Final answer:
To calculate the value of the security, we need to calculate the present value of its future dividends. The dividend is expected to grow by 12% for the first two years and then by 3% afterwards. The required rate of return is 15%. The security's value is closest to $167.29.
Step-by-step explanation:
To calculate the value of the security, we need to calculate the present value of its future dividends. The dividend is expected to grow by 12% for the first two years and then by 3% afterwards. The required rate of return is 15%. We can use the formula for the present value of a growing perpetuity to calculate the present value of the future dividends.
First, calculate the present value of the dividends for the first two years:
Present Value = Dividend1 / (1 + r) + Dividend2 / (1 + r)^2
= $9.50 / (1 + 0.15) + ($9.50 * 1.12) / (1 + 0.15)^2
= $8.26 + $7.03
= $15.29
Then, calculate the present value of the dividends after the first two years:
Present Value = Dividend3 / (r - g)
= $9.50 * 1.03 / (0.15 - 0.03)
= $9.8034
Next, calculate the total present value of the dividends:
Total Present Value = Present Value of Dividends 1-2 + Present Value of Dividends 3
= $15.29 + $9.8034
= $25.0934
Finally, divide the total present value by the required rate of return to get the value of the security:
Value of Security = Total Present Value / r
= $25.0934 / 0.15
= $167.2893
Rounded to the nearest cent, the security's value is closest to $167.29.