Question

Suppose you are considering buying a stock. The stock is currently trading for $15. You expect the price in one year to be $16 and it will pay a dividend of $0.75. You estimate the stock’s beta at 2, the risk-free rate at 1.5%, and the expected return on the market at 7.5%. According to the CAPM, should you consider purchasing this stock?

a) The intrinsic value is $14.76. The current price is $15. You should not consider buying the stock.

b) The intrinsic value is $15. The current price should be $14.76. You should consider buying the stock.

c) The intrinsic value is $14.76. The current price $15. You should consider buying the stock.

d) The intrinsic value is $13.72. The current price $55. You should not consider buying the stock.

Answer 1

Using the CAPM formula, the expected return is calculated at 13.5%. Based on this, the intrinsic value of the stock is $14.76. Since the market price is $15, which is higher than the intrinsic value, you should not consider purchasing the stock.

Step-by-step explanation:

According to the Capital Asset Pricing Model (CAPM), the expected return on a stock can be calculated using the formula: expected return = risk-free rate + beta x (market return - risk-free rate). In this case, you have a stock with a beta of 2, a risk-free rate of 1.5%, and an expected market return of 7.5%. Plugging these values into the formula gives us an expected return of 1.5% + 2 x (7.5% - 1.5%) = 13.5%.

To evaluate whether you should purchase the stock, calculate the stock's intrinsic value by discounting the expected price in one year plus the dividend by the expected return. The intrinsic value can be found using the formula: intrinsic value = (expected price + dividend)/(1 + expected return). Plugging in the expected price of $16 and the dividend of $0.75, we get: intrinsic value = ($16 + $0.75)/(1 + 0.135) = $14.76.

Given that the current price of the stock is $15 and the intrinsic value you calculated is $14.76, the stock is overvalued based on your expectations and the CAPM. Therefore, you should not consider buying the stock as the market price is higher than what the CAPM model suggests its value should be. The correct answer to the initial question is option (a).

Answer 2

According to CAPM, the intrinsic value of the stock is calculated to be $14.76. Since the intrinsic value is less than the current trading price of $15, it is not advisable to purchase the stock.

Step-by-step explanation:

Using CAPM to Determine Stock Purchase Decision

The question involves using the Capital Asset Pricing Model (CAPM) to assess whether one should consider buying a stock. First, we calculate the expected return of the stock using the CAPM formula: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). For this stock, the expected return would be 1.5% + 2 * (7.5% - 1.5%) = 1.5% + 2 * 6% = 1.5% + 12% = 13.5%. Next, we calculate the stock's intrinsic value by adding next year's expected price ($16) and the dividend ($0.75), and then discounting this sum by the expected return we just calculated.

To work out the present value you would do the following calculation: Intrinsic Value = ($16 + $0.75) / (1 + 13.5%) which gives $14.76 (rounded to two decimal places). If the intrinsic value ($14.76) is less than the current price ($15), it would not be recommended to buy the stock, according to CAPM as you would be paying more than what the stock is worth based on its expected returns.

Therefore, the correct answer is: a) The intrinsic value is $14.76. The current price is $15. You should not consider buying the stock.