# 1 Risk, Return, and Capital Budgeting Chapter 12.

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1 Risk, Return, and Capital Budgeting Chapter 12

2 In evaluating projects, all future cash flows are discounted using a discount rate called cost of capital When the cash flow is risk-less, we use the risk-less discount rate When the cash flow is risky, we have to use the discount rate that takes into account of risk. The appropriate discount rate can be computed from the CAPM Model and the Constant Growth Dividend Model. We will first calculate the cost of capital based on two assumptions: (1) The firm is all equity financed. (2) Risk of the project = risk of the whole firm. We will relax the assumptions later on.

3 The Cost of Equity Based on the previous two assumptions, the cost of capital is the cost of equity. Equity Beta:  S =  Sm /  m 2 The Cost of Equity (CAPM): E(r s ) = r f +  s [E(r m ) – r f ] Example: The following are BCE stocks and TSX300 index returns for the 1994-1997 period: Year BCETSX300 1994 4.00%-0.18% 199530.0014.53 199642.0028.35 199734.0014.98

4 Step 1: Calculating the Equity Beta 1)Calculating average returns: 2)Calculating the covariance: 3)Calculating the market variance: 4)Calculating beta of BCE:

5 Cost of Equity (CAPM): Given the current T-bill rate is 5.09% and expected market return is 14.42%. Expected market risk premium = 9.33%. Based on the CAPM, the cost of BCE’s equity is given by: E(r s ) = r f +  BCE [E(r m ) - r f ] Step 2: Calculating the Cost of Equity

6 An alternative Method for Calculating the Cost of Equity In the Chapter 5, we reviewed the constant dividend growth model. Where r s is the required rate of return of shareholders or the firm’s cost of equity. g is the growth rate of dividends. The above model can be refomulated as

7 Example: The stock price of BCE Inc. is \$19.70 per share today. The dividend is paid annually. The next dividend is \$2.50 one year from now. The expected dividend growth rate is 5% per year indefinitely. Calculate the cost of equity for BCE.

8 Suppose that BCE is an all equity firm. The following are the expected cash flows for a new project. Year CFs (’000) 0(40,000) 1 5,000 IRR = 13.41% 2 17,000 3 15,000Calculate NPV and take decision 4 20,000 Assume: The BCE Inc. is an all equity firm The new project’s beta is the same as BCE’s beta (1.35) Decision: =>. Or: Since by the CAPM (SML) the required return for beta of 1.35 is _____, and IRR=13.41 => reject or accept (which one) the new project The Investment Decision

9 The SML and the Investment Decision Expected Return (%) Beta 17.69 5.09 1.35 IRR = 13.41 Whole firm New Project SML

10 Determinants of Beta Factors affecting Equity Beta: Business Risk 1)Cyclicity of Revenues: Typically there are years of good return followed by poor returns. 2)Operating Leverage: The use of fixed costs in operations may result in magnification of operating incomes and losses with changes in sales. Operating leverage increases as fixed costs rise and as variable costs decline. Financial Risk 3)Financial Leverage The use of fixed costs in financing (e.g. Once the firm accumulated debt, the firm must make interest payments regardless of the firm’s sale)

11 Asset Beta and Equity Beta The asset beta is the beta of the assets of the firm. 1)When the firm is financed with equity only 2)When the firm is financed with debt and equity Typically:

12 The Cost of Capital When debt is used Assume: Cost of debt = r B Cost of equity = r S In principal, the cost of capital is the weighted average of r B and r S. Since the interest payment is a tax deductible expense, the actual after tax interest cost to the firm is r B (1-T c ) The Weighted Average Cost of Capital(WACC):

13 Example: BCE has a debt/equity ratio of 0.4. Assume  s = 0.8; the T- bill rate =4.4%; the market risk premium = 12%; pre-tax borrowing rate = 10%; the corporate tax rate is 37%. Calculate the WACC for BCE.

14 When the Firm’s beta Differs from the Project’s Beta The project and the firm may have different betas When the project and the firm are not from the same line of business Use industry beta (not always available) When the project’s risk is inherently different (even if same industry) Estimate the individual project’s beta If the project’s risk is higher than the firm’s risk, the project beta should be used. The higher beta higher r s higher r wacc lower project NPV If the project’s risk is lower than the firm’s risk, the project beta should be used Otherwise 2 errors may occur: Accept too many high-risk projects Reject too many low-risk projects