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# capm & cost of capital

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• 1. CAPM and Cost of Capital• A firm’s cost of capital for a project is the expected return that its investors could earn on other investments with the same risk.• Systematic risk determines expected returns, thus for an investment project, “the same risk” = “the same systematic risk”, “the same beta”.
• 2. The cost of capital for investing in aproject is:Ke = Rf + β (Km – Rf)Ke = Cost of equity CapitalRf = Rate of return required on a risk free asset/security investmentKm= Required rate of return on the market portfolio at assets.β = The Beta co-efficient
• 3. • The H Limited wishes to calculate its cost of equity capital using the CAPM approach. It found that risk-free rate of return equals 10%; beta co-efficient 1.5 and the return on the market portfolio equals 12.5%. Calculate the Cost of Equity CapitalKe = 10% + (1.5 x(12.5% - 10%);Ke = 13.75%.
• 4. • The beta co-efficient of a company is 1.6, required rate of return on risk-free security 8%, required rate of return on market portfolio of investment is 13%. Calculate the cost of equity capital by using CAPM.Ke = 8% + 1.6(13%-8%)Ke = 16%.
• 5. • Suppose that in the coming year, you expect Microsoft stock to have a volatility of 23% and a beta of 1.28, and McDonalds stock to have a volatility of 37% and a beta of 0.99.• 1.Which stock carries more total risk? Which has more systematic risk?• If the risk-free interest rate is 4% and the markets expected return is 10%,• Estimate the cost of capital for a project with the same beta as McDonalds stock and a project with the same beta as Microsoft stock. Which project has a higher cost of capital?
• 6. • Total risk is measured by volatility; therefore, McDonalds stock has more total risk. Systematic risk is measured by beta. Microsoft has a higher beta, so it has more systematic risk.• Given the estimated beta for Microsoft of 1.28, Microsofts risk premium will be 1.28 times the risk premium of the market, and the cost of capital for investing in a project with the same risk as Microsoft stock is• E[RMSFT] = rf + 1.28 * 6% = 11.7%• McDonalds stock has a lower beta of 0.99. The cost of capital for investing in a project with the same risk as McDonalds stock is• E[RMcD] = rf + 0.99 * 6% = 9.9%• Because systematic risk cannot be diversified, it is the systematic risk that determines the cost of capital; thus, Microsoft has a higher cost of capital than McDonalds, even though it is less volatile.
• 7. To conclude• Investor differ in their willingness to accept risk for a greater return.• By using CAP Model, and comparing beta of a stock, its historical return, and its market return, one can determine whether the return of stock is worth its risk.
• 8. Criticisms of the CAPM– CAPM is a single-period model.– CAPM ignores transaction costs.– Although betas can be based on a very large number of observations over time.– Even within one year, there can be significant variations from the mean in respect of market returns and even in risk-free returns.– CAPM depends on an efficient investment market, so that if such a market has imperfections it is more difficult for investors to eliminate specific risk from their portfolios.– The assumption that well-diversified portfolios are subject only to systematic risk can also be questioned.