Investment Appraisal and Risk

Lecture Outline

• Company and Project Costs of Capital

• Measuring the Cost of Equity

• Analysing Project Risk

• Certainty Equivalents

• Discount Rates for International Projects

Present Value

• Formula:

  ​Present Value =\frac{FV}{(1 + r)^n} )

  where:

  FV=Future Value

  r=Rate of return

  n=Number of periods​
  

• Example: Cash flows for an investment where cash flows are €50, €80, €100, €120 over five years and a discount rate of 8%.

• Calculation of Present Value: PV = \frac{50}{(1+0.08)} + \frac{80}{(1+0.08)^2} + \frac{100}{(1+0.08)^3} + \frac{120}{(1+0.08)^4}

  • Result: Present value approximately €199.64.

Net Present Value (NPV)

• NPV Rule: Invest in projects where NPV > 0.

• Formula:
  NPV = PV - investment

• Example: If the PV is €199.64 and the initial investment is €100,
  NPV = 199.64 - 100 = 99.64 > 0

• Conclusion: Project is worth investing in.

Discount Rate

• Definition: The rate used to discount future cash flows to present values.

• Factors: Depends on risks associated with the cash flows and reflects the investors' expected return, also known as the cost of capital.

• Opportunity Cost: Chance of earning a return on alternative investments with similar risks.

Capital Asset Pricing Model (CAPM)

• Purpose: Establishes relationship between risk and expected return.

• Key Assumption: Only non-diversifiable risks impact expected returns.

  • Assumptions include:

  • Investors are risk-averse.

  • All participants share the same information and opportunities.

  • No transaction costs and all assets can be divided infinitely.

• Formula for Expected Return:
  E(rx) = rf + \betax (E(r{market}) - r_f)

Company Cost of Capital

• Definition: The average return required by all of a company's investors (both equity and debt).

• Components:

  • Market value of debt (D)

  • Market value of equity (E)

• Formula:
  COC = \frac{D}{V} \cdot r{debt} + \frac{E}{V} \cdot r{equity}
  where (V = D + E)

• WACC (Weighted Average Cost of Capital): WACC = \left(1 - T\right)\frac{D}{V}r{debt} + \frac{E}{V}r{equity}

  • Example Calculation: If the WACC is calculated with a tax rate of 21%, the resulting WACC could be 12.3%.

Measuring the Cost of Equity

• Formula Expansion of CAPM:
  r{equity} = rf + \beta (rm - rf)
  where - (rf) is the risk-free rate, (rm) is the market return, and (\beta) measures the sensitivity of the asset in comparison to the market.

• Beta Values: Measurement of risk relative to the market.

Analysing Project Risk

• Importance of Assessing Risk:

  • Scenarios: Projects may have uncertain outcomes.

• Example of Project Z: Predicted cash flow of $1 million with uncertainty possibly leading to zero cash flow.

Certainty Equivalents

• Definition: Represents guaranteed values of cash flows adjusted for risk.

• Risk-Free Discount Rate: Used when calculating certainty equivalents, reflecting no risk premium.

International Project Risks

• Risks include: Variability in market conditions across countries.

• Metrics to Consider: Standard deviations, correlation coefficients, betas of individual countries compared to a benchmark (e.g., S&P).

Practical Applications with Calculation Examples

• Estimating Required Returns: Based on market values of equity and debt, taking into account risk (beta) and market returns.

• Example Company Analysis: Current market scenarios highlighting risk calculations and required return transformation.

Review Questions

• Example calculation for the Okefenokee Real Estate Company:

  • Required return on stock based on beta and risk premium.

  • Estimate total company cost of capital.

• Consider variations like diversifying into different ventures and their corresponding risk metrics and required rates of return.