Final answer:
Due to missing coefficients and factor premiums in the question, it's not feasible to calculate the expected rates of return for stocks A and B. Expected rate of return accounts for various risks and the baseline risk-free rate, requiring additional data to complete the calculation.
Step-by-step explanation:
To calculate the expected rate of return for each company using the Fama-French 3-factor APT model, we would typically use the following formula:
Expected Return = Risk-Free Rate + (Beta₁ * Market Risk Premium) + (Beta₂ * Size Premium) + (Beta₃ * Value Premium)
However, the details regarding the coefficients (Beta₁, Beta₂, Beta₃) for stocks A and B, as well as the specific risk premiums for each factor, have not been provided in the question. Assuming that these values were given, one would plug them into the formula to find the cost of equity capital for each stock.
The Risk-Free Rate is already given as 4%, so it would serve as the baseline for the calculation. The Betas represent the sensitivity of the stock's returns to the corresponding factors and would be multiplied by their respective risk premiums.
The key point is that risk alters the expected rate of return, with investors requiring higher returns to compensate for higher perceived risk. For instance, if the market risk premium was 5%, and the Beta for stock A regarding the market risk was 1.2, then this portion would add 6% (1.2 * 5%) to the risk-free rate.
In essence, higher Betas and larger risk premiums would result in a higher expected rate of return. The actual rate of return might differ from the expected rate, as it will also factor in the realized outcomes from these risks, including both gains and losses.