DBP Inc. just paid a dividend of $2.50. The expected growth rate of dividend is 5 percent. The required return for investors in the first three years is 12 percent and 10 percent for the following three years. After those six years the required return is 8 percent. What is the current share price of the stock?
A. $74.94 B. $73.00 C. $70.74
Work:
2.5/ (1.12) + 2.5(1.05)/ (1.12^2) + 2.5(1.05^2)/ (1.12^3) + 2.75625/ (1.10) + 2.75625(1.05)/ (1.10^2) + 2.75625(1.05^2)/ (1.10^3) + 3.03876/ (.10-.05)
= 6.2866 + 7.1805 + 60.7753 = 74.66738855
74.98
To find the current share price of the stock, you will need to calculate the present value of all the future dividends. The formula for calculating the present value of a dividend is:
Present Value = Dividend / (1 + required return rate)^n
where Dividend is the dividend payment, required return rate is the rate of return required by investors, and n is the number of years in the future.
In this case, you will need to calculate the present values of dividends for the first three years, the next three years, and after the sixth year.
Let's go through the calculations step by step:
1. Present Value of Dividends for the First Three Years:
Dividend = $2.50
Required return rate = 12%
n = 1, 2, 3
Present Value = 2.5 / (1 + 0.12)^1 + 2.5 * (1 + 0.05) / (1 + 0.12)^2 + 2.5 * (1 + 0.05)^2 / (1 + 0.12)^3
= 2.5 / 1.12 + 2.5 * 1.05 / 1.12^2 + 2.5 * 1.05^2 / 1.12^3
= 2.2386 + 2.0801 + 1.9679
= 6.2866
2. Present Value of Dividends for the Next Three Years:
Dividend = $2.75625
Required return rate = 10%
n = 1, 2, 3
Present Value = 2.75625 / (1 + 0.10)^1 + 2.75625 * (1 + 0.05) / (1 + 0.10)^2 + 2.75625 * (1 + 0.05)^2 / (1 + 0.10)^3
= 2.501136 + 2.139650 + 2.132388
= 7.1805
3. Present Value of Dividend after the Sixth Year:
Dividend = $3.03876
Required return rate = 8%
n = 1
Present Value = 3.03876 / (0.10 - 0.05)
= 3.03876 / 0.05
= 60.7753
Finally, to find the current share price, you need to sum up the present values of all the dividends calculated above:
Current Share Price = 6.2866 + 7.1805 + 60.7753
= 74.6674
Therefore, the current share price of the stock is approximately $74.67.
None of the answer options provided match the calculated share price.