What is the current value of Frocks & Socks Clothiers, Inc., to an investor who has a required rate of return of 12 percent? The current dividend is $1.00, and the dividends are expected to grow 8 percent per year for 3 years. At the end of 3 years the investor expects to sell the security for $76.
A) $79.51
B) $56.90
C) $51.13
D) $76.00

Question

Quizplus · Accepted Answer

To find the current value of Frocks & Socks Clothiers, Inc., to an investor, we use the Dividend Discount Model (DDM) for a period of growth followed by a sale of the stock. The formula to calculate the present value (PV) of each dividend and the sale price is:$$ PV = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3 + P}{(1+r)^3} $$Where:- $D_1, D_2, D_3$ are the dividends for years 1, 2, and 3, respectively.- $P$ is the sale price at the end of year 3.- $r$ is the required rate of return (12% or 0.12 in decimal form).Given:- Current dividend ($D_0$) = $1.00- Growth rate = 8% or 0.08- Sale price at the end of year 3 = $76- Required rate of return = 12% or 0.12First, calculate the dividends for years 1, 2, and 3:- $D_1 = D_0 \times (1 + \text{growth rate}) = 1.00 \times (1 + 0.08) = $1.08$- $D_2 = D_1 \times (1 + \text{growth rate}) = 1.08 \times (1 + 0.08) = $1.1664$- $D_3 = D_2 \times (1 + \text{growth rate}) = 1.1664 \times (1 + 0.08) = $1.2597$Next, calculate the present value of each dividend and the sale price:$$ PV = \frac{1.08}{(1+0.12)^1} + \frac{1.1664}{(1+0.12)^2} + \frac{1.2597 + 76}{(1+0.12)^3} $$$$ PV = \frac{1.08}{1.12} + \frac{1.1664}{1.2544} + \frac{77.2597}{1.404928} $$$$ PV = 0.9643 + 0.9298 + 54.996 $$$$ PV = 56.8901 $$Therefore, the current value of Frocks & Socks Clothiers, Inc., to an investor is approximately $56.90.

What Is the Current Value of Frocks & Socks Clothiers