Hanoi April Capital budgeting decisions with the Net Present Value rule 2. Cost of capital Professor André Farber Solvay Business School University of Brussels, Belgium

Hanoi April Risk-Free Projects Use risk-free interest rate Discount rate might vary with maturity (term structure) Example : Current bond prices Maturity Spot interest rate 5% 6% 7%

Hanoi April Risk-free project (cont.) Consider now the following project: Time t0123 Cash flow Discount rate 5% 6% 7% PV NPV =

Hanoi April Risky Project Discount rate = cost of capital Consider all equity firm (more on debt later) Cost of capital = opportunity cost = expected return that an investor forecasts from financial investment with same risk as project Expected return =

Hanoi April How to set the discount rate for a risky project ? Each company, each project has a specific discount rate. Usually expressed as: r = Risk-free interest + Risk premium Risk premium = Risk premium on the market portfolio  Systematic risk

Hanoi April Risk premium on the market portfolio Suppose you invest in a well diversified portfolio of stock. What return could you expect? Lessons from the past (US ) Arithmetic Standard mean deviation Common Stocks 13.0% 20.3% LT Gov. Bonds 5.6% 9.2% US TBills 3.8% 3.2% Inflation 3.2% 4.5% Historical risk premium (relative to TBills) = 9.2%

Hanoi April Lessons from the past Average return on stocks > Average return on TBills $1 invested in : Value in 1997 Stocks $1,823 TBills § 14 But stocks much more risky: Max annual return = 52% (1954) Min annual return = -43% (1931) Investors require compensation for the risk that that take. Risk premium function of: –risk aversion –market volatility

Hanoi April The World Price of Market Risk US historical risk premium probably overstates the current risk premium. A highly topical question. Probably varies over time (volatility ). Also affected by globalization (diversification). Suggested value: 4% to 6%

Hanoi April Risk premium for individual projects Risk calculation for individual projects should take into account diversification. An example: You hold the following portfolio: Boom Recession Return +20% -10% You are offered the following project: Boom Recession Return -10% + 40% Is this a risky project? Would you require a risk premium to invest in the project.

Hanoi April Diversification illustrated Suppose you invested 50% of you money in this project. Boom Recession Return +5% 5% (0.5   (-10)) (0.5  (-10)  (40)) By investing in this project, your portfolio become riskless. The project has negative risk. You should accept a very low expected return.

Hanoi April Systematic risk The only risk that require a risk premium is systematic risk. Systematic risk is the risk that can not be diversified away. Systematic risk is measured by the sensitivity of stock return relative to the market portfolio. r =  +  r Market + e Market Stock 

Hanoi April Systematic risk - some examples Yaho3.57 Amazon.com2.88 Microsoft1.45 General Electric1.22 General Motor1.01 Royal Dutch0.93 Homestake Mining0.74 Consolidated Edison0.28 GoldFiels So.Af.0.20

Hanoi April Inside Beta Determinants of systematic risk: –1. Relative volatility Standard deviation of stock / Standard deviation of market –2. Correlation with market portfolio

Hanoi April Capital Asset Pricing Model Risk - expected return relationship Example: Risk-free rate = 6%, risk premium on mkt port. = 5% Amazon : r = 6% + 5% x 2.88 = 20.4% Goldfield So.Af. : r = 6% + 5% x 0.20 = 7%

Hanoi April Security Market Line Beta r 1 Risk-free rate Risk premium on market portfolio