1. 1 Ch 7: Project Analysis Under Risk Incorporating Risk Into Project Analysis Through Adjustments To The Discount Rate, and By The Certainty Equivalent Factor.

2. 2 Introduction  Cash flows cannot be forecast with absolute accuracy.  In the previous chapter, one single series – the best estimate of the project’s future cash flows – was used to compute the net present value. This series may be viewed as the best estimate of a range of possible outcomes.  There is a risk or uncertainty associated with this cash flow. All the forecasted cash flows have a risk or uncertainty attached to them.

3. 3 Introduction: What is Risk?  Risk is a complex and multi-faceted problem. There are several measures to asses risk and one strong single measure has not been developed.  Investment analysts often look at more than one risk measure in the process of incorporating risk into their project evaluation.

4. 4 Introduction: What is Risk?  Risk is the variation of future expectations around an expected value.  Risk is measured as the range of variation around an expected value.  Risk and uncertainty are interchangeable words to cover situations in which the outcomes are not known with certainty.

5. 5 Handling Risk  Measuring the risk associated with the expected cash flows of the project and incorporating this risk into the determination of the net present value (NPV) is essential for any real world project evaluation.  There are various ways in which risk can be incorporated into the NPV computation and capital budgeting decision support.  These include : The risk-adjusted discount rate, The certainty equivalent, Sensitivity and break-even analysis Simulation.

6. 6 Introduction  This chapter relaxes the certainty assumption and incorporates risk into project analysis. Risk and uncertainty are briefly discussed and two approaches to incorporating risk into project analysis:- The risk-adjusted discount rate and the certainty equivalent

7. 7 Where Does Risk Occur?  In project analysis, risk is the variation in predicted future cash flows.

8. 8 Using a Risky Discount Rate  RADR method is most frequently employed by practitioners.  A discount rate (k ) higher than the risk-free rate is used to allow for the project’s risk. k =r + u + a

9. 9 Using a Risky Discount Rate  The structure of the cash flow discounting mechanism for risk is:-  The $ amount used for a ‘risky cash flow’ is the expected dollar value for that time period.  A ‘risky rate’ is a discount rate calculated to include a risk premium. This rate is known as the RADR, the Risk Adjusted Discount Rate.

10. 10 Defining a Risky Discount Rate  Conceptually, a risky discount rate, k, has three components:- 1. A risk-free rate (r), to account for the time value of money 2. An average risk premium (u), to account for the firm’s business risk 3. An additional risk factor (a), with a positive, zero, or negative value, to account for the risk differential between the project’s risk and the firms’ business risk.

11. 11 Defining a Risky Discount Rate 1.A risk-free rate (r), to account for the time value of money.  The risk-free rate may be arrived at by considering government bond yields or insured banks’ term deposit rates. The yield of those government bonds which have terms to maturity similar to the project life of the capital investment should be selected.

12. 12 Calculating a Risky Discount Rate A risky discount rate is conceptually defined as: k = r + u + a Unfortunately, k, is not easy to estimate. Two approaches to this problem are: 1. Use the firm’s overall Weighted Average Cost of Capital, after tax, as r + u and then a is added. The WACC is the overall rate of return required to satisfy all suppliers of capital. 2. A rate estimating (u) is obtained from the Capital Asset Pricing Model CAPM, and then a & r is added.

13. 13 Calculating the WACC Assume a firm has a capital structure of: 50% common stock, 10% preferred stock, 40% long term debt. Rates of return required by the holders of each are : common, 10%; preferred, 8%; pre-tax debt, 7%. The firm’s income tax rate is 30%. WACC = (0.5 x 0.10) + (0.10 x 0.08) + (0.40 x (0.07x (1-0.30))) = 7.76% pa, after tax.