Caribou Gold Mining Corporation is expected to pay a dividend of $6 in the upcoming year. Dividends are expected to decline at the rate of 3% per year. The risk-free rate of return is 5%, and the expected return on the market portfolio is 13%. The stock of Caribou Gold Mining Corporation has a beta of 0.5. Using the constant-growth DDM, the intrinsic value of the stock is _________.
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To calculate the intrinsic value of the stock using the constant-growth Dividend Discount Model (DDM), we use the following formula:
\[ P_0 = \frac{D_1}{r - g} \]
Where: - \( P_0 \) is the intrinsic value of the stock today. - \( D_1 \) is the expected dividend in the upcoming year. - \( r \) is the required rate of return for the stock. - \( g \) is the growth rate of the dividends.
In this case, \( D_1 \) is given as $6. The growth rate \( g \) is the decline rate, which is -3%, or -0.03 in decimal form.
To calculate the required rate of return \( r \), we use the Capital Asset Pricing Model (CAPM):
\[ r = r_f + \beta (r_m - r_f) \]
Where: - \( r_f \) is the risk-free rate of return, given as 5% or 0.05 in decimal form. - \( r_m \) is the expected return on the market portfolio, given as 13% or 0.13 in decimal form. - \( \beta \) is the measure of the stock's volatility in relation to the market, given as 0.5.
Let's calculate \( r \) first:
\[ r = 0.05 + 0.5 (0.13 - 0.05) \] \[ r = 0.05 + 0.5 (0.08) \] \[ r = 0.05 + 0.04 \] \[ r = 0.09 \] or 9%
Now we know both \( r \) and \( g \), so we can calculate \( P_0 \):
\[ P_0 = \frac{6}{0.09 - (-0.03)} \] \[ P_0 = \frac{6}{0.12} \] \[ P_0 = 50 \]
The intrinsic value of Caribou Gold Mining Corporation's stock using the constant-growth DDM is $50.