Chapter 7 – Introduction to Risk, Return and the Opportunity Cost of CapitalComputing the opportunity cost of capital for risky cash flows of a projectStatistical and other tools used in the calculation of the beta of a project’s risky cash flowsAs discussed earlier, competition in the financial markets (plus market perfection and efficiency) causes:The cost of the financial asset (reflected in the initial investment) to equal the present value of the future expected cash flows (NPV = $0)However, this should also happen for any asset that trades in an active and competitive market place (land, fine art, coins)Chapter 7 and 8 Practice Problems - Plenty of practice problems are given in the notes. Here are a couple more practice problems.Chapter 7 – Introduction to Risk, Return and the Opportunity Cost of CapitalChapter 8 – Risk and Return (section 8-2 and 8-3, skim)These chapters describe how risk is measured and is part of a three-chapter sequence describing how the risk of a project’s cash flows determines the discount rate (the opportunity cost of capital) for these cash flows. We then use the discount rate to calculate the present value of the project’s future expected cash flows. Subtracting the initial investment gives us the project NPV.You will notice a slight difference in notation between these notes and the text. Please take this into account in your studying.************************************************************Through most of our discussion of Chapter 6, we assumed that the future cash flows of a project are known with certainty. However, in most circumstances future cash flows are uncertain. When a corporation’s future cash flows are uncertain:- Step one - Calculate expected future cash flows.Calculation of project cash flows (under certainty) was discussed in Chapter 6. This involved determining project revenues, expenses, tax depreciation, corporate income taxes, working capital adjustments, inflation, etc.To calculate expected cash flows for risky projects, the types of calculations done in Chapter 6 may have to be performed many times resulting in something like this:Project A’s time one cash flow in a booming economy = $155Project A’s time one cash flow in a normal economy = $135Project A’s time one cash flow in a recession economy = $40To calculate expected cash flows, you need to determine the probabilities:Probability of a booming economy = 20%Probability of a normal economy = 60%Probability of a recession economy = 20%What is the expected project cash flow for time one in the above example?If the initial investment is $100, what is the IRR for this project?In the above example, I have assumed that project cash flows depend only on the type of economy. This is obviously a simplification. Several other factors can affect project cash flows, each with their own cash flows and probabilities. For example, consider consumer demand:Project A’s time one cash flow in a booming economy and high consumer demand = $200 (10% prob.)Project A’s time one cash flow in a booming economy and low consumer demand = $110 (10% prob.)Project A’s time one cash flow in a normal economy and high consumer demand = $165 (30% prob.)Project A’s time one cash flow in a normal economy and low consumer demand = $105 (30% prob.)Project A’s time one cash flow in a recession economy and high consumer demand = $60 (10% prob.)Project A’s time one cash flow in a recession economy and low consumer demand = $20 (10% prob.)- Step two - Discount expected cash flows at the opportunity cost of capital to determine their present value.The opportunity cost of capital is based on the cash flow’s risk (higher risk, higher opportunity cost of capital)Notice that the above example gives project cash flows and probabilities. We use these to calculate expected project cash flows (and the present value of these cash flows).1Sometimes you might want to calculate present values of individual parts of the project. For example:Economy Probability Project Product 1 Product 2Boom 0.20 $155 $115 $40Normal 0.60 $135 $95 $40Recession 0.20 $40 $0 $40Expected $120 $80 $40PV of cash flows from product 1 + PV of cash flows from product 2 = PV of project cash flowsSeparate present value calculations (of the two parts) will give you the same answer as you would get by calculating the PV of the project cash flows.However, separate calculations may allow you to focus on the risks of the different parts of the project.How could you use this concept in the above example?The opportunity cost of capital for cash flows is the expected return for financial assets with the exact same amount of risk as these cash flows.- Risk-free cash flows should use a discount rate equal to the expected return for risk-free securities (e.g., the one-month Treasury-Bill interest rate). We are using 5% as the risk-free rate in this class.- Higher risk cash flows should be discounted at a higher discount rate to reflect their higher level of risk. For example, consider a project with cash flows that are just as risky as large U.S. firm common stocks.Examine Table 7.1 (page 149 of the textbook). Then describe how the opportunity cost of capital would be determined for the risky cash flows of this particular project.Relevant Table 7.1 informationAverage annual return for the large U.S. firm common stocks (1900 – 2003) = 11.7%Average annual return for Treasury Bills (1900 – 2003) = 4.1%Source: Yahoo FinanceS&P 500 for 2004: 10.7% Treasury Bills for 2004: 1.5% (approximate)S&P 500 for 2005: 3.0% Treasury Bills for 2005: 3.0% (approximate)S&P 500 for 2006: 15.2% Treasury Bills for 2006: 5.0% (approximate)(Note: For purposes of class discussion, ignore what has happened so far in 2007, i.e., assume we are at the beginning of the year.)Updated (approximate) averages including information from 2004 - 2006Average annual return for large U.S. firm common stocks (1900 – 2006) = 11.6%Average annual return for Treasury Bills (1900 – 2006) = 4.1%Average difference (1900 – 2006) = 7.5%- Arithmetic versus geometric averagesAssume you buy a stock for $100 (at t = 0). The stock falls 50% in year 1, but increases 50% in year 2. What isyour stock selling for at t = 2?What do you need to earn in the second year to get you back to $100?We should use arithmetic averages for estimating risk premiums (discussed below)We should use geometric averages for computing growth in investment2- Example