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Present Value and the Opportunity Cost of Capital Fundamental Question: How are asset prices determined? • Companies invest in a variety of real assets. • Objective is to find real assets which are worth more than they cost. • Essence of the capital budgeting process. • Asset valuation's relationship to a well-functioning capital market: If there is a good market for an asset, its value is exactly the same as its market price. Present Value Example (B&M): Suppose your house burns down leaving you with a lot worth $50,000 and a check for $200,000. Option 1: Rebuild Option 2: Build an office building; cost is $350,000; you predict you can sell for $400,000 in one year. • Rule: You should go ahead if the present value of the expected $400,000 payoff is greater than the investment of $350,000. Question: What's the value today of $400,000 one year from now? PV = Discount Factor x C1 where, Discount Factor = 1/1+r , where r is the reward investors demand for accepting delayed payment. Assume that the $400,000 payoff one year from now is a sure thing. EB545 – Corporate Finance 54 Now, how else could you make $400,000 one year from now? • Invest in government securities (assume 7% ROR) • How much must you invest? $400,000/1.07 = $$373,382 • Now assume you've committed land and begun construction - now you decide to sell. How much would you sell it for? • Since it produces $400,000, well-informed investors would be willing to pay $373,832. • NOTE: This is the only feasible price that satisfies buyer and seller. Present Value is also the market price. TO CALCULATE PRESENT VALUE, WE DISCOUNT EXPECTED FUTURE PAYOFFS BY THE RATE OF RETURN OFFERED BY COMPARABLE INVESTMENT ALTERNATIVES. RATE OF RETURN (ROR) IS OFTEN REFERRED TO AS THE "DISCOUNT RATE", "HURDLE RATE" OR "OPPORTUNITY COST OF CAPITAL". Net Present Value EB545 – Corporate Finance 55 Found by subtracting required investment from present value of cash flows. NPV = C0 + C1/(1+r) Net Present Value Rule: Accept investments that have a positive NPV. Rate of Return Rule: Accept investments that offer rates of return in excess of their opportunity cost of capital. NOTE: The NPV rule and the IRR rule can conflict when we have multiple period cash flows. Present Value Techniques • Valuation of Cash Flows (components) EB545 – Corporate Finance 56 1. Magnitude 2. Timing • Timeline Example: We wish to calculate the PV of the cash flow stream, $100 received in one year and $200 received in two years, where r = 10% $100 $200 -------|------------------|-------------------|-------------------- t =0 t=1 t=2 PV = $100/(1+.10) + $200/(1+.10)2 = $256 • Discount Factors (Appendix Table 1 in B&M) - Very useful when the same discount or interest rate is applied over the life of the project. Example: EB545 – Corporate Finance 57 Discount Cash Present Period Factor Flow Value ---------- ------------ ------------ ----------- 0 1.0 -$150,000 -$150,000 1 1/1.07 = .935 -$100,000 -$ 93,500 2 1/(1.07)2 = .873 +300,000 +261,900 -------------- Total NPV = + $18,400 Intuition Behind Present Value • Think about the problem in terms of future value. EB545 – Corporate Finance 58 • If you have $100 and put it in the bank for one year at 6%, how much do you have after one year? • So, $100 received now is equivalent to $106 received in one3 year. • Thus, to translate money from its value at t=0 to its value at t=1, we multiply by (1+r) • Correspondingly, to translate value from t=1 to t=0, we divide by (1+r). • This notion is easily extended to multiple time periods. • Provides a powerful means to value long-lived assets. Oil and gas reserves Value of a mine EB545 – Corporate Finance 59 Perpetuities and Annuities Perpetuities • Securities issued by the British government • No obligation to repay • Offer fixed income for each year to perpetuity. • Rate of return is equal to promised annual payment divided by PV - Return = Cash flow/PV • Rearrange, and find the PV, given discount rate and annual cash payment EXAMPLE: Suppose you have $1000 in bank drawing 5%; how much can you withdraw at year end and still have same amount in bank as at the beginning of the year? This process can continue forever or in "perpetuity". EXAMPLE: Endowed chair at CSM; r = 10% and annual cash payment for chair is $100,000. PV of perpetuity = C/r = $100,000/0.10 = $1,000,000 EB545 – Corporate Finance 60 Growing Perpetuity - Allows for growth in annual cash payment. PV = C1/(1+r) + C1(1+g)/(1+r)2 + C2(1+g)2/(1+r)3 + . . . Simple formula for this is the sum of a geometric series: PV of growing perpetuity = C1/(r-g) EXAMPLE: Endowed chair where g = 0.04. PV = C/(r-g) = $100,000/(0.10-0.04) = $1,666,666 EB545 – Corporate Finance 61 Annuities • An asset that pays a fixed sum each year for a specific number of years, i.e. house mortgage. • An annuity that makes payments in each of years 1 to t is equal to the difference between two perpetuities. PV of Annuity (for year 1 to year t): C/r - [(C/r)(1/(1+r)t)] or C[(1/r) - (1/(r(1+r)t)] NOTE: Expression in brackets is the annuity discount factor, which is the PV at discount rate, r, for an annuity of $1 paid at the end of each of t periods. EXAMPLE: Endowed chair - cost to endow chair for 20 years at $100,000 per year? PV = $100,000[(1/.10) - (1/(.10(1.10)20)] = $100,000 x 8.514 = $851,400 EB545 – Corporate Finance 62 Compund vs. Simple Interest • Compund Interest - each interest payment is reinvested to earn more interest in subsequent payments. • Simple Interest - no opportunity to earn interest on interest. NOTE: Discounting is a process of compound interest. EXAMPLE: What is the PV of $100 to be received 10 years from now, if the opportunity cost of capital is 10%? PV = 100/(1.10)10 = $38.55 • Simple interest and continuously compounded interest are rarely used in the business world. For virtuallly every application, compound interest is the accepted technique. Rule of 70: Number of years that it takes for an investment to double in value at an annually compounded interest rate of r, is approximately 70/r. So, if interest rate is 10%, then 7 years is the amount of time. EB545 – Corporate Finance 63 Valuing Stocks and Bonds Key Issues • Focus on cash flows (magnitude and timing) • Caclculate the PV of those cash flows Bonds • Fixed set of cash payoffs - usually semi-annual. • Interest payments and face value at maturity. • Treasury bonds, municipal bonds, corporate bonds, foreign bonds, mortgage bonds EXAMPLE: Suppose in August of 1989, you invest in a 125/8% 1994 U.S. Treasury bond. Coupon rate = 125/8% Face Value = $1000 Each year you receive .1265 * 1000 = $126.50 In August, 1994 you receive $1126.25 CASH FLOWS EB545 – Corporate Finance 64 1990 1991 1992 1993 1994 $126.25 $126.25 $126.25 $126.25 $1126.25 WHAT IS THE 1989 MARKET VALUE OF THIS STREAM?Compare return to similar securities.Medium term Treasury bonds at that time offered ROR of 7.6% NOTE: 7.6% ROR is what investors gave up to invest in bond. 5 Ct PV = ∑ t = $1202.77 t =1(1+ r ) NOTE: Bond price quotes are expressed in a percentage of face value; i.e. $1202.77 = 120.28 percent Consider the alternative view: If the price of the bond is $1202.77, what return do investors expect? 1202.77 = $126.25 + $126.25 + $126.25 + $126.25 + $1126.25 1+ r (1+ r )2 (1+ r )3 (1+ r )4 (1+ r )5 So, r = 7.6% • r is yield to maturity or internal rate of return NOTE: Bond yields are usually quoted as semi-annual compond rates. Valuation of Common Stock EB545 – Corporate Finance 65 • Cash payoffs to owners of common stock - cash dividends - capital gains or losses Suppose: PO = current price P1 = expected price Div1 = expected divdend Rate of return, r, that investors expect from a share over the next year is defined as the expected dividend per share, Div1, plus the expected price appreciation per share, P1 - P0, all divided by the beginning year price. Div1 + P1 − P0 ER = r = P0 • r is the market capitalization rate or expected return on a security. EB545 – Corporate Finance 66 EXAMPLE: Company X is selling for $100/share; investors expect a $5 dividend and the stock to sell for $110 one year from now. The expected return, r, then is: r = $5+ $110 − $100 = 0.15 $100 Correspondingly, given investors' forecasts of dividend and price and the expected return offered by other equally risky stocks, then today's price: Div1 + P1 Price = P0 = If r, the expected return on securities 1+ r in the same risk class as Firm X is 15 percent, then today's price should be: P0 = $5+ $110 = $100NOTE: All securities in an . 115 equivalent risk class are priced to offer the same return. No other price could survive in competitive capital markets. Multiple Period Valuation EB545 – Corporate Finance 67 Just as price at P0 is dependent on investors expectations about year 1's dividends and stock price appreciation, so also can we compute P1, based on expectations about year 2. Div2 + P2 P1 = 1+ r EXAMPLE: Suppose a year from now investors will be looking at dividends of $5.50 in year 2 and a subsequent price of $121. This would imply a price at the end of year 1 of: P1 = $5.50 + $121 = $110 . 115 Today's price then can be computed either as: Div1 + P1 $5.00 + $110 P0 = = = $100 1+ r . 115 or EB545 – Corporate Finance 68 Div1 Div2 + P2 $5.00 $5.50 + $121 P0 = + = + = $100We can 1+ r (1+ r )2 . 115 . (115) 2 extend this result to multiple periods in the following manner: H Divt PH P0 = ∑ + t = 1 (1+ r ) (1+ r ) H t where H is the final period and the summation is the discounted present value of the dividend stream from year 1 to H. NOTE: Stock valuation is nothing more than the sum of the present value of the expected cash flows from dividend streams during the period and the present value of the end- of-period stock price. In the case where H goes to infinity, we can ignore P because this value goes to 0. So, then we can think of P0 as the present value of a perpetual stream of cash dividends, where EB545 – Corporate Finance 69 ∞ Divt P0 = ∑ t = 1 (1 = r ) t Growth Rate and the Gordon Model Dividend growth Rate Incorporation of growing perpetuities Div1 P0 = r − g g = anticipated growth rate (must be < r) r = market capitalization rate NOTE: As g approaches r, stock price becomes infinite - r must be greater than g if growth is perpetual. Estimating Capitalization Rate Market capitalization rate, r, equals the dividend yield (Div1/P0) plus the expected rate of growth in dividends (g), where EB545 – Corporate Finance 70 Div1 r= +g P0 EXAMPLE (B&M): Sears, Roebuck & Company is selling for $42/share early in 1989; dividend payments for 1989 are expected to be $2.00 per share. Div1 $2.00 Dividend Yield = = = 0.048 P0 $42.00 What about g, the rate of growth in dividends? Methodology: EB545 – Corporate Finance 71 1. Observe Historical payout ratio, ratio of dividends to earnings per share. for Sears, historically been about 45%; 55% of earnings is reinvested: plowback ratio. 2. Sears' return on equity, ROE, or ratio of earnings per share to book equity per share is about 12%. EPS1 ROE = = 0.12 BookEquity / Share 3. Assume fairly stable ROE and payout ratios. 4. If we forecast 12% ROE and reinvest 55%, then book equity should increase by 0.55 x 0.12 = 0.066. (Since we assume that ROE and payout are constant, earnings and dividends per share will also increase by 6.6%). Therefore dividend growth rate is: g = plowback ratio x ROE = 0.55 x 0.12 = 0.066 So, utilizing the Gordon Model, we may now compute the market capitalization rate, r. EB545 – Corporate Finance 72 Div1 r= + g = 0.048 + 0.066 = 0.114 P0 or about 11.5% is the market capitalization rate. Methodological shortcomings of the Gordon Model: 1. Constant growth? 2. Constant Plowback? 3. Constant ROE? 4. Single stock analysis may be inappropriate - may need to look at a class of stocks, i.e. FERC sets market capitalization rates for utility industry. 5. Rule of thumb only. 6. Avoid use when firm is in a high growth period (Remember, g is a long-term growth rate.) Stock Price and Earnings per Share EB545 – Corporate Finance 73 • Growth Stock - those stocks purchased primarily for the expectation of capital gains; interested in future growth or earnings rather than next year's dividends. • Income Stock - purchased primarily for the cash dividends. Consider the case of a company that does not grow at all, i.e. no plowback of earnings - simply produces a constant stream of dividends. Special case where: Expected return = dividend yield = earnings-price ratio Div1 EPS1 Expected Return = = P0 P0 For example, if the dividend is $10/sher and stock price is $100, then market capitalization rate, r, is 0.10. Similarly, price equals: Div1 EPS1 $10. 00 P0 = = = = $100 r r 0.10 EB545 – Corporate Finance 74 NOTE: E(r) for growing firms can also equal the earnings-price ratio. Key is whether earnings are reinvested to provide a return greater or less than the market capitalization rate. EXAMPLE (B&M): Effect on stock price of investing an additional $10 in Year 1 at different rates of return. Project Costs are $10.00 - EPS1. NPV = -10 + C/r, where r = 0.10 Project's Impact Project Rate Incremental Project NPV on share Price Share Price of Return Cash Flow, C in Year 1 in Year 0 in Year 0, P0 EPS/P0 r ----------------- ------------------- ------------------ -------------------- ------------------ ------------- ----- 0.05 $0.50 -$5.00 -$4.55 $95.45 .105 .10 0.10 $1.00 0 0 $100.00 .10 .10 0.15 $1.50 +$5.00 +$4.55 $104.55 .096 .10 0.20 $2.00 +$10.00 +$9.09 $109.09 .092 .10 0.25 $2.50 +$15.00 +$13.64 $113.64 .088 .10 NOTE: The earnings-price ratio equals the market capitalization rate (r) only when the new project's NPV = 0. Managers frequently make poor financial decisions because they confuse earnings-price ratios with the market capitalization rate. EB545 – Corporate Finance 75 PVGO - Present Value of Growth Opportunities • Think of stock price as the capitalized value of avaerage earnings under a no-growth policy, plus PVGO, where EPS P0 = r 1 + PVGO Rearranging, we see the earnings-price ratio is equal to: EPS1 = r(1− PVGO ) P0 P0 • Earnings-price ratio will underestimate r if PVGO is positive and overestimate it if PVGO is negative. Valuation of PVGO • We can compute the PVGO using the simplified DCF formulation, replacing dividends with forecasted NPV1, where NPV PVGO = r − g1 EB545 – Corporate Finance 76 SUMMARY: • For "growth" stocks, PVGO is high and P/E ratio is high (or earnings-price ratio is low. • Growth stocks are those which PVGO is large relative to the capitalized value of earings per share - not because it's rate of growth is high. EXAMPLE: P0 = $30, EPS = $1.00, r = 0.10 1. Capitalized value of earnings equals $10 2. PVGO = $20. 3. PVGO is very large relative to the price of the stock. EB545 – Corporate Finance 77 Price-Earnings Ratio (or Multiple) • Market price divided by its current earnings per share. • Measures how much investors are willing to pay for a company with that level of earnings. • Importance: 1. changes in P/E ratio directly impacts stock prices. 2. current price is just the product of a stock's P/E ratio and EPS Current Price = P/E Ratio x EPS 3. P/E ratio translates earnings into value; as the P/E ratio expands or contracts, so does price. 4. P/E ratios tend to accelerate changes (in either direction) as earnings/share changes. • P/E Determinants - in general, P/E's increase when: 1. Growth rate of earnings are expected to increase. 2. Dividend payout ratio is expected to increase. 3. Riskiness of a stock decreases. EB545 – Corporate Finance 78 Three important factors associated with P/E ratios: 1. Earnings potential 2. Dividends 3. Investment quality NOTE: Since firms have relatively stable dividend policies, the variables most likely to affect P/E are risk and expected growth. High P/E Ratio • Good growth opportunities • Earnings are relatively safe • Deserves low capitalization rate (r). Low P/E Ratio • Low or no growth opportunities • Unstable earnings P/E Ratios Can Be Misleading EB545 – Corporate Finance 79 • Firms can have high P/E ratios and almost 0 earnings - generates exptremely high P/E ratio. • No reliable association between P/E ratio and the market capitalization rate, r; ratio of EPS to P0 measures r only if PVGO = 0; EPS must represent earnings with no growth. • Earnings per share means different things to different firms because of arbitrary accounting practices, i.e., depreciation methods, valuation of inventory, capitalizing vs. expensing, etc. P/E Ratios - Wall Street Journal (10/7/92) EB545 – Corporate Finance 80 Company P/E Ratio Company P/E Ratio ------------- ------------ ------------- ------------ Exxon 17 Coca-Cola 29 Mobil 23 Hewlett-Packard 14 Chevron 25 Goodyear 12 Texaco 17 General Mills 20 Amoco 25 Phillip-Morris 3 Shell 16 Paine-Webber 4 ARCO 32 Shell Oil 16 Anadarko 97 EB545 – Corporate Finance 81 Investment Criteria • Net Present Value • Discounted/Undiscounted Payback (Payout) • Average Return on Book Value • Internal Rate of Return • Profitability Index Net Present Value EB545 – Corporate Finance 82 • Any investment rule which does not recognize the time value of money is useless. • A dollar today is worth more than a dollar tomorrow. • Depends solely on forecasted future cash flows and opportunity costs of capital • Additivity Rule: Because present values are all measured in units of today's dollars, you can add them up. NPV(A+B) = NPV(A) + NPV(B) Year Project 1 Project 2 Project 3 Proj. 1&3 Proj. 1&2 Proj. 2&3 0 -100 -100 -100 -200 -200 -200 1 0 225 450 450 225 675 2 550 0 0 550 550 0 IRR 135% 125% 350% 213% 131% 238% NPV (10%) 354 105 309 663 459 414 Payback (Payout)• Initial investment should be recoverable within some specified cutoff period.• Computed by EB545 – Corporate Finance 83 counting the number of years it takes before cumulated cash flows equal initial investment. EXAMPLE: Cash Flow Project Period 0 Period 1 Period 2 Period 3 Payback NPV (10%) A -2000 2000 0 0 1 -182 B -2000 1000 1000 5000 2 3492 Payback rule says accept A over B; NPV rule says reject A and accept B. NOTE: Payback criterion gives equal weight to all cash flows before payback date and no weight at all to subsequent cash flows. EXAMPLE: Cash Flow EB545 – Corporate Finance 84 Project Period 0 Period 1 Period 2 Period 3 Payback NPV (10%) A -2000 1000 1000 5000 2 3492 B -2000 0 2000 5000 2 3409 C -2000 1000 1000 100,000 2 74,867 Firm accepts too many short-lived projects, possibly with negative NPV's. Choosing a Cutoff Period • Firms typically arbitrarily choose the cutoff period. • If one knows the typical pattern of cash flows, then you can find the optimal cutoff period that maximizes NPV. EB545 – Corporate Finance 85 • CAUTION: Only works if cash flows are spread relatively evenly over the life of the project. Optimal Cutoff Period = 1 − 1 n r r (1+ r ) where n = life of the project EXAMPLE: 10% discount rate, 10 year project. So, optimal cutoff is 6 years. Discounted Payback • More appropriate because opportunity cost of capital is integrated - but still ignores after payout cash flows. Average Return on Book Value • Book rate of return EB545 – Corporate Finance 86 • Divide average forecasted profits (after depreciation and taxes) by the average book value of the investment. • Ratio is then measured against book rate of return (ROR) of the firm as a whole. EXAMPLE: Assume $9000 investment, depreciated at $3000 per year; assume no taxes. Cash Flow Project Period 1 Period 2 Period 3 Book ROR A Cash Flow 6000 5000 4000 Net Income 3000 2000 1000 44% B Cash Flow 5000 5000 5000 Net Income 2000 2000 2000 44% C Cash Flow 4000 5000 6000 Net Income 1000 2000 3000 44% Average Book Value of Investment: Year 0 Year 1 Year 2 Year 3 Average $9000 $6000 $3000 $0 $4500 EB545 – Corporate Finance 87 NOTE: All projects have 44% book ROR (2000/4500), yet Project A clearly has a higher NPV. Limitations to Average Return on Book Value: • No allowance for immediate cash flows being more valuable than distant ones. • Not based on cash flows, but accounting income; these are often very different due to accounting practices. • Yardstick for evaluating average book ROR is arbitrary. Internal (or Discounted Cash Flow) Rate of Return • Rule: Accept investment opportunities offering rates of return in excess of the opportunity cost of capital. • Single period model ROR = Payoff −1 Investment EB545 – Corporate Finance 88 or C1 NPV = C0 + =0 1+ r where discount rate that makes NPV = 0 is the internal rate of return. EXAMPLE: Year 0 Year 1 Year 2 -$4000 $2000 $4000 so, NPV = −4000 + 2000 + 4000 2 = 0 (1+ IRR ) (1= IRR ) IRR = 0.28 (28%) NOTE: IRR and the opportunity cost of capital are not the same. EB545 – Corporate Finance 89 • IRR gives the same answer as NPV rule whenever NPV os a project is a smoothly declining function of the discount rate. Pitfalls Associated with the IRR Rule 1. Lending versus Borrowing Situations Project Period 0 Period 1 IRR NPV-10% A -1000 1500 50% $364 B 1000 -1500 50% -$364 • Lending (A) versusBorrowing (B) -When we lend money, we want a high rate of return; conversely, when we borrow, we want a low rate of return. EB545 – Corporate Finance 90 2. Multiple Rates of Return • When there is more than one change in the sign of the cash flows, there is generally not a unique internal rate of return. EXAMPLE: Project Period 0 Period 1 Period 2 IRR NPV-10% C -4000 25,000 -25,000 25% & 400% -$1,934 NPV = −4000 + 25,000 + −25,000 = 0 1.25 (1.25)2 NPV = −4000 + 25,000 + −25,000 = 0NOTE: There can 5.0 (5.0)2 be as many different IRR's for a project as there are changes in the sign of the cash flows.3. No Internal Rate of Return Project Period 0 Period 1 Period 2 IRR NPV-10% D 1000 -3000 2500 None $339 4. Mutually Exclusive Projects Project Period 0 Period 1 IRR NPV-10% E -10,000 20,000 100% $8,182 F -20,000 35,000 75% $11,818 EB545 – Corporate Finance 91 NOTE: Maximizing NPV is inconsistent with IRR rule. Incremental IRR - • Dealing with differences in scale and timing. • Evaluate IRR on incremental cash flows from mutually exclusive projects. EXAMPLE: • Consider smaller project (E) where IRR is in excess of opportunity cost of capital. • Is it worth making an additional investment of $10,000 in F? Incremental Flows: Project Period 0 Period 1 IRR NPV-10% F-E -10,000 15,000 50% $3,636 NOTE: Incremental NPV is consistent with additivity rule. 1. Differences in Timing of Projects EB545 – Corporate Finance 92 EXAMPLE: Project Year A B B-A 0 -23,616 -23,616 0 1 10,000 0 -10,000 2 10,000 5,000 -5,000 3 10,000 10,000 0 4 10,000 32,675 22,675 IRR 25% 22% 16.6% NPV - 10% $8,083 $10,347 $2,264 2. Differences in Scale of Projects EXAMPLE: Project Year X Y Y-X EB545 – Corporate Finance 93 0 -10,000 -15,000 -5,000 1 12,000 17,700 5,700 IRR 20% 18% 14% NPV - 10% $908 $1089 $181 • Compare incremental IRR to opportunity cost of capital; if greater, take Y instead of X.• Incremental IRR will give same investment decisions as NPV. 3. Other Issues associated with IRR • Term structure of interest rates - short-term versus long- term interest rates for short and long-lived projects. • Difficult to set benchmark for acceptance of project when opporunity cost of capital changes over time. • Project Ranking - should we use IRR? Maximizing NPV subject to capital constraints is better approach. EB545 – Corporate Finance 94 Profitability Index • Present value of forecasted future cash flows divided by initial investment. PI = PV/C0 • Rule: Accept all projects with a PI > 1 because this implies they must have NPV >0. • This rule most closely resembles the NPV rule. • Inconsistency in PI Rule EXAMPLE: Project Period 0 Period 1 PV-10% PI NPV-10% K -100 200 182 1.82 $82 L -10,000 15,000 13,636 1.36 $3,636 • Profitability Index suggests that K should be selected over L; however, L's NPV is greater than K's.• Solution: Look at P.I. on incremental investment. Project Period 0 Period 1 PV-10% PI NPV-10% EB545 – Corporate Finance 95 L-K -9,900 14,800 13,454 1.36 $3,554 • Profitability Index on the additional investment is greater than 1, so you know that L is a better project. EB545 – Corporate Finance 96 Net Present Value Rule and Investment Decisions 1. Only Cash flow is Relevant • Dollars received minus dollars paid. • NOT accounting profits. • Estimate cash flows on AFIT basis 2. Estimate Cash Flows on Incremental Basis • Don't confuse average cash flows with incremental cash flows. EXAMPLE: Decisions about investing in a losing division where "turnaround" opportunities exist should be made based on incremental analysis, not average analysis. • Forget sunk costs EB545 – Corporate Finance 97 "spilled milk" past and irreversible outflows cannot be affected by accept/reject decision • Include opportunity costs- cost of a resource may be relevant to the investment decision. EXAMPLE: Decision to construct a new plant on land that could be sold for $1 million (opportunity cost) NOTE: Very difficult to assess when no freely tradeable market exists. • Treat Inflation Consistently Do not confuse nominal and real dollars When using nominal dollars, use nominal discunt rates When using real dollars, utilize real discount rates. 1+ nominal discount rate Real Discount Rate = − 1 1+ inf lation rate 4. Separating Investment and Financing Decisions EB545 – Corporate Finance 98 • Treat all projects as if equity financed. • Treat all cash outflows as coming from stockholders and all cash inflows as going to them. • Caculate NPV, then undertake separate analysis of financing decisions. 5. Depreciation • Non-cash expense • Important because it reduces taxable income (which are cash flows). • Provides an annual tax shield (product of depreciation and marginal tax rate) • Accelerated depreciation (for IRS) versus straight-line (for stockholders' income statement). 6. Discounting Inflows and Outflows EB545 – Corporate Finance 99 • Proper discount rate depends on the risk of the cash flow - not whether it is an inflow or an outflow. • One person's inflow is another person's outflow - in equilibrium, all sellers and buyers must agree on asset values at the margin. • Assumes homogeneous expectations or a well functioning information market. 7. Choice of Discount Rate • We are only concerned with rates that are available in the capital market today. • What is the value of $1 discounted at today's 1-year interest rate (same for n years). EB545 – Corporate Finance 100 Other Capital Budgeting Issues Optimal Timing of Investment • The fact that a project has a positive NPV does not mean that it is best undertaken now. • Negative NPV projects today might become a valuable opportunity at some later date. • Examine alternative dates and find the one which adds the most to the firm's current value. Net future value as of date t (1+ r)t EXAMPLE: Timber cutting (B&M) EB545 – Corporate Finance 101 Year of Harvest 0 1 2 3 4 5 Net Future Value 50 64.4 77.5 89.4 100 109.4 NPV if harvested in Year 1 = $64.4/1.10 = $58.5 Year of Harvest 0 1 2 3 4 5 Net Present Value 50 58.5 64.0 67.2 68.3 67.9 Optimal Point of Investment is Year 4 - where NPV is maximized. Equipment Utilization and Replacement Weigh increased costs of utilization against cost of replacement. EB545 – Corporate Finance 102 Equivalent annual cost: represents an annuity with the same PV and life as the equipment or machine. PV of Annuity = PV of Cash outflows for Machine = annuity payment x t -year annuity factor EXAMPLE: The president's executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $20,000 per year and would save $100,000 a year in airline bills.A new jet costs $1.1 million and (at its current low rate of use) has a life of 6 years. Assume the opportunity cost of capital is 12% and the company pays no taxes. Should you try to persuade the president to allow other officers to use the plane. With a 6 year life the equivalent annual cost (at 12%) of a new jet is $1,100,000/4.111 = $267,575. If the jet is replaced at the end of year 3 rather than 4, the company will incur an EB545 – Corporate Finance 103 incremental cost of $267,575 in Year 4. The present value of this cost is: $267,575/1.124 = $170,049 The present value of the savings is: 3 $80,000 ∑ 112t = $192,147 . t =1 So, the president should allow wider use of the present jet because the PV of the savings is greater than the PV of the cost. NOTE: As an aside, although a decision on usage of the new jet can be postponed, it appears that other officers should continue to use the plane. If the increased usage causes the plane life to be reduce 25% (i.e. 6 to 4.5 years), the increase in the equivalent annual cost is $330,420-267,548 = $62,872. This is less than the annual saving of $80,000. Equipment Replacement 1. Present Value of Incremental Cash Benefits EB545 – Corporate Finance 104 Consider the following: CF = Cash flow ∆ = New minus Old S = Sales C = Operating Costs D = Depreciation t = tax rate ∆CF = (∆S - ∆C - ∆D)(1-t) + ∆D 2. Salvage Value • New machine • Old machine 3. Initial Capital Investment • Proceeds from sale of old machine EB545 – Corporate Finance 105 • Tax consequences of sale or disposal of old machine • Cost of new machine EB545 – Corporate Finance 106 Capital Rationing • Basic assumption is that capital is limited. • Inconsistent with notion of perfect capital markets. • "Soft" rationing vs. "hard" rationing • Soft Rationing • Provisional and arbitrary limits set by management of the firm. • Not indicative of any real imperfections in capital markets. • Means of controlling investment among managers. • Means of dealing with biased cash flow forecasts. • For projects with significant NPV's, firm is capable of raising more money and loosening the artificial constraint. EB545 – Corporate Finance 107 • Hard Rationing • Wealth of firm's shareholders is maximized when the firm accepts every project that has a positive net present value. • Refleccts a barrier between the firm and capital markets - market imperfections • Shareholders lack free access to well-functioning capital markets • Projects with positive NPV's are passed up • Often there are other issues at work, i.e. control of the firm. • Must not ignore risk of the project - opportunity cost of capital takes this into account. Capital Rationing Models • Assume there are capital budget limitations. • Must incorporate a method of selecting among the available opportunities that maximizes NPV of the firm. EB545 – Corporate Finance 108 1. PROFITABILITY INDEX EXAMPLE (B&M): Suppose there is a 10% opportunity cost of capital, company has total resources of $10 million and has the following opportunities: Cash Flow Millions $ NPV - 10% Project Period 0 Period 1 Period 2 $ Millions P.I. A -10 +30 +5 21 3.1 B -5 +5 +20 16 4.2 C -5 +5 +15 12 3.4 • Firm has sufficient resources to invest in either project A or in projects B&C. • Individually, B&C have lower NPV's - but together they have a greater NPV than A. • Choosing among projects based solely on individual NPV's may lead to sub-optimal decision. EB545 – Corporate Finance 109 • Alternative: Select projects that offer the highest ratio of PV to initial outlay (PI). Profitability Index = Present Value Investment Limitations to PI: 1. May only be applicable to a single period model. 2. When there are other constraints on the choice of projects 3. Unable to utilize when there are project dependencies. EXAMPLE (B&M): Cash Flow EB545 – Corporate Finance 110 Millions $ NPV - 10% Project Period 0 Period 1 Period 2 $ Millions P.I. A -10 +30 +5 21 3.1 B -5 +5 +20 16 4.2 C -5 +5 +15 12 3.4 D 0 -40 60 13 1.4 • If we accept B&C, we cannot accept D which is more than budget limit in Period 1. • However, we can select A in Period 0 and have sufficient cash to take D in Period 1. • NOTE: A&D have lower PI's than B&C -but have a higher NPV. • Because constraint applies to two periods, PI index fails us as an appropriate capital rationing criteria. 2. Linear Programming Models • General optimization procedure. EB545 – Corporate Finance 111 • Mathematical model with the folowing properties: 1. A linear objective function which is to be maximized or minimized. 2. A set of linear constraints. 3. Variables which are all restricted to nonnegative values. EXAMPLE: The Ice-Cold Refrigerator Company can invest capital funds in a variety of company projects which have varying capital requirements over the next 4 years. Faced with limited capital resources, the company must select the most profitable projects and budgets for the capital expenditures. The estimated present values of the projects, the capital requirements and the available capital projections are shown below: Present Capital Require. Project Value Year 1 Year 2 Year 3 Year4 Plant Expansion 90,000 15,000 20,000 20,000 15,000 EB545 – Corporate Finance 112 Warehouse Expansion 40,000 10,000 15,000 20,000 5,000 New Machinery 10,000 10,000 0 0 4000 New Product Research 37,000 15,000 10,000 40,000 35,000 Available Capital 40,000 50,000 40,000 35,000 Funds The following definitions are chosen for decision variables: • x1 = 1 if the plant expansion project is accepted; 0 if rejected. • x2 = 1 if the warehouse expansion project is accepted; 0 if rejected. • x3 = 1 if the new machinery project is accepted; 0 if rejected. • x4 = 1 if the new product research project is accepted; 0 if rejected. Linear Programming formulation has: 1. Separate constraint for each year's available funds; 2. Separate constraint requiring each variable is less than or equal to 1. EB545 – Corporate Finance 113 3. Integer Programming Models • Applicable to real-world problems where accept/reject decisions must be made. • Method avoids fractional values in solution set. • Involve 0-1 or binary integer variables. • Widely use method in capital budgeting problems. 4. Multi-Objective Decision Models • Utility theory based model - applicable in a world of certainty or uncertainty. • Means of incorporating multiple investment criteria • Profitability index, NPV, IRR, Payout, etc. EB545 – Corporate Finance 114 • Evaluate firm's relative strength of desirability on each objective. • Evaluate relative importance of each criteria (set of weights). • General mathematical form: EB545 – Corporate Finance 115 Risk and Return • "Opportunity cost of capital depends on the risk of the project" • Major topics of interest Security Risk Portfolio Risk Diversification • Risk-return relationships in capital market over the last 60 years 1. Common stocks - (S&P composite index) 2. Government bonds 3. Corporate Bonds 4. Treasury Bills EB545 – Corporate Finance 116 Average Annual Rate of Return Nominal Real (versus T-Bills) ROR ROR Risk Premium Treasury Bills 3.6% 0.5% 0 Government Bonds 4.7% 1.7% 1.1% Corporate Bonds 5.3% 2.4% 1.7% Common Stocks 12.1% 8.8% 8.4% (Note: Average inflation - 3.1%) 1. Treasury Bills: short maturity and no risk of default (inflation risk). 2. Government Bonds: longer term asset, sensitive to changes in interest rates (bond prices fall when interest rates rise and vice versa). 3. Corporate Bonds: similar to government bonds, except risk of default. 4. Common Stocks: direct share in the risk of the enterprise. • Evaluating and investment opportunity with same risk as S&P 500 - or market portfolio. EB545 – Corporate Finance 117 Hypothesis: Opportunity cost or discount rate should be E(r) on market portfolio (rm). Assumption: Future is like the past and we use a 12.1% ROR. Methodological Shortcoming: Market returns are not stable over time. Alternative: Look at the individual components of rm a. risk-free rate (rf) b. risk premium where, rm (1990) = rf (1990) + normal risk premium = 0.08 + 0.084 = 0.164 (16.4%) (NOTE: This assumes a normal, stable risk premium) • Evaluating and investment opportunity with risk characteristics different from S&P 500. EB545 – Corporate Finance 118 • Measures of Risk and Return 1. Expected Return: a measure of central tendency. n E (r ) = ∑ hri i (mean) i =1 where h = probability of occurrence of return i 2. Variance: An average deviation meaure of dispersion, obtained by averaging the squares of deviations of individual observations from the mean. n σ2 (r ) = ∑ hi[ri − E (r )]2 i =1 3. Standard Deviation: an average deviation measure of dispersion equal to the positive square root of the variance. σ2 = σ 4. Covariance: an absolute measure of the extent to which two sets of variables move together over time. EB545 – Corporate Finance 119 n ∑[(rat − ra )(rb − rb )] Covr r = t =1 t (sample covariance) a b n −1 EXAMPLE: Month 1 2 3 4 5 Mean Stock A 0.04 -0.02 0.08 -0.04 0.04 0.02 Stock B 0.02 0.03 0.06 -0.04 0.08 0.03 (0.04-0.02)(0.02-0.03) = -0.0002 (-0.02-0.02)((0.03-0.03) = 0.0000 (0.08-0.02)(0.06-0.03) = 0.0018 (-0.04-0.02)(-0.04-0.03) = 0.0042 (0.04-0.02)(0.08-0.03) = 0.0010 ----------- EB545 – Corporate Finance 120 Total 0.0068 Covr r = 0.0068 = 0.0017 a b (5−1) • Positive Covariance: when one stock produces a return above its mean, the other tends to do as well. • Note: Covariance number tells us little about the relationship between returns on the two stocks. • Population Covariance n Covr r = ∑ hi[ra − E (ra )][rb − E (rb )] a b i i i =1 5. Correlation Coefficient: normalized measurement of joint movement between two variables. • Covariance number is unbounded (- to + infinity) • Put bounds on covariance by dividing by the σ of the two investments. • Correlation coefficient, ρ, ranges from +1 to -1. EB545 – Corporate Finance 121 Covr ρa , b = σ σ ra b r r a b EB545 – Corporate Finance 122 Correlation Coefficient r r b b r r a Perfect negative a Perfect Positive Correlation Correlation (-1) (+1) rb r Uncorrelated a Returns (0) EB545 – Corporate Finance 123 • Note that in the case of perfect positive and negative correlation, if we know the returns on stock b, then we could predict a. • Magnitude of the slope is irrelevant. • Coefficient may range from -1 to +1. Also, it follows that: Covr r = ρa , bσr σr a b a b 6. Characteristic Line' • Extension of covariance to relationship between individual stock and market portfolio. EXAMPLE: Month 1 Month2 Month 3 Month 4 Month 5 Stock J 0.02 0.03 0.06 -0.04 0.08 Market Port. 0.04 -0.02 0.08 -0.04 0.04 EB545 – Corporate Finance 124 CHARACTERISTIC LINE 0.08 0.06 Slope of Line = Bj 0.04 j's Return 0.02 0 -0.04 -0.02 0 0.02 0.04 0.06 0.08 -0.02 -0.04 Market Return EB545 – Corporate Finance 125 • Characteristic Line 1. Describes the relationship between returns on the stock and the market portfolio. 2. Shows the return that you expect the stock to produce, given a particular market ROR. 3. The slope of the characteristic line is the stock's beta factor or βj (refer to the intercept of the characteristic line as a.) 7. Beta Intercept EB545 – Corporate Finance 126 Cov(rj ,rm ) Bj = a j = r j − β jrm σ2r m (rm, t − rm )2 n Variance of market returns: σ =∑ 2 m t =1 n −1 From preceding Table, market σ2 = 0.0024; So, βj = 0.0017/0.0024 = 0.708 aj = 0.03-0.708(0.02) = 0.0158 • Beta is an indicator or the degree to which a stock responds to changes in the return produced by the market. • If we knew the market was going to be higher by 1% next month, we would increase our expectation for stock j's return by 0.708% Reducing Risk Through Diversification EB545 – Corporate Finance 127 • Most stocks are substantially more variable than the market portfolio - only a few have lower standard deviation of returns. • Why doesn't the market's variability reflect the average variability of its components? • Diversification works to reduce risk because prices of different stocks do not move exactly together. • Even in a 2 stock portfolio, a decline in the value of one stock in the portfolio can be offset by a rise in the price of the other stock. • Result: Variability of portfolio is less than the average variability of the two stocks in the portfolio. EB545 – Corporate Finance 128 Portfolio Standard Deviation 1 5 10 15 Number of Securities Systematic versus Unsystematic (unique) Risk 1. Unsystematic Risk (unique) • Risk that can be potentially eliminated by diversification. • Firm or industry specific. • Management Risk • Financial or operating leverage • Able to diversify away. EB545 – Corporate Finance 129 2. Systematic Risk • Stems from economy wide perils which affect all businesses. • Interest rate risk • Purchasing power risk (inflation) • Stock market risk • Unable to completely diversify away. • For a reasonably diverisfied portfolio, this is the only risk that matters. EB545 – Corporate Finance 130 Portfolio Analysis • Expected Return: weighted average of the expected returns on the individual stocks contained in the portfolio. E (rp ) = ∑ x j E (r j ) n j =1 where, xj is the percent of investment in stock j • Variance: function of the variance of each stock included in the portfolio as well as the covariance between stocks' returns. σ2 = xi2σi2 + x2σ2j + 2 xi x jρi , jσi σ j p j where, xi = % of portfolio invested in asset i σi2 = variance of returns on asset i ρij = correlation coefficient between assets i & j where -1 ≤ ρij ≤ 1 EB545 – Corporate Finance 131 Example of Portfolio Effect: Return & Probabilities for investments 1 and 2 State of Economy Probability 1's Return 2's Return Recession 0.20 5% 20% Slow Growth 0.30 7% 8% Moderate Growth 0.30 13% 8% Strong Economy 0.20 15% 6% Expected Value = E(r1) = ∑ r1 p1 = 10.0% Expected Value = E(r2) = ∑ r2 p2 = 10.0% Standard Deviation = σ1 = ∑ (r1 − r1)2 p1 = 15.4% = 3.9% Standard Deviation = σ2 = ∑ (r2 − r2 )2 p2 = 25.6% = 51% . PORTFOLIO EFFECT: E (rp ) = ∑ x j E (r j ) n j =1 E(rp) = 10% EB545 – Corporate Finance 132 (%) Possible Outcomes (j) 20% 15% (i,j) 10% (i) 5% Recession Slow Semi- Strong Growth Strong Growth PORTFOLIO STANDARD DEVIATION: σ2 = xi2σi2 + x2σ2j + 2 xi x jρi , jσi σ j p j where, x1 = 0.50, σ1 = 3.9 x2 = 0.50, σ2 = 5.1 ρ1,2 = -0.70 σp = 1.8% EB545 – Corporate Finance 133 • Portfolio standard deviation is less than the standard deviation of either investment (3.9% or 5.1%). • Any time two investments have a correlation coefficient less than +1, some risk reduction will be possible by combining the assets in a portfolio. • The extent that we can still get risk reduction from positively correlated items gives extra meaning to portfolio management. Impact of various assumed correlation coefficients for Investments 1 and 2: Correlation Coefficient Portfolio Stand. Dev. +1.0 4.5% +0.5 3.9% 0.0 3.2% -0.5 2.3% -0.7 1.8% -1.0 0.0% EB545 – Corporate Finance 134 EXAMPLES OF PERFECT POSITIVE AND NEGATIVE CORRELATION State Probability RA RB 1 0.25 0.06 0.12 2 0.25 0.08 0.10 3 0.25 0.10 0.08 4 0.25 0.12 0.06 E(RA) = 0.09 Var(RA) = 0.0005 E(RB) = 0.09 Var(RB) = 0.0005 Cov(RA,RB) = ∑ Pi[ RA − E ( RA )][ RB − E ( RB )] = −0.0005 n i =1 Correlation Coefficient = ρ A, B = COV ( RA RB ) = −0.0005 = −1 σ Aσ B ( 0.0005)( 0.0005) Portfolio with 50% in A and 50% in B: E(Rp) = 0.09 Var(Rp) = 0 EB545 – Corporate Finance 135 • In this portfolio the expected return is a certain return. No matter which state occurs, the return is 0.09. • If there is a perfect negative correlation between two assets, then the Var(Rp) equals 0. This means it is a risk-free portfolio. Alternatively, if perfect positive correlation exists between two assets, the portfolio standard deviation is a weighted average of the assets' standard deviation. EXAMPLE: Asset A: E(R) = 0.10 σ = 0.05 xA = 0.50 Asset B: E(R) = 0.12 σ = 0.08 xA = 0.50 Assuming ρA,B = 1.0, then σp = 0.065 • INDIVIDUAL SECURITIES AFFECT ON PORTFOLIO RISK EB545 – Corporate Finance 136 1. Risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio. 2. In other words, how sensitive are each of the stocks in the portfolio to market movements, both individually and collectively? 3. Stocks with β greater than 1.0 tend to amplify overall movements in the market - both upward and downward. • LIMITS TO DIVERSIFICATION EB545 – Corporate Finance 137 1. The variabilityof a portfolio reflects mainly the covariance. 2. When there are just two securities in a portfolio, there are an equal number of variance and covariance boxes. 3. As the number of stocks, n, increases in the portfolio, you steadily approach the average covariance. 4. If average covariance were zero, it would be possible to eliminate all risk; however, covariances are almost always positive. 5. No matter how many stocks you include, there are limits to the benefits of diversification. EB545 – Corporate Finance 138 Maximizing Return Given Risk The Minimum Variance and Efficient Sets (Markowitz Model) 1. Given the level of risk, or standard deviation, we prefer portfolio positions with higher expected rates of return. 2. Given the level of expected return, we prefer portfolio positions with lower risk. 3. Given the characteristics of the available population of stocks, the investment opportunity set has a perimeter that is represented by a bullet-shaped curve. 4. This perimeter is referred to as the minimum variance set. EB545 – Corporate Finance 139 Expected Return (%) 20 15 10 5 5 10 15 Standard Deviation (%) EB545 – Corporate Finance 140 THE MIMIMUM VARIANCE SET: • Each point on the minimum variance set represents a portfolio, with portfolio weights allocated to each of the stocks in the population. • Given a particular expected rate of return, the portfolio on the MV set has the lowest possible standard deviation achievable with the available population of stocks. • The terms minimum variance set and minimum standard deviation set can be used interchangeabley. • The minimum variance set can be divided into two halves, a top and bottom - separated at the minimum variance point (MVP). The MVP represents the single portfolio with the lowest possible standard deviation, the global minimum variance portfolio. • The most desirable portfolios for us to hold are those in the top half of the bullet. • Top half of the bullet is call the efficient set - Given a particular level of standard deviation, the portfolios in the efficient set have the highest attainable expected rate of return. EB545 – Corporate Finance 141 Finding the Minimum Variance Portfolio Consider an example where we build portfolios from three available stocks with the following expected returns: A, Acme Steel: 5% B, Brown Drug: 10% C, Consolidated Electric: 15% The covariance matrix for the stocks is given by: A B C A 0.25 0.15 0.17 B 0.15 0.21 0.09 C 0.17 0.09 0.28 By taking the square root of the variances going down the diagonal of the matrix, we can compute the standard deviations of the stocks as follows: A, Acme Steel σ(rA): 0.50 B, Brown Drug σ(rB): 0.46 C, Consolidated Electric σ(rC): 0.53 EB545 – Corporate Finance 142 Expected Return (%) MINIMUM VARIANCE SET FOR CONSOLIDATED, BROWN & ACME 30 20 MVP Consolidated Brown 10 Acme 10 20 30 40 50 60 Standard Deviation (%) EB545 – Corporate Finance 143 Portfolio Weight in Stock B xB R 1.0 Q L U S T xA -1.0 0 1.0 Portfolio Weight in Stock A -1.0 EB545 – Corporate Finance 144 • Acme Steel (A) and Brown Drug (B) portfolio weights are plotted. • Consolidated Electric's portfolio weight is implied by the value for xA and xB • For example, if we are at Point U, portfolio weight in Brown is equal to 0.30 and portfolio weight in Acme is 0.0. Since there are only three stocks, portfolio weight in Consolidated is equal to 1- xA - xB = 0.70. • Each point represents a portfolio with particular weights assigned to each stock. DEF. "Selling Short": When you sell short, you borrow shares of stock from someone (usually through your broker). You are obligated to return to this person, after a certain period of time, the same number of shares you borrowed. When short-selling a stock as part of your portfolio, the weight assigned to the stock is negative. EB545 – Corporate Finance 145 Now consider the triangle area bounded by points R,S & T.: 1. All points in the triangle represent portfolios where we have invested positive amounts in each of the three stocks. 2. Consider Point L, where we invest 50% in Acme, 45% in Brown and 5% in Consolidated. 3. For portfolios on the perimeter, we invest a combined total of 100% of our money in two stocks and 0 position in the third. 4. At point Q, we invest 60% in Brown, 40% in Conslolidated and nothing in Acme. Conversely, on perimeter RT we are taking no position in Consolidated. 5. If we are outside the triangle, at any point to the northeast of the line Y'X, we are selling Consolidated short. 6. If we are positioned to the west of the figure's vertical axis, we are selling Acme short. 7. If we are anywhere to the south of the horizontal axis, we are selling Brown short. 8. At point Y', we are selling Acme short and adding the proceeds to our equity to invest in Brown. EB545 – Corporate Finance 146 Iso-expected Return Lines: Line, drawn on a mapping of portfolio weights, which shows the combinations of weihts all of which provide for a particular portfolio rate of return. • In general, the slope and relative position of the iso-expected return lines are dependent on the relative expected returns of the stocks considered. • If we want to see combinations of weights that are consistent with a different value for portfolio return, then we must look at different iso-expected return lines. Iso-variance ellipse: Ellipse, drawn on a mapping of portfolio weights, which shows the combinations of weights all of which provide for a particular portfolio variance. • Ellipses are all concentric about the point MVP. • Similar to lines denoting points of equal altitude on a topographic map. • Iso-variance ellipses represent points of constant variance. Critical Line: A line tracing out, in portfolio weight space, the portfolio weights in the minimum variance set. • Critical line can be found by tracing out points of tangency between iso-expected return lines and iso-variance ellipses. • Finding the minimum variance set is tantamount to finding the location of the critical line. EB545 – Corporate Finance 147 Portfolio Weight in Stock B x B 1.0 Q L xA -1.0 0 1.0 Portfolio Weight in Stock A 12% 10% -1.0 16% 18% EB545 – Corporate Finance 148 Portfolio Theory with Borrowing and Lending • Suppose that you can lend and borrow money at some risk- free interest rate, rf. • For example: Invest some of your money in T-Billls and some in common stock portfolio M. E(r) Borrowing M Lending rf EB545 – Corporate Finance 149 Since borrowing is negative lending, you can borrow at rf and invest more in stock portfolio M. NOTE: What we see is that regardless of the level of risk preferred, you get the highest expected rate of return by a mixture of portfolio M and borrowing or lending. Meaning: 1. The best portfolio of stocks must be selected and that is the portfolio where the capital market line is tangent to the efficient frontier. 2. Blend this portfolio with borrowing and lending to match individual risk preferences. EB545 – Corporate Finance 150 Capital Asset Pricing Model ASSUMPTIONS: 1. All investors seek to invest in Markowitz efficient portfolios. 2. Unlimited borrowing and lending at the risk-free rate. 3. All investors have homogeneous expectations. 4. No taxes and no transaction costs. 5. Capital markets are in equilibrium. Central Message: In a competitive market, the expected risk premium varies in direct proportion to beta. EB545 – Corporate Finance 151 SECURITY MARKET LINE E(r) B M rm A Market Portfolio r f 0.5 1.0 2.0Beta Expected Risk Premium on investment = (Beta) x (Expected Risk Premium on Market) ri - rf = βi(rm-rf) So, the expected risk premium on portfolio A is 1/2 the risk premium on the market, and portfolio B has twice the expected risk premium. EB545 – Corporate Finance 152 CAPM In terms of Beta: E (ri ) = rf + βi[ E (rm − r f )] and Cov(ri ,rm ) βi = σ2 (rm ) So, for capital budgeting purposes, where the risk characteristics of the project are consistent with the risk of firm i, the the opportunity cost of capital for further investment is E(ri). EB545 – Corporate Finance 153 Four Basic Principles of Portfolio Selection: 1. Investors like high expected returns and low standard deviation; stock portfolios that offer highest E(r) for a given σ are efficient portfolios. 2. To know the marginal impact of a stock on a portfolio, you must look at its contribution to portfolio risk; contribution depends on the stock's sensitivity to changes in the value of the portfolio. 3. Stock's sensitivity to changes in the value of market portfolio is Beta (β) - measures marginal contribution of a stock to risk of the market portfolio. 4. If investors can borrow and lend at the risk-free rate of interest, then they should always hold a mixture of the rf investment and one particular common stock portfolio. EB545 – Corporate Finance 154 WHAT WOULD HAPPEN IF A STOCK DID NOT LIE ON THE SECURITY MARKET LINE? E(r) SML M B r m Market Portfolio rf A Beta 0.5 1.0 2.0 EB545 – Corporate Finance 155 WHAT WOULD HAPPEN IF A STOCK DID NOT LIE ON THE SECURITY MARKET LINE (SML)? 1. Would you buy stock A? If you wanted an investment with a Beta of 0.50, NO! If every rational investor shares your view, then the price of A drops and E(r) goes up. 2. What about stock B? Again, one can achieve higher return (with equivalent risk) by investing in a stock or portfolio on the SML. Again, price of B must fall until E(r) is equivalent. EXAMPLE: 1. Assume initially, that stock A's expected dividend and expected market price are $5.00 and $100 respectively. The beginning market price is $100 and consequently, the expected rate of return is equal to: E (rA ) = E (dividend + ending market price) −1 beginning market price EB545 – Corporate Finance 156 E (rA ) = E ($5.00 + $100) −1 = 0.05 (or 5%) $100 2. Now suppose an item of good news is received by the market place and the information does nothing to change the market's assessment of the risk characteristics of the stock; however, it does change its assessment of the dividend and ending price. 3. The new expected dividend is $7.00 and the new expected ending price is $105.00. If there is no change in the beginning price, the new expected rate of return is: E (rA ) = E ($7.00 + $105) −1 = 0.12 $100 4. It is now in everyone's interest to increase their investment in stock A. The buying pressure on the stock will force its price up and its expected rate of return down, until it resumes its equilibrium position. The market price at that point will be: EB545 – Corporate Finance 157 0.05 = E ($7.00 + $105) −1 $106.67 • NOTE: This same kind of market pressure holds each stock in its equilibrium position. Should anything disturb the stock from its position, opportunities will arise to earn superior returns by either buying or selling it short. The buying or selling pressure immediately forces the stock back to its equilibrium price. CONCLUSIONS: 1. In equilibrium, all stocks must lie on the security market line. 2. An investor can always obtain an expected risk premium of β(rm-rf) by holding a mixture of the market portfolio and the risk-free investment. 3. Stocks on average lie on the security market line; so, if none lie on the line then none can lie above the line. Validity and Role of CAPM EB545 – Corporate Finance 158 • While the capital asset pricing model is not perfect, it does seem to capture important elements of risk. • There is an important role in this theory of the market portfolio. For any efficient portfolio, the expected risk premium on each stock (ri-rf) must be proportional to its beta measured relative to that efficient portfolio. • If the market portfolio is efficient, then (ri-rf) will be proportional to beta measured relative to the market portfolio. • The market portfolio should in principle include all assets; the available market indexes clearly fall short of that ideal. • If a particular index is, ex post, part of the efficient set, then returns and beta will plot along a straight line; the problem is how close is close enough in terms of fitting a line. • Beta is, however, a valuable measure of risk: simple, objective, plausible and consistent with theory - it correctly excludes diversifiable risk. • Regard CAPM as a useful rule of thumb - not as the final word on how the world works. Arbitrage Pricing Theory (APT) EB545 – Corporate Finance 159 • Fundamental assumption is that security returns are generated by a process identical to a single index (CAPM) or multi- index (Markowitz) model. • APT suggests that the covariances that exist between security returns can be attibuted to the fact that securities respond, to one degree or another, to the pull of one or more factors. • Basic assumption is that each stock's return depends partly on macroeconomic influences and partly on firm-specific factors. • Factors may include oil prices, interest rates, level of industrial activity, inflation rate, etc. • Assume that the relationship between security returns and factors is linear. rj = aj + β1,jI1,j + β2,jI2,j +. . .+ βn,jIn,j where, I = value of any one of the indices which affects the rate of return of the security. β = individual beta for each index (may be positive or negative) EB545 – Corporate Finance 160 • The portfolio's Beta with respect to any one of the factors is a simple weighted average of the betas of the securities in the portfolio: β1, P = ∑ x jβ1, j M j =1 • As in the CAPM, diversification does eliminate unique or business risk and diversified investors can ignore it when deciding to buy or sell a stock. • APT states that the expected risk premium on a stock should depend on the expected risk premium associated with each factor and the stock's sensitivity to each factor. EB545 – Corporate Finance 161 Arbitrage? • If we assume that Beta for each index is 0, then the expected risk premium is equal to 0; the portfolio is essentially risk- free and should offer a return equal to the risk-free rate. • If the portfolio offered a higher return, investors could make a risk-free (or "arbitrage") profit by borrowing to buy the portfolio. • If the portfolio offered a lower return, investors could sell the portfolio and invest the funds in U.S. Treasury Bills. If the arbitrage pricing relationship holds for diversified portfolios, it must generally hold for the individual stocks. EB545 – Corporate Finance 162 APT vs. CAPM • Similar in that both theories stress that E(r) depends on risk stemming from economy-wide influences and is not affected by unique risk. • If each of APT's factors is proportional and cumulative to CAPM's market portfolio beta, then result is equivalent. • Identifying the factors of importance in APT is difficult. • APT must have (1) reasonably short list of macroeconomic factors; (2) risk premium measures associated with each of these factors; and (3) measurement of stock sensitivity to each factor. EB545 – Corporate Finance 163 Capital Budgeting Under Uncertainty Company Cost of Capital • Rate of return required by investors; • Opportunity cost of capital for firm's existing assets. Project Beta • Measure of risk for a specific project or investment opportunity. • Relate risk of project to market risk. • Difficult to assess. EB545 – Corporate Finance 164 E(r) SML Company Cost of Capital 15% r f (7%) 1.0 1.30 Project Beta Average Beta of Firm's Assets = 1.30 Note: True cost of capital depends on the use to which the capital is put. EB545 – Corporate Finance 165 • Accept any project that more than compensates for project beta. • Emphasis is on project beta - not firm beta! • Note Difference between company cost of capital rule and project beta rule: 1. Company cost of capital rule say accept any project with E(r) greater than 15% (above horizontal line). 2. Project Beta rule would exclude certain projects above the company cost of capital line. • Project Beta: E(project return) = rf + (project Beta)(rm - rf) Example: State Prob. rm r1 r2 1 0.10 -0.15 -0.30 -0.09 2 0.30 0.05 0.10 0.01 3 0.40 0.15 0.30 0.05 4 0.20 0.20 0.40 0.08 Assume EB545 – Corporate Finance 166 Risk-free rate = 0.05 E(r1) = 0.20 E(r2) = 0.03 E(rmarket) = 0.10 σmarket = 0.10 Capital Structure and Company Cost of Capital • Cost of capital is a hurdle rate that depends on business risk of firm's investment opportunity. • But, shareholders also bear financial risk to the extent that the firm issues debt. • The more a firm relies on debt financing, the riskier its common stock. • Borrowing creates financial leverage. Pushes up risk of common stock. Leads to higher E(r) EB545 – Corporate Finance 167 Weighted Average Cost of Capital (WACC) Definition: Expected return on a portfolio of all the firm's securities. Used as a hurdle rate for capital investment. WACC = (Aftertax cost of debt x % of debt in capital structure) + (Cost of Preferred x % of Preferred in Capital Structure) + (Cost of common x % of common in capital structure) EXAMPLE:Consider you own 100% of firm A's debt and equity. What is your E(r) on this portfolio? Company Cost of Capital = rassets = rportfolio = debt rdebt + equity requity debt + equity debt + equity Asset Value = $100 Debt Value = $40 Equity Value = $60 --------------------- -------------------- Asset Value = $100 Firm Value = $100 rassets = debt rdebt + equity requity value value EB545 – Corporate Finance 168 If you demand 8% return on debt and 15% return on equity, ACC = 40 (0.08) + 60 (0.15) = 0.122 or 12.2% 100 100 Effect of Changes in Capital Structure Assume the firm issues an additional $10 of equity and uses it to payoff debt. Balance sheet changes to the following: Asset Value = $100 Debt Value = $30 Equity Value = $70 --------------------- -------------------- Asset Value = $100 Firm Value = $100 NOTE: Change in financial structure does not affect the amount or risk of the cash flows on the total package of debt and equity. WACC is 12.2% both before and after the change. However, • Change does affect the required rate of return on individual securities. • Risk is the same but shifted from one security holder to another. • Stockholders and bondholders required rates of return will change. EB545 – Corporate Finance 169 EXAMPLE: Since firm carries less debt load, let's assume bondholder require less return - suppose it decreases from 8% to 7.3%. Then, rassets = debt rdebt + equity requity value value rassets = 30 (0.073) + 70 (requity ) = 0.122 100 100 So, requity = 14.3% NOTE: Lower leverage makes equity safer and reduces shareholder required rate of return. If we take this to the limit, where debt is equal to 0, then requity = 12.2% EB545 – Corporate Finance 170 WACC and Taxes EXAMPLE: Tax rate (t) = 50% Market Value Market Yield % of Cap. Struc. Debt $400 0.08 40% Preferred $100 0.10 10% Common $500 0.12 50% Total $1000 100% After Tax Cost of Debt = 0.08 x (1-t) = 0.08 x 0.5 = 0.04 (Because interest is deductible) WACC = (0.40 x 0.04) + (0.10 x 0.10) + (0.50 x 0.12) = 0.087 Caution: WACC does not consider risk of project - while appropriately applied, CAPM does! EB545 – Corporate Finance 171 Financial Leverage - Effect on Beta • Stockholders and debtholders receive cash flow and share risk. • Debtholders bear much less risk than shareholders; for example, debt betas are near 0 for blue-chip stocks. • Firm's asset beta is equal to beta of firm's debt and equity (weighted average) βassets = βportfolio = D/V(βdebt) + E/V(βequity) Consider Prior WACC Example where: Asset Value = $100 Debt Value = $40 Equity Value = $60 --------------------- -------------------- Asset Value = $100 Firm Value = $100 Assume that the βdebt = 0.2 and the βequity = 1.2 then, βassets = (0.4 x 0.2) + (0.6 x 1.2) = 0.80 What happens after refinancing? Suppose βdebt falls to 0.1 βassets = 0.80 = (0.3 x 0.1) + (0.7 x βequity) So, βequity = 1.1 EB545 – Corporate Finance 172 Asset Betas: Example: Morgan Company Beta = 2.0 rf = 0.10 E(rm) = 0.20 Cost of Capital: E(ri) = rf + βi(E(rm) - rf) = 0.30 Suppose Year 1 payoff for asset i = $130 then Value of firm, PV0 = $130/1.30 = $100 Now suppose the firm raises $100 to invest in the risk-free asset, which will have a payoff of $110: PV0 C1 β Req. ROR Co. Before Inv. $100 $130 2.0 0.30 New Investment $100 $110 0 0.10 Co. After Inv. $200 $240 1.0 0.20 NOTE: Beta for company after investment can be computed by weighted average. EB545 – Corporate Finance 173 E(r) SML 30% Company Befo Company After r f (10%) 1.0 2.0 Beta Operating Leverage EB545 – Corporate Finance 174 • Fixed operating costs, so called because they accentuate variations in profits. • Just as commitment to fixed debt increases financial leverage, commitment to fixed production charges adds to the beta of a capital project. • Cash flows generated by any productive asset are made up of revenues, fixed costs and variable costs. • Variable Costs: raw materials, sales commissions, some labor. • Fixed costs: wages of workers under contract, property taxes. • Fixed costs are cash outflows, whether asset is idle or not. • Other things being equal, projects with higher ratio of fixed costs to project value have higher project betas. Operating Leverage = % ∆EBIT % ∆Sales EXAMPLE: Selling Price per unit: $20 (p) Variable Costs per Unit: $12 (v) Fixed Operating Costs: $60,000 (Fo) EB545 – Corporate Finance 175 Interest Expense: $25,000 (Ff) Degree of Operating Leverage at 15,000 units (x): DOL = % ∆ EBIT = x( p − v) = 15, 000(20 − 12) = 2.0 % ∆ Sales x( p − v) − FO 15, 000(20 − 12) − 60,000 So, for each 1% change in sales( up or down), EBIT will change by two times that. Note that this is at a single point in time. Degree of Financial Leverage at 15,000 units (x): DFL = % ∆Net Earnings % ∆EBIT x( p − v) − FO 15, 000(20 − 12) − 60, 000 DFL = = = 1.71 x( p − v) − FO − Ff 15, 000(20 − 12) − 60, 000 − 25, 000 • For each 1% change in EBIT, net earnings will change by 1.71 times that. • The more fixed financial costs, the higher the degree of finanical leverage (DFL). EB545 – Corporate Finance 176 Degree of Combined Leverage at 15,000 units: DCL = x( p − v) = 15, 000(20 − 12) = 3.4 x( p − v) − ( Fo + F f ) 15, 000(20 − 12) − 85, 000 or DCL = DOL x DFL = 2.0 x 1.7 = 3.4 • The more leverage you have, the riskier you are. • Relationship between DOL and DFL is positively related. • Higher DOL or DFL will generate a higher beta for the firm. EB545 – Corporate Finance 177 • Financial leverage could include lease payments, preferred dividends, interest payments and some types of taxes. • Different companies use different definitions for fixed item in DFL. • Empirical tests confirm that companies with high operating leverage actually do have high betas. EB545 – Corporate Finance 178 Risk Analysis Techniques for Capital Budgeting Sensitivity Analysis • Pro forma cash flows are evaluated with specific variables in the analysis forecasted at various levels, one at a time. • For example, commodity price levels may be forecasted under pessimistic, most likely and optimistic scenarios and resulting NPV's calculated. • Simple and useful method for ranking the relative impact on project value from various variables. • Useful in terms of establishing a floor value or worst case scenario. • Major drawback is that only one variable's probability spread can be evaluated at a time. • NOTE: Underlying variables may be interrelated. EB545 – Corporate Finance 179 Simulation • Primary Objective is to define the distribution of profit (or NPV) which could be anticipated for the project. • Unlike sensitivity analysis, simulation considers the impact of changes on all variables simultaneously. • Accommodates for both independent and dependent random variables. EXAMPLE: Consider an investment which ultimate net profit is a function of three separate, independent variables x, y & z. Suppose the relationship is defined as: Pr ofit = 3.4 x − [( 1 + 17.9)(0.4 z 2 )] 14 y where Profit is the dependent variable. Using an oil exploration example, x, y & z may be net pay thickness, recovery factors, productive area, drilling costs, crude price, operating expense, etc. Now suppose we know the exact values which x, y , z take on. EB545 – Corporate Finance 180 DO WE KNOW THE RESULTING PROFIT? Yes, this is a deterministic computation; no uncertainty with regard to the variables of interest. a. Given we live in an uncertain world, though, suppose all we know are ranges of outcomes for x, y, & z - which value do we use? b. Simulation allows us to model all the values in a range, for each random variable and compute a distribution of profit. Pr ofit = 3.4 x − [( 1 + 17.9)(0.4 z 2 )] 14 y EB545 – Corporate Finance 181 f(z) f(x) f(y) x y z RESULTS OF SIMULATION: (-) 0 (+) NOTE: Consider full range and distribution of outcomes on each random variable - not just average or most likely outcome. EB545 – Corporate Finance 182 c. Actual state of nature: Variables x, y , z will have one specific value; howwever, before the decision or action we do not know what that value is. d. Do not use only mean or most likely case of each random variable to solve for "mean" or "most likely" profit; this approach ignores the uncertainty as defined by each distribution. e. There are a few special situations when the analytic approach (as opposed to simulation) is possible. For example, if we can find the PDF associated with each distribution, then insert into profit equation and solve. EB545 – Corporate Finance 183 PROCESS OF SIMULATION: 1. Define the distributions for each of the independent variables. 2. Make a series of repetitive calculations for our profit expression. 3. Each value is computed using a value of x, y & z selected from their respecitive distributions and represents one possible state of nature. 4. Each repitition of the dependent variable calculation is called a "simulation pass". 5. Values of the independent variables used for each pass are obtained through a random number sampling procedure which honors the shape and range of each variable's distribution. 6. Passes are made until a sufficient number is made to define the profit distribution (i.e. at least 100, and as many as thousands.) NOTE: It is inappropriate to use same (single) random number to sample all distributions on a pass. Using same number implies fixed values for all variables. ADVANTAGES TO SIMULATION: EB545 – Corporate Finance 184 1. Capability to define uncertainty as a range and distribution of possible outcomes for each unknown factor. 2. May be applied to any type of non-deterministic calculation. 3. No limit to the number of variables that may be modeled. 4. Distributions of random variables can be of any type. 5. Different individuals can describe uncertainty about different variables. 6. Lends itself well to sensitivity analysis. 7. Provides valuable inputs to decision tree modeling (by converting continuous to discrete distributios.) Independent versus Dependent Variables. EB545 – Corporate Finance 185 EXAMPLE: Compare distributions of net pay thickness and initial production rates. ERROR: If the value of thickness sampled was high (which implies large reserves) and in the same pass, the IP sampled was very low then the resulting field life would be unrealistic, • Suppose that we are concerned about whether variables x and y are related to one another. Make a cross-plot of x versus y. EB545 – Corporate Finance 186 CASE OF INDEPENDENCE r.v. y r.v. x Sample each r.v. separately in the simulation pass. EB545 – Corporate Finance 187 CASE OF COMPLETE DEPENDENCY r.v. y y = f(x) r.v. x If we know x, then we know y (or vice versa); therefore, we only need specify one distribution in the simulation. EB545 – Corporate Finance 188 CASE OF PARTIAL DEPENDENCY r.v. y r.v. x 1. x-y relationship not clearly independent or explicitly dependent. 2. Variable y has a substantial range of values, given x - so we need to sample from y on each pass. 3. Also, range of variation of ychanges as x increases. 4. Therefore, the distribution of y changes as x changes and we must accommodate that change in the simulation. EB545 – Corporate Finance 189 ACCOUNTING FOR PARTIAL DEPENDENCIES: 1. Prepare a cross-plot. 2. Draw a boundary or envelope around the observed x-y data point. This boundary defines the limits within which x and y can vary. 3. Any combination of x-y values outside the boundary have a zero probability of occurrence. 4. Determine the variation of y within the boundary as a function of x and define a normalized distribution of y (0 to 1) which represents the observed variation. 5. In this normalized distribution, 0 corresponds to the minimum value of y for a given value of x and 1.0 corresponds to the maximum. Such that, y − ymin ynorm = ymax − ymin where y = ymin, then 0 and y = ymax, then 1.0 6. Inputs to the simulation model are: EB545 – Corporate Finance 190 a. x distribution cumulative frequency; b. cumulative frequency of the normalized y distribution; c. value of y for each pass: y = ymin + ( ymaxx − ymin x )( ynorm) x where, yminx = minimum value of y, given a sampled x ymaxx = maximum value of y, given a sampled x ynorm = value of the dimensionless, normalized y distribution y = computed value of r.v. y to use for each pass. EB545 – Corporate Finance 191 Securities Markets • Primary functions are resource allocation and exchange of assets. • Role of Different Segments of Security Markets • Mechanics of Securities Markets 1. Brokers and Brokerage Firms 2. Type of Accounts 3. Types of Orders • Role of Regulation EB545 – Corporate Finance 192 Types of Security Markets 1. Primary or "New Issue" Market • Involves only new stock or bond issues. • Ex.: New sale of Texaco stock or Treasury bills. • Major component of primary market is the bond market. About 3/4's of all new corporate issues are bonds. ncluding government issues makes this percentage even higher. • Investment banker or underwriter Middleman in the primary markets. Ex.: Merrill Lynch or Salomon Bros. For well-known issues, new issue is boughts by investment banker and then resold to investors. • Underwriting a new issue Gurantee of a successful issuance. Underwriter syndicate utilized to share risk, purchase cost and geographical allocation. EB545 – Corporate Finance 193 • How is new issue price set? Negotiated Privately agreed upon Auctioned competitively (i.e., state and local bond issues) Prevailing prices for comparable issues Current market conditions dictate an issue's price. 2. Secondary or "Used Issue" Market • Provides a means for trading existing securities among investors. • Ex.: NYSE, OTC market, etc. • "Market-makers" - professionals who hold an inventory of a stock. Provides marketability Allows for easy transfer from sellers to buyers. "Specialists" on organized exchanges and "delaers" in the OTC. EB545 – Corporate Finance 194 • "Organized exchanges" provide a fixed location where trading occurs. • "OTC" market is not physically located in one place; it is a communications network. • Pricing Securities in an "Auction" market. Prices determined by bidding of market participants called brokers. Occurs in organized exchanges • Pricing securities in a "Negotiated" market Involves a dealer network Dealers stand ready to buy/sell securities at their specifed prices. Dealers do have a vested interest because they buy (sell) securities from (to) you. Dealer's profit comes from the difference in their "bid-ask spread" - the price at which they will buy (bid) and sell (ask). Ex.: OTC market for stocks and government securities. EB545 – Corporate Finance 195 • New York Stock Exchange (NYSE) Largest and most prominent secondary market for stocks. Over 200 issues are traded here. Represents over 75% of the dolar volue traded in the U.S. ("Big Board") 1400 members - partners or directors of brokerage firms. 25% of members are specialists - assigned specific stocks and one of the 89 trading posts on the exchange's floor. • American Stock Exchange (AMEX) Organization and trading procedures similar to NYSE. Smaller nationally organized exchange. Fewer seats (650) and stocks listed (1000) Listing requirements are also less strict. Smaller (especially energy and natural resource companies) dominate the types of firms listed/ • Regional Exchanges Listing requirements are more lenient. Specialize in smaller companies with limited geographical interest. "Dual listings - chief attraction is lower commissions. Ex.: Boston , Cincinnati, Midwest, Pacific Coast Stock Exchanges EB545 – Corporate Finance 196 • Over-the-Counter (OTC) Market Smaller firms tend to be found in the OTC market (over 10,000) Trades take place by telephone or other telecommunication devices. NASD (National Association of Securities Dealers) Markets exist for stocks, bonds, federal securities, municipal bonds, negotiable CD's, mutual funds, etc. Three levels: "national market", "regular market" and "additional OTC" NASDAQ - The NASD Automated Quotation System - computerized system that provides quotations on up to 3500 stocks. • Listed Options Offer trading in standardized call and put option contracts. Listed call-put options are traded on the Chicago Board Options Exchange (CBOE), AMEX, NYSE, etc. EB545 – Corporate Finance 197 3. Participating in the Market • Cash Account Cash transactions only "Type 1" account • Margin Account Buy securities with a combination of cash and borrowed funds. "Type 2" account By using securities as collateral, you may borrow a certain percentage of the purchase price, called margin. Margin call - requirment to put up more collateral when doolar amount of collateral falls below a certain level. Note: Using margins can increase or decrease your potential investment returns - "leveraged" investment. Because margin magnifies both gains and losses, using a margin account is a much riskier type of investing. Ex.: Assume: 1. You buy 200 Exxon shares at $50 per share. 2. Margin requirement = 50% 3. Broker loan rate = 8% EB545 – Corporate Finance 198 • Asset Management Account Combines checking, credit card, money market and margin accounts. Funds are moved among accounts to minimize your interest expense and maximize short-term yields. Simplifies cash management problems. • "Street-Name" Account Securities are left with a broker Offers safe storage and makes trading easier. Alternative to taking delivery. 3. Types of Trade Positions • Long Position Involves initially purchasing a position in the hope that the security's price will increase. Objective in being long is to buy low and sell high. Entitles you to any dividends or interest paid plus the capital gains. Strategy when you are "bullish" about a security's future prospects. EB545 – Corporate Finance 199 • Short Position Involves initially selling a security in the hope that the security will decline in price. Objective is still to buy low and sell high - however, you reverse the order of the transaction. "Bearish" strategy. Mechanics: 1. Your broker borrows the security or shares from the account of another customer (or brokerage firm). 2. He then sells the security to you. 3. Sale proceeds are held in escrow until you liquidate your position by buying back the (replacing the borrowed) security. 4. If the security is purchased at a lower price in the future, then you realize a capital gain and vice versa. EB545 – Corporate Finance 200 5. Types of Orders • Market Order - Buy or sell ASAP at the best price available. • Limit Order - Restricts the order to a specified price. • Stop-Loss (Stop) Order - An order to buy (sell) a security when its market price trades at or above (below) a specified level. EB545 – Corporate Finance 201 Regulation of Securities Markets Securities Act of 1933 • Major Objective - Full disclosure in order to protect investors from fraud and to provide them with a basis for informed judgments. • Applies to all interstate offerings to the public over a certain amount ($1.5 million). Note: Does not apply to government and regulated industry offerings. • Securities must be registered at least 20 days before offering. • Company must issue a prospectus. EB545 – Corporate Finance 202 Securities Act of 1934 • Major Objective - Applies full disclosure principle to secondary securities markets. • Creation of the Securities and Exchange Commission • SEC's purpose is to regulate the organized securities markets. • Requires registration and regulation of national security exchanges. • Regulates insider trading. • Watches for price manipulation. • Gives SEC power over proxy machinery and practices. • Gives Federal Reserve Board the power to set margin requirements. Blue-Sky Laws EB545 – Corporate Finance 203 • State laws which govern securities issues and matters in individual states. • Company must be registered or "blue-skyed" in state to issue shares there. • Individual states have tougher rules and regulations on the sale of securities than does the SEC. Industry Self-Regulation • National Association of Security Dealers (NASD) • Individual exchanges • Control trading practices among their members. EB545 – Corporate Finance 204 Financing vs. Investment Decisions • Financing decisions involve the firm directly in capital markets. • Capital Markets: Any activity which serves to allocate resources to their most productive activity. • Capital markets generally work well with respect to the efficient allocation of resources. EB545 – Corporate Finance 205 Differences between Investment and Financing Decisions 1. Not the same degree of finality; financing decisions are easier to reverse, i.e. higher abandonment value. 2. More difficult to generate rents or positive NPV's with financing decisions - more competitive market. • All firms compete in financial market. • Investment market is differentiated in terms of competition. EB545 – Corporate Finance 206 Efficient Capital Markets (Informationally) • Def.: An efficient capital market is one in which market prices fully reflect all information available at that time ("well functioning"). • If capital markets are efficient, then purchase or sale of any security at the prevailing market price is never a positive NPV transaction. • Implication is that information is widely and cheaply available to investors and that all relevant and ascertainable information is already reflected in security prices. EB545 – Corporate Finance 207 1. Abnormal Returns - An abnormal return of firm i at time t is the deviation between its realized return and the expected return as per CAPM model. 2. "Beating the Market" (risk-adjusted basis) - Must take risk into consideration before deciding if you "beat the market". 3. Ex ante vs. ex post market efficiency - The key here is that if the information had been available to you ex ante could you have earned abnormal returns. 4. Consistency - Are abnormal returns luck or consistent behavior? EB545 – Corporate Finance 208 Three Forms of Market Efficiency 1. Weak Form - Def.: Prices reflect all information contained in the record of past prices. • "Random-walk" model a. Prices changes are random. b. Given a price, the size or direction of next change is unknown. • "Technical Rules" a. Used by investors to exploit "patterns" they claim to see in stock prices. b. Weak form would suggest these are inappropriate rules because there is no useful information in the sequence of past changes in stock prices. EB545 – Corporate Finance 209 • Tests of Random-Walk Model a. Is there statistical evidence that the "random-walk" model does not hold? b. Is there economic significance? • Serial correlation studies: Is today's price significantly related to yesterday's price? • Result: There is slight statistical significance but not economic significance. • Runs Test: Are there more positive or negative price changes over a given period than at random? (Looking at a string of price changes.) • Results: No difference than at random. • Implications of Random Walk or Weak Form a. If prices always reflect all relevant information, then they will change only when new information arrives. b. However, new information by definition cannot be predicted ahead of time. c. If stock prices already reflect all that is predictable, then stock price changes must reflect only the unpredictable. d. Therefore, the series of changes must be random. EB545 – Corporate Finance 210 • Two Important Notes Concerning Random Walk Model: 1. Randomness is often confused with irrationality; however, randomness is the predicated result of rational valuation. 2. Random Walk Hypothesis does not say actual prices are random but that price changes are random (size and direction). EB545 – Corporate Finance 211 2. Semi-Strong Form - Def.: Prices reflect not only past prices, but all other published or publicly available information. • Empirical Tests: a. Reaction to earnings announcements. b. Reaction to stock splits and dividend announcments. c. Effects of secondary distributions Large blocks sold outside of market hours generates "combination effect" Liquidity effect drives price down because it is a large block (temporary phenomenon). Information effect drives price down but does not come up. Combination effect is that price drops and comes back partially, NOTE: Key here is that most of this information was rapidly and accurately impounded in the price of the stock. EB545 – Corporate Finance 212 • Anomalies (Risk-Adjusted Basis): a. P/E Effect - Low P/E stocks have positive abnormal returns; high P/E stocks have negative abnormal returns. b. Size Effect - Small firms on average have earned positive abnormal returns; large firms, on average, earn negative abnormal returns. NOTE: Both a & b could be caused by the fact that there is more information risk in small firms. c. January effect - Firms tend to do better in January (generate higher returns). d. Day of the Week Effect - Monday's tend to have lower returns than other days of the week. e. Value Line Investment Survey - Abnormal returns could be earned if you could trade the instant Value-Line was available. NOTE: Semi-strong form is most commonly accepted form by academics and practitioners. EB545 – Corporate Finance 213 3. Strong Form - Def.: Prices reflect all information contained in the record of past prices. EB545 – Corporate Finance 214