Question

Assume the current dividend of a security is $9.50. The dividend is expected to grow by 12% each year for two years and then 3% afterwards. The required rate of return is 15%. The security's value is closest to:

a) $69.12
b) $86.40
c) $84.34
d) $62.00

Answer 1

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.