percent per year thereafter. If the required rate of return on the stock is 18 percent, what is the current value of the stock?
Networks Ltd is experiencing a period of rapid growth. Earnings and dividends are expected to grow at a rate of 18% during the next two years, 15% in the third, and then at a constant rate of 6 per cent thereafter. Networks’ last dividend, which has just been paid, was $0.115. If the required return on the shares is 12%, what is the price of the share today?
Downtown Brothers paid an annual dividend of $1.15 per share this year. Today, the company announced that future dividends will be increasing by 2.6 percent annually. If you require a 12 percent rate of return, how much are you willing to pay to purchase one share of this stock today? Group of answer choices $12.55 $13.70 $9.83 $9.58 $12.23
According to the prospectus of New Start Ltd, the company anticipates paying its first dividend of $0.85 in 4 years time, and thereafter expects the dividend to increase by 4% each year indefinitely. If the required return is 15%, what is the current value of a New Start share today? Group of answer choices $4.42 $5.67 $7.73 $5.28 $5.08
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.