Capital Asset Pricing Model (Part 2)

Question 8: You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars): The project’s beta is 1.8. Assuming that rf = 8% and E ( rM ) = 16%, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative? A consultant is evaluating a project which requires $40 million as initial cash outlay. The life of the project is 10 years. Annual after-tax cash flow from the project is $15 million. If the NPV (net present value) of the project is positive the project will be accepted by the company. If the NPV of the project is negative the project will be rejected by the company. Net Present Value is the difference between the present values of the inflow and outflow. Following is the formula to calculate the NPV: Here, Following is the CAPM equation: Here, Calculate the expected rate of return on the stock/discount rate as follows: Calculate the NPV of the project using the formula of the NPV: NPV will be zero at IRR (Internal Rate of Return). Hence, the beta which makes the expected rate of return equals to IRR is the highest possible beta before the NPV becomes negative Hence, it is required to find the IRR Follow the below steps to find the IRR: Step 2: Enter the IRR formula in cell B13 with given cash flows as follows Therefore, the IRR of the project is 35.7333% Calculate the highest possible beta before the NPV becomes negative: Question 10: If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently. Capital asset pricing model: It is a model that defines the relation between the risk of the security measured in terms of beta and the required rate of return. It is a situation where the portfolio has a return of 20% and beta (risk) of 1.4, whereas the other portfolio that has a return of 25% with beta of only 1.2 is not possible, because if the CAPM holds valid, then this situation will not exist as according to this model the portfolio with high risk or high beta will give higher returns. On the contrary, in this situation it is clearly visible that the portfolio with more beta is giving less returns in comparison to the other portfolio. Question 11: If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently. CAPM (capital asset pricing model) shows a relationship that exists between expected return and market risk of the stock. This model states that the expected rate of return is equivalent to risk premium plus risk free-rate. CAPM depicts the relationship between return on risky asset and risk associated with it. Rate of return on stock is directly proportional to rate of return of stock market using beta. There are two portfolios. The expected returns on portfolio A and portfolio B are 30% and 40% respectively. The standard deviations of portfolio A and portfolio B are 35% and 25% respectively. The risk associated with the security are systematic risk and non-systematic risk. Systematic risk is related to all the firms in the industry and cannot be diversified whereas non-systematic risk is specific to the firm and can be diversified. β (beta) is the measure of firm’s systematic risk. The investors are compensated for the risk which cannot be diversified, i.e., β. It (beta) represents the change in the return of assets due to the change in the market return. The contributors of market risk are macroeconomic factors like, interest rate, inflation rate, recession etc. The standard deviation of stock is the measure of volatility in return for a span of time. It only represents the non-systematic risk. Also, the CAPM does not consider it in calculation of required return of a stock. Thus, the rate of return on A can be paired with the higher standard deviation up until the beta of B (for the given situation) is higher than the beta of A. Therefore, the given situation is. Question 12: If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently. Capital asset pricing model (CAPM): It is a model that defines the relation between the risk of the security measured in terms of beta and the required rate of return. If the CAPM is valid, then this situation will not exist as the reward to variability ratio of market is not better than portfolio A, which is impossible according to the CAPM, because prediction of the CAPM is that the market is the most efficient portfolio. The variability of portfolio A and market portfolio with the risk free portfolio is observed. It can be seen that for portfolio A is The Market portfolio is: This proves that portfolio A will not provide a better risk trade-off than the market portfolio.