Question

Assume a major investment service has just given Big Lake Realty its highest investment​ rating, along with a strong buy recommendation. As a​ result, you decide to take a look for yourself and to place a value on the​ company's stock.​ Here's what you​ find: This​ year, Big Lake paid its stockholders an annual dividend of ​$4.93 a​ share, but because of its high rate of growth in​ earnings, its dividends are expected to grow at the rate of 9​% a year for the next five years and then to level out at 5 % a year. So​ far, you've learned that the stock has a beta of 1.15​, the​risk-free rate of return is 4.8​%, and the expected return on the market is 10.8​%.

Using the CAPM to find the required rate of​ return, put a value on this stock.

Answer 1

To value the stock of Big Lake Realty, we can use the CAPM to find the required rate of return and the Dividend Discount Model (DDM) to estimate the value of the stock. Using the given data, the required rate of return is 11.11% and the value of the stock is approximately $71.98.

Step-by-step explanation:

To put a value on the stock of Big Lake Realty, we can use the Capital Asset Pricing Model (CAPM) to find the required rate of return. The CAPM formula is: Required rate of return = Risk-free rate + Beta * (Expected return on the market - Risk-free rate). In this case, the risk-free rate is 4.8%, the beta is 1.15, and the expected return on the market is 10.8%. Plugging in these values, we get: Required rate of return = 4.8% + 1.15 * (10.8% - 4.8%) = 11.11%.

Next, to estimate the value of the stock, we can use the Dividend Discount Model (DDM). The DDM formula is: Stock value = Dividend / (Required rate of return - Dividend growth rate). For the next five years, the dividend growth rate is 9%, and after that, it levels out at 5%. Plugging in the values, we get: Stock value = $4.93 / (11.11% - 9%) + (0.05 - 0.09) = $71.98. Therefore, the value of the stock is approximately $71.98.