2001 YearbookCORPORATE FINANCE:AN INTRODUCTORY COURSEDISCUSSION NOTESMODULE #101RISK AND RETURNI. Review of Financial Management Concepts:- An investment should be accepted if, and only if, it earns at least the as much as comparablealternatives (i.e., with the same risk) available in the capital markets.- The required rate of return for projects or securities is determined in the capital markets.Assets with the same risk should earn the same expected return, r.- NPV = PV inflows - PV outflows when discounted at the required rate of return, r. Acceptpositive NPV projects; reject negative NPV projects. This acceptance/rejection rule, theNPV Rule, implies that (when everything works nicely) the asset being valued is accepted(rejected) if the estimated return, IRR, on the assets exceeds (is less than) the marketrequired return.Until this point we have finessed the topic of risk, specifically the risk of the cash flows of aproject. The discount rate used was either given or taken to be the risk-free rate, rf. If theproject's cash flows are certain, i.e., will occur with probability = 1 (100%), the risk-free rate is infact appropriate.In the November 5, 2001, Wall Street Journal (WSJ) we find that the T-Bill rate, our proxy for therisk-free rate, was 1.97%. Consider a project that costs $1,000 at t = 0 and returns $1,050 at t =1. If this project is “riskfree,” would you accept it? NPV = $1,050/(1.0197) - $1,000 = $29.71. Yes, take the project. Taking the project willincrease wealth by $29.71. Alternatively, if we invested the $1,000 in the capital market at1.97%, we would have only $1,019.70 at t = 1, versus the $1,050 generated by theproject. Conceptually, it’s very simple. The capital market is the benchmark, do better ordon’t do it.1 This lecture module is designed to complement Chapter 10 in B&D.1II. But What About Risk? (The question of the hour.)What if the above project does not pay off $1,050 at t = 1 with certainty? What if the project isriskier than a T-Bill? For instance, maybe the payoffs at t=1 could be as low as $1,000 or as highas $1,200, i.e. was risky. Would you require a return greater than rf? A "yes" answer means youare a typical risk-averse investor, i.e., you dislike risk and must be compensated (in the form of ahigher expected return) for exposing your wealth to it (bearing risk). Do we observe risk-averse behavior by individuals and institutions? Yes! People buy insurance,even if they are not required by law to be insured. Individuals and institutions invest in portfoliosof securities; they do not invest in a single security, or “put all of their eggs in one basket." Ifpeople were not risk-averse, they would not voluntarily buy insurance, nor would they diversifytheir investments. In short, we observe many phenomena that lead us to believe individual andinstitutional investors are risk-averse. Risk-averse investors require higher expected returns tocompensate them for higher risk. The assumption of risk-averse investors is critical to the development of our risk versus returnrelationship. With this assumption, we can draw an upward-sloping relation between expectedreturn, E(r), and Risk, where the vertical intercept (zero risk), rf, is the risk-free rate of return:E(r) rfRiskWhat if our proposed investment is risky and requires a 5.0% return, versus 1.97% forrisk-free investments?NPV = $1,050/(1.05)1 - $1,000 = $0. Therefore, we are indifferent to this project. Why?This return can easily be duplicated in the capital markets. However, what if the project is very risky and requires a return of 15.0%?NPV = $1,050/(1.15)1 - $1,000 = -$87. Reject the project! It earns less than the required rate of return of 15%. (Rate of return criterion: 5% < 15% so reject.)2Observe that the relationship between E(r) and NPV is an inverse one. The higher the E(r), or therisk-adjusted required rate of return for a given project, the lower the NPV. In our example, we observed that: E(r) NPV1.97% $29.71 5.0% $ 015.0% -$87Raising the discount rate, E(r), is a way to "penalize" a project that has more risk. In otherwords, you require more return for more risk. The required return for a risky project can beexpressed asE(r) = rf + risk premium, or E(r) = rf + θ, where θ is the symbol for the risk premium.The simple notion (which we will soon complicate) is that if you are to invest in a risky asset youdemand an expected return at least equal to what you could get holding a risk free asset plus somecompensation for bearing the risk, -.A primary goal in the forthcoming material is to give you the intuition and analytic tools toestimate this risk premium, θ. We need to understand how E(r) and θ are related. We requiremeasures of expected return in order to evaluate capital budgeting projects, to understand howsecurities are priced in the capital markets, to design firms' capital structures, etc.III. Returns, Returns, and More Returns:A) Realized Returns:In turn, we will discuss: - $ Returns, - % Returns, - % Holding Period Returns, - Compound Annual Returns, and - Arithmetic or Average Returns.3Assume that an investor bought 100 shares of a $10 (ex-dividend price) stock at the end of 1996.The investor has maintained this position and reinvested all dividend payments to acquireadditional shares of the stock. The following information is relevant to this investment.End ofEnd ofPeriodEnd ofPeriod# SharesWithInvestmentPeriodStock PriceDividend/SharertFullReinvestmentLevel, ILtILt/ILt-11996 $10.00 - -100.0000 $1,000.00 -1997 $11.25 $0.50 17.50%* 104.4444**$1,175.0041.1750***1998 $13.00 $0.75 22.22% 110.4701$1,436.111.22221999 $10.50 $0.50-15.38% 115.7305$1,215.170.84622000 $6.00**** $0.40**** 21.90% 246.8917$1,481.351.2190 * rt = (Pt - Pt-1 + Divt)/Pt-1 = Capital Gain Return + Dividend Return = Total Return, or($11.25 - $10.00 + $0.50)/$10.00 = 0.1750 for 1997** ($0.50)(100 Shares) = $50 received at the end of 1994 in dividends; $50/$11.25 = 4.4444 additional shares are purchased with thedividends. Therefore, the total new position is 100 shares (original position) + 4.4444 new shares, or 104.4444 shares.*** Notice that this ratio of investment levels = (1 + rt)**** 2:1 Stock Split during 2000. Therefore, the position size in shares doubles while the share price at