1 CORPORATE FINANCE OUTLINE FALL 1997 SIEGEL 1. valuations -PV, future cash flow, risk estimation, project valuations, contemporary financial theories 2. analysis of how mrkt works -in what conditions (under what legal & economic structures), why I. NPV -Chapter 4 1. discounted cash flow a. reasons for focusing on cash flow 1. cash is objective 2. cash is useful -tangible 3. cash tells us how much we can invest 4. real net income from business only knowable when business shuts down & can compare cash in vs. cash out 2. goals -to reduce level of ambiguity & reach decision to invest or reject 3. terms a. PV -worth now at time 0 • PV = C /(1+ i) → one period case b. NPV -difference btwn future cash flow & current price of investmt • NPV = -c + sums of PV/(1+ i )^n c. FV -worth in future at a specific point 1. measured by time value of $, time risk, amt of cash flow → multiple period case • FV = c (1+i)^n, c is initial investmt • FV = c (1+i/x)^n(x) -interest rate & # of periods have to be consistent → compounding periods d. PMT -regular paymt • length of annuity depends on time, interest rate & amt of per paymt e. i a. if compounds more frequently then effectively higher interest rate than nominal → compounding periods • nominal = c (1 + i/n) ^ n • effective = [(1 + i/n) ^ n] -1 b. continuous compounding used in business • FV = PV (e)^i(n), e is constant of 2.718 • bldg or investing now is better b/c compounding feature of interest rate & inflation f. n -referring to end of period b/c paymts made at end of each period w/exception of rent 4. simplifications a. perpetuity -constant stream of cash flows w/out end 1. ie, consols 2. PV = C /i b. growing perpetuity -growing return rate 1. PV = C /(i -g) c. annuity -level stream of regular paymts that lasts for fixed # of periods 1. ie, leases, mortgages, pension plans 2. use PMT button on calculator 3. PV = C [ (1/i) -(1/i(1+i)^n)] → not covered in class d. growing annuity -finite # of growing cash flows due to real growth or inflation 1. formula & concept not covered in class 5. what is a firm worth? a. not covered in class 6. risk a. idiosycratic risk b. systemic risk -expectation of inflation, difference btwn longterm & shorterm risk c. uncertainty of return on investmt 2 7. taxes -paying later is better than paying now b/c taxes don’t take into account PV calculations II. Valuation of Bonds & Stocks -Chapter 5 1. bonds -borrower owes specified sum (interest + principal) a. valued as an annuity b. paid semiannually c. interest rate 1. compounds annually 2. mrkt rate can differ daily from face rate & more greatly in longterm a. premium -sale price is greater than face value b. discount -sale price is less than face value 3. real rate determined by: a. inflation b. expected industrial activity c. GNP d. differences btwn longterm & shorterm debt structures d. not really risk free b/c real interest rate fluctuations 1. price of bond decreases (value of all investmts) as interest rate increases 2. bond prices & investmt values increases as interest rate decreases e. mrkt assumptions 1. mrkt is not immediatly at equillibrium -fluctuates until equillibrium is reached 2. buyers & sellers make the mrkt 3. both buyer & seller think that they are getting a good deal when buying & selling at premium or discount f. types 1. pure discount bond (aka zero coupon bond) -no periodic paymts, only one lump sum paymt at end including principal & interest a. ie, US savings bond b. PV = F /(1+i)^n, F is face value of bond 2. level-coupon bond -typical bonds that offer level coupon (interest) paymts semiannually for life of bond & then balloon paymt at end (principal + interest for that period) a. examples 1. consumer debts -level paymt, same paymt amt each time that covers interest & principal 2. commercial loans -partially amoratizing, loan for 30yrs but treat as if paid over 5yrs (at 30yrs rate & one lump sum paymt at end), leads to refinancing • banks like b/c less riskier for them a. concern over inflation drives up interest rates so banks don’t like to be locked into lower interest loans b. borrower bears risk of mrkt fluctuation b. PV = sum of PV of interest paymts + [$1000/(1 + i) ^ n] 1. PV of interest paymts 2. PV of face value 4. consols -consolidated English bonds, only pays interest indefinitely, never recover principal a. PV = PMT/i → PV of annuity in perpetuity • reasons for having these types of bonds 1. deferring interest is best deal 2. potential tax advantages -if don’t receive paymt then don’t have to pay taxes, then receiving effectively higher interest rate on return 3. depends on terms & how they affect risk • affect of principal on PV of bond as a function of time -longer the investmt period, more risky b/c uncertainties in mrkt 1. longterm bonds -principal has less affect on PV of bond so demand higher interest rate 2. shorterm bonds -principal affects PV of bond 3 2. stocks a. difference from bonds 1. stocks -fixed dividend paymts but varying end paymt (sale) 2. bonds -fixed interest paymts & fixed lump paymt at end b. PV based on dividend paymts & capital gains 1. zero growth stocks -stock w/constant dividend a. PV = div /i, i = return rate 2. constant growth stocks -stock w/growing dividend a. ie, growing perpetuity b. PV = div /( i -g), i = discount rate 1. g = (retained earnings/total earnings) return rate on retained earnings 2. i = (div /PV) + g 3. differential growth stocks -not covered in class c. valuing firm 1. external approach -take NPV of growth opportunity to determine increase in value of co. due to growth opportunity 2. internal approach -discount expected future cash flows from investmt, then take assets of co. & divide by # of shares to arrive at new value of co. 3. dividend policy does not affect value of firm -distributive cash is not same as net income which is earnings minus costs a. if co. earns 10% & can reinvest at 9%, co. should not reinvest it so shareholders can invest elsewhere for at least 10% → but done for other reasons b. if co. earns 10% & can reinvest at 12%, co. does not always but distributes at least part 1. to keep shareholders from selling & investing in another stock b/c they invest expecting some return now 2. to signify to mrkt that it is healthy enough so has no need for $ 4. problems a. discounting by steady growth rate is inaccurate b/c no co. can sustain such continued compounded growth indefinitely, empirically impossible b. assumes that mrkt knows what is going on c. assumes that mrkt operates efficiently d. assumes that there are no transaction costs affecting dividend rate d. growth opportunities 1. when firm acts as a cash cow -distributing all of its earnings a. EPS /i = div /i 1. EPS = net income/# of share outstanding 2. problems w/this approach -no analytical significance a. net income -no agreemt on what constitutes or how it should be calculated, can be seriously affected by nonreoccuring event b. # of shares outstanding -generally use weighted average of shares outstanding but problems when co. issues new or buys back shares, preferred stock convertible to common shares, stock options (usually reflected in fully diluted #) c. 4 possible different EPS 1. net income that includes one time extraordinary events 2. net income that excludes one time extraordinary events -Speigel 3. # of shares excluding all misc. shares 4. # of shares including all misc. shares to arrive at fully diluted # of shares -Speigel a. stock price after commitmt = (EPS /i) + NPVGO, NPVGO = NPV of growth opportunity e. price-earnings ratio 1. price per share/EPS = (1/i) + (NPVGO/EPS) 4 a. problems w/P/E ratio 1. P/E uses earnings as of end of prior yr & price at close of yesterday 2. rate of return does not equal dividend divided by purchase price 3. price per share is based on expected future earnings & other factors & not past earnings per share b. utility 1. relative comparison of P/E ratios → higher P/E ratio means it has a higher expected return than another stock w/lower P/E ratio III. Alternative Investmt Rules -Chapter 6 1. payback period rule -looking at how long it will take to recover investmt based on project’s expected cash flow a. benefits 1. longer payback period has more risk 2. earlier payback allows one to reinvest at higher rates or may need $ back by certain time b. problems 1. doesn’t consider paymts beyond payback period 2. doesn’t consider timing of recovery -recovering more $ sooner is better than later c. cures 1. discounted payback rule -discount paybacks & figure out when investmt is recovered a. problems 1. doesn’t consider timing after recovery 2. ignores really important factor of what happens after receiving payback 3. doesn’t provide any criteria for investmt decisions 2. average accounting return on investmt (ARR/ROI) -average project earnings after taxes & appreciation, divided by average bk value of investmt during its life → compare this % figure to co. required rate of return a. ARR = average net income/invesmt, accounting net income, answer is % b. problems 1. doesn’t tell us the significance of this figure 2. doesn’t reflect project’s risk 3. uses backward looking data 4. uses net income instead of cash flow which is more concrete data a. net income varies depending on method used b. additional capital investmts made throughout life of project is not captured b/c averages it all out c. doesn’t capture timing also 5. compares to an arbitrary rate of return, we don’t know where it comes from 6. doesn’t tell us if we should invest or not c. cure 1. comparative study of similarly situated firms w/similar risk levels to see if one ARR is better than others (the higher the better) 3. internal rate of return (IRR) -that rate of return (%) that makes NPV = 0 a. rule -compare this figure to discount rate to determine whether to accept or reject project 1. consider project as if co. was borrowing -cash inflow then cash outflow a. accept project if IRR < discount rate b. reject project if IRR > discount rate 2. consider project as if co. was lending -cash outflow then cash inflow a. accept project if IRR > discount rate b. reject project if IRR < discount rate b. context 1. independent project -one whose acceptance or rejection is independent of that of other projects 2. mutually exclusive projects -can reject both but cannot accept both c. utility 5 1. operates as a benchmark d. limitations 1. investing or financing -leads to 2 different rules a. consider project as if co. was borrowing -cash inflow then cash outflow 1. accept project if IRR < discount rate 2. reject project if IRR > discount rate b. consider project as if co. was lending -cash outflow then cash inflow 1. accept project if IRR > discount rate 2. reject project if IRR < discount rate 2. multiple rates of return -when there are reversals of cash flows, there will be multiple correct nominal rates of return 3. for mutually exclusive projects a. scale -while one project may have IRR, other project may have considerably higher absolute return → not considered in this approach 1. potential cure -calculate incremental IRR which is the IRR on the incremental investmt from choosing larger project instead of small project & compare it to discount rate b. timing -earlier recovery of $ may have higher PV depending on discount rate → not considered in this approach 4. profitability index -ratio of PV of future expected cash flows after initial investmt divided by amt of initial investmt → didn’t go over in class a. rule accept independent project if its PI > 1, reject if PI < 1 b. PI = PV of cash flows subsequent to initial investmt /initial investmt c. problems 1. leads to wrong decision for mutually exclusive projects 2. cannot handle capital rationing over multiple time periods 5. net present value a. rule -accept project if it has positive NPV & reject if negative NPV, indifferent if NPV = 0 b. NPV = -C + PV of all parts c. advantages 1. qualitatively & quantitatively decisive 2. discounts back all estimated future cash flows a. includes costs of avoidance -ie, if buying instead of renting bldg, would include as part of cash flow avoided cost of paying rent 3. leads to definite conclusions a. investmt decisions b. can determine how much value project adds to firm c. permits adjustmts for differences in scale & time of multiple investmts -“finding the biggest bang for your buck” 1. compare profitability index of various projects c. limitations 1. doesn’t provide investmt strategy when $ constraints • making no investmt is an investmt where NPV will be 0 at best 2. difficulty in comparing projects of different duration a. don’t know what will happen beyond a certain point so can’t estimate cash flows to discount them back b. may not always be better to recover more $ at beginning if earning a high rate of return → b/c these high return opportunities less likely to exist c. may not always be better to invest $ now for bld to last only a few yrs vs. longer 3. difficulty in comparing projects of different scale (different investmt amts required & different return amt) a. doesn’t consider availability of other projects b. doesn’t consider amt $ available so may be able to invest in more than one project 6 6. real world -most co. use combination of these methods, most popular being NPV, payback, accounting return method IV. NPV & Capital Budgeting -Chapter 7 1. incremental cash flows a. cash flow is not net income but projects net income numbers to come up w/cash flow projections 1. examples a. operating expenses b. operating revenues c. depreciation -add into positive cash flow d. capital expenditures -add into negative cash flow e. working capital -add into negative cash flow (will usually recover at end) 1. to cover $ used for inventory before products are sold to bring in revenue 2. to cover $ that hasn’t not been received through account receivables 3. to operate as a cash buffer f. corporate taxes g. operating cash flow -net of above factors h. opportunity costs -add into negative cash flow i. inflation -taken into account via discount rate, have to be consistent w/its application 2. have to pick base yr to project from 3. terminal value projection a. uses last projectable yr as base yr b. uses net income & not cash flows c. valued as permanent annuity b. sunk costs -costs that have already occurred → ignored in the analysis c. opportunity costs -forgone opportunities of using the assets by taking on a project → included in analysis d. side effects -effects on other parts of the firm caused by proposed project → included? 1. ie, erosion -cash flow transferred to new project from customers & sales of other products of firm 2. cash flow = sales revenues -operating costs -taxes + (machine + opportunity cost + in net working capital) • figures expressed as negative # a. operating cash flow after taxes = revenues -expenses -taxes b. net working capital -different btwn current assets & current liabilities c. taxes = tax rate (revenues -expenses -depreciation) d. interest expenses → not reflected in cash flow but in discount rate 3. inflation & capital budgeting a. interest rate & inflation 1. nominal interest rate 2. real interest rate similar to (nominal interest rate -inflation rate) • real interest rate = [ (1 + nominal interest rate) /(1 + inflation rate) ] -1 b. cash flow & inflation 1. nominal cash flow 2. real cash flow -same equation as above c. discounting 1. nominal cash flows must be discounted at nominal rate 2. real cash flows have to be discounted at real rate 4. investmts of unequal lives -equivalent annl cost method a. attempting to determine whose operating costs have lower NPV b. replacemt chain problem 1. can match cycles a. limitations -assume long time horizon 2. can calculate equivalent annl costs 7 3. limitations -assumes replacemt V. Strategy & Analysis in Using NPV -Chapter 8 1. creating positive NPV a. introduce new product/technology b. create barrier to entry c. create product variation d. utilize organizational innovation 2. decision trees -used to identify sequential decisions in NPV analysis where future outcomes are uncertain a. analysis 1. apply values/payoff (single #) to future outcomes 2. multiply this # to its probability of occurrence a. total probability is 1 or 100% b. probability of certain outcome on some branch is mulitiplication of probabilities of branches 3. expected payoff = (probability of success x payoff if successful) + (probability of failure x payoff if failure) 4. discount back to present using risk-free rate a. already seem to be discounting risk so only need to discount at risk-free rate b. purpose 1. way of summarizing NPV that is indeterminate a. about projecting possibilities & not necessarily outcomes b. doing more than just measuring cash flows but valuing choice → core of options trading 2. leads to decision to invest amt & in what form or to just abandon 3. shows that decisions themselves also have value c. examples 1. actuarial tables used in determining costs & benefits of life insurance 3. sensitivity analysis -measures how sensitive a particular NPV calculation is to changes in underlying assumptions a. assumptions 1. revenues -function of mrkt share, size of mrkt, price/product 2. costs a. variable costs -changes as quantity of output changes, 0 when production is 0 → proportional to production b. fixed costs -fixed over a predetermined time period b. purpose 1. try to identify items of potential uncertainty that are most likely to affect outcome of project c. limitations 1. may give false sense of security b/c pessimistic forecast may be optimistic 2. treats variables in isolation when they may be related d. scenario analysis -variant of sensitivity analysis that examines # of likely scenarios 4. break-even analysis -determines sales necessary to break even a. accounting profit break-even point = [ (fixed costs + depreciation) (1-tax rate) ] /[ (sales price -variable costs) (1 -tax rate) ] 1. depreciation understates true costs of recovering initial investmt b. PV break-even point = [ EAC + fixed costs (1-tax rate) -depreciation (tax rate)] /[ (sales price -variable costs) (1 -tax rate) ] 1. initial investmt can be treated as an equivalent annl cost (EAC) for fixed # of yrs • EAC = initial investmt /x yrs annuity factor at y % c. purpose 1. answers question of how low, ie, sales can drop before NPV will equal 0 5. options 8 a. option to expand b. option to abandon c. such options should be included in project’s value to calculate true value of project & to decide whether to pursue & in what amt & in what form • mrkt value of project = NPV + options values VI. Capital Mrkt Theory Overview -Chapter 9 1. deals w/capital budgeting w/risky cash flows a. necessary to find a way to measure risk b. calculation contribution of stock to risk of entire portfolio c. β is appropriate measure of contribution of stock to risk of lg portfolio d. investors will hold risky stock only if its expected return is high enough to compensate for its risk • expected return on stock = risk free rate + β(expected mrkt return rate -risk free rate) → CAPM e. relationship btwn risk & return derived differently by arbitrage pricing theory f. if project has same risk as firm & firm is all equity financed, expected return on stock should be project’s discount rate 2. returns a. $ returns • total return = dividend income + capital gain/loss 1. dividend yield -% of income return 2. capital gain -change in price of stock divided by initial price b. % returns • % return = (divident paid at end of period + in mrkt value over period) /beginning mrkt value c. holding period returns -includes return from reinvesting dividends 3. statistics → deviations from average return is risk a. average/mean = sum of all values divided by total # of values • average of returns is the expected return b. variance ( δ^2) -amt deviating from mean of expected return c. standard deviation ( δ) -square root of variance • square to give more weight to those returns that deviate more from mean (expected return) 4. discount rate for risky projects a. if risk of project is equal risk of mrkt • expected return on mrkt portfolio = risk free rate + expected risk premium • risk premium = mrkt return -risk free return b. if risk of project is different from risk of mrkt, appropriate discount rate for project is not project’s standard deviation of project’s return but involves determining effect of asset on total risk of investor’s portfolio 5. risk a. diversification -total risk is lower than risk of components b/c can eliminate idiosyncratic risk although not systemic risk b. β coefficient of stock -represents stock’s risk 1. tells us tendency of stock to covary w/mrkt 2. CAPM tells us that β is appropriate measure of stock’s risk & not its standard deviations VII. Return & Risk : CAPM -Chapter 10 1. individual securities a. expected return -average of stock’s returns b. variance ( δ ^ 2) -measures variability of stock’s return therefore its risk 1. calculate expected return (average of stock’s return) 2. calculate deviations from expected return 3. square deviations 9 4. average squared deviations c. standard deviation ( δ) -square root of variance 1. take square root of variance d. covariance -measures interrelationship btwn 2 stocks 1. multiply A’s deviation from its expected return & B’s deviation from its expected return 2. calculate average of these of all such figures • δ of A,B = expected value of [ (A return -A average return) x (B return -B average return) ] 3. just correlation btwn securities multiplied by standard deviations of each e. correlation 1. divide covariance by standard deviations of both • correlation btwn A,B = δ of A,B /(δ of A x δ of B) 2. positive correlation -both are above or below their respective average returns at same time, perfect if 1 3. negative correlation -one is below its average return while other is above its average return, perfect if -1 4. uncorrelated -return on one is completely unrelated to return on other, 0 • usually not whole #s • most stocks are positively correlated w/each other 2. portfolios a. consider: 1. relationship btwn expected return on securities & expected return on portfolio containing these securities 2. relationship btwn δ of individual securities & their correlations & δ of portfolio made up of these securities b. expected return -weighted average of expected returns of individual securities • expected return on portfolio = (% of A x A average return) + (% of B x B average return) c. variance → risk of portfolio • variance of portfolio = (% of A ^ 2 x variance of A) + ( 2 x % of A x % of B x covariance of A,B) + (% of B ^ 2 x variance of B) 1. positive covariance btwn 2 -increases variance of entire portfolio 2. negative covariance btwn 2 -decreases variance of entire portfolio → hedge d. standard deviation -square root of variance 1. measures variability of each security e. diversification effect -standard deviation of portfolio is less than weighted average of standard deviations of individual securities as long as correlation of securities is < 1 1. when correlation = 1, portfolio standard deviation is equal to weighted average of standard deviations of individual securities 2. in portfolio as more securities are added, portfolio variance drops & becomes the covariance → elimination of idiosyncratic risk but retention of systemic risk 3. in portfolio as more securities are added, covariance btwn securities remain → systemic risk remains • risk of security in portfolio = portfolio risk -diversifiable risk • graph -x-axis # of securities, y-axis variance of portfolio’s return (risk) -curve 3. efficient sets of 2 assets a. graph of x-axis standard deviation of portfolio’s return (%) (risk), y-axis expected return of portfolio (%) → backward curve btwn 2 points 1. greatest bend when correlation is perfectly negative 2. straight line when correlation is perfectly positive b. MV = minimum variance portfolio → greatest return for least risk c. efficient set -that portion of curve including & above MV to high point • no matter how many investmt choices we add, will always add up into another curve • in mrkt curve, risks of all individual investmts will be under curve 10 4. riskless borrowing & lending -borrowing to invest in risky asset a. borrowing increases variability of investmt b. capital mrkt line -represents efficient set of all assets, risky & riskless asset is straight line c. separation principle -investor makes 2 separate decisions 1. estimates expected return & variances of individual securities, covariance btwn them, efficient set of risky assets, tangent btwn risk-free rate & efficient set of risky assets 2. determine how to combine portfolio of risky assets w/riskless asset 5. mrkt equilibrium a. mrkt portfolio -in world of homogeneous expectations (returns, variances, covariances), all investors would hold portfolio of risky assets represented by point A b. β of security in portfolio -risk of security in portfolio is its β 1. β = covariance btwn return on security & mrkt /variance of mrkt δ^2 • standardized covariance btwn return on security & on mrkt 2. purpose a. provides a relationship btwn systemic risk of individual security to risk of mrkt b. measures sensitivity of change in return of security to change in return of mrkt portfolio c. used to project expected return & not actual returns d. used to calculate discount rate • systemic error -object is to find out how much we should pay now for expected return but here using β that is based on historical data which measured actual return & not expected return 3. factors affecting β a. time period used to get β matters • Fama & French criticism a. for period of 1963-1990 relationship btwn β & expected return is weak b. relationship btwn expected return & firm size c. relationship btwn expected return & bk equity (BE)/mrkt equity (ME) d. issue -time period for which β is calculated b. sensitive to change in debt structure c. sensitive to material change in portfolio of investmt assets • isn’t affected by changes in mgt or product • those types of changes affect idiosyncratic risk which gets reflected in security price 4. generally a. β of most securities are positive b. β of few securities are negative • means that security’s return & risk < risk free • may be possible b/c risk free govt bonds is not effectively risk free c. firm β is different from its security β 5. graph -x-axis return on mrkt (%), y-axis return on security (%) a. characteristic line -line’s slope is β of security 6. implications a. average β across all securities weighted by proportion of security mrkt value to mrkt portfolio is 1 6. relationship btwn risk & expected return a. expected return on mrkt = risk free return + risk premium 1. best estimate of risk premium in future is average risk premium in past 2. risk a. idiosyncratic risk -can be eliminated by diversification b. systemic risk -cannot be eliminated by diversification • tends to be less than idiosyncratic risk b/c is a compilation of all idiosyncratic risks of all stocks 3. empirical relationship btwn risk & return 11 a. durable over time b. linear relationship c. over shorter periods, there may be more volatility for each stock & w/in industry b/c inflation 1. bonds -inflation can affect real rate of return although will get fixed nominal rate • nominal return = interest paymt + difference in purchase & sale price 2. stocks -inflation will already be adjusted for in mrkt price but will be at risk of es in inflation if hold longterm • nominal return = dividend paymt + difference in purchase & sale price b. CAPM: expected return on security = risk free rate + β of security (expected mrkt return -expected risk free return) 1. mrkt risk premium = expected mrkt return -expected risk free return a. depends on inflation, state of economy 2. implications a. relationships dealing w/β 1. expected return on security is linearly related to its β 2. higher β securities have higher expected return than low β securities 3. also holds for expected return on portfolios 1. β of portfolio -weighted average of β of its securities b. suggests that idiosyncratic risk (negative & positive) of securities can be eliminated via diversification in a portfolio c. applicability 1. not applicable to options (put & call) 2. applicable to investmts in projects & stocks 3. security mrkt line (SML) -graph x-axis β of security, y-axis expected return on security (%) a. intercept is risk free rate b. slope -upward if expected return on mkrt > risk free rate c. securities above this line are underpriced (trading at discount) d. per class -adding risk free invesmt produces tangent line called the SML (security mrkt line) 1. lower portion of SML occurs in real world → CML a. CML (capital mrkt line) -represents line that would be created by using portfolios 2. upper portion of SML created by leverage (borrowing) a. ie, borrowing at lower rate than rate where one can invest b. line does not extend out indefinitely -stops when β = 2,3 c. leveraging produces fixed outflow from variable inflow d. spread of return for leveraged portion is higher indicating higher risk e. reality 1. lower risk produces higher return than model asserts b/c has lower price 2. higher risk produces lower return than model asserts b/c has higher price 3. developed from CML a. if consider systemic risk of security & measure that against return it offers, there is line coincident to CML which is SML b. SML represents potential returns that can be had by manipulating securities 4. relationship to CAPM a. SML is basis of CAPM 12 b. CAPM suggests that all securities will reach an equilibrium that will place them on the SML 5. in reality line is not perfect a. sometimes line tilts down → lower risk can produce higher return b. sometimes line has smaller slope → taking higher risk doesn’t reward as much in return 4. SML vs. CML (see above also) a. CML -traces efficient set of portfolios formed from risky assets & riskless asset • y-axis is expected return on portfolio, x-axis is standard deviation (δ) of portfolio • only for efficient portfolios b. SML -relationship btwn expected return w/β for securities & portfolios • holds for all securities & portfolios 5. assumptions a. investors are knowledgeable b. investors are rational c. investors are profit maximizing d. investors are risk averse 1. risk of getting 1 more $ < risk of getting 1 less $ • greater utility at lower end than at higher end • although probability may be same • rare cases where people seek risk, ie, playing lottery 2. applies at any point 3. applies to all items 4. applies to large actors also 6. function a. to determine how much one should pay for future cash flows b. to determine what appropriate discount rate should be c. discount rate has to do w/inherent risk of investmt relative to mrkt return rate for risk free & risky investmts at time investmt is made VII. Arbirtrage Pricing Theory -Chapter 11 1. APT & CAPM a. APT 1. positive relationship btwn expected return & risk 2. advantage a. specifies basis of correlation btwn returns on securities b. shows how diversification gets rid of idiosyncratic risk b. CAPM 1. measures correlation btwn returns on securities but does not specify basis of correlation 2. imply positive relationship btwn expected return & risk 3. advantage a. discussion of efficient sets 2. factor models a. actual return = expected part of return + unexpected part of return 3. risk -unanticipated portion of return a. systematic risk -risk that affects lg # of assets 1. ie, general economic conditions -GNP, interest rates, inflation b. idiosyncratic risk -risk that specifically affects a single asset or sm group of assets c. actual return = expected part of return + mrkt risk + idiosyncratic risk 4. systematic risk & β a. β -tells us response of security’s return to systematic risk (changes from expected inflation, GNP, interest rates) 1. positive inflation β if security is positively related to risk of inflation 13 2. negative inflation β if security is negatively related to risk of inflation 3. 0 β if security is uncorrelated w/inflation b. factor model 1. actual return = expected part of return + β of inflation of security (change from expected inflation) + β of GNP (change from expected GNP) + β of interest rates (change from expected interest rate = difference btwn long-term & short-term interest rates) + idiosyncratic risk • model may already take into account mrkt risk premium via its factors 2. disagreemt as to how many factors & which factors are appropriate to measure in this way 3. mrkt model : actual return = expected return + β of mrkt return (change from expected mrkt return) + idiosyncratic risk a. β is just merely security’s β same as that in CAPM 5. portfolios & factor models a. portfolio return is weighted average of returns of individual assets in portfolio b. portfolio return determined by following factors: 1. expected return on each asset 2. β of security multiplied by factor 3. idiosyncratic risk of each individual security • in equation -multiply weight of each security to all variables c. effect of diversification 1. eliminates idiosyncratic risks variables in equation 2. doesn’t affect systematic risk b/c it arises from positive covariances btwn securities 6. parametric approaches to asset pricing a. CAPM, APT 1. measure expected return on risky assets 2. measure risk of security by its β 3. expected excess return is proportional to its β b. empirical methods 1. look for patterns in history of mrkt data 2. relationship btwn these attributes & expected return c. mgt styles VIII. Risk, Return, & Capital Budgeting -Chapter 12 1. discount rate a. NPV -valued riskless cash flows b. CAPM, APT -can compute appropriate discount rate for risky cash flows 1. uses SML to determine firm’s required return -weighted average cost of capital (includes cost of equity & debt) 2. CAPM alone -problem b/c multiple regression method may produce discontinuous or cureved SML 3. APT alone -problem b/c impractical & expensive b/c requires data collection & comparison 2. cost of equity capital a. rule -discount rate of project should be expected return on financial asset of comparable risk 1. means that firm should undertake project if its expected return > expected return of financial asset of comparable risk b. cost of equity capital is expected return 1. expected return = risk free return + β (expected mkrt return -expected risk free return) 3. determinants of β -determined by characteristics of firm (& of projects) • β of CAPM & APT different a. cyclicality of revenues -function of systematic risk 1. highly cyclical -high β a. firms do well when in expansion phase of business cycle b. firms do poorly when in contraction phase of business cycle • ie, discretionary investmts like high tech entertainmt 14 2. not very cylical -low β • ie, essentials 3. different from variability -function of systematic risk & idiosyncratic risk • stocks w/high standard deviations do not necessarily have high β b. operating leverage -refers to firm’s fixed costs of production 1. higher operating leverage -lower variable costs & higher fixed costs a. higher risk than below, higher β 2. lower operating leverage -higher variable costs & lower fixed costs a. means that it is less risky, higher β 3. contribution margin -difference btwn price & variable cost a. less risk if contribution margin sm b. riskier if contribution margin is lg 4. general a. every firm has floor & ceiling of fixed & variable costs b. most costs are semi-fixed -certain level of variable costs become fixed costs c. financial leverage -refers to firm’s fixed costs of finance (debt) 1. equity β refers to β of firm’s stock a. equity β > asset β w/financial leverage • equity β = asset [1 + (debt/equity)] 2. debt β -generally very low, close to 0 • asset β = [equity/(debt + equity)] β of equity 3. asset β refers to β of firm’s assets • asset β = [debt/(debt + equity)] β of debt + [equity/(debt + equity)] β of equity a. higher asset β if ratio of debt to equity is higher b. asset β will double if debt equals equity 4. riskiness is function of 2 factors a. amt of debt b. interest debt bears relative to return of co. 4. asset a. asset value = (# of outstanding shares x price per share) + value of debt 5. extensions of basic model a. discount rate of firm 1. cost of capital w/debt (WACC) = weighted average of cost of equity (expected return of CAPM) & cost of debt (borrowing rate) • average cost of capital after tax = [ equity/(debt + equity) ] average cost of equity + [debt/(debt + equity) ] average cost of debt x (1 -tax rate) 2. always use mrkt values & not book values • possible that buyers are buying based on perception of good bargain & sellers selling on same b/c have different perceptions of expected returns b. when risk of project is different from risk of firm, project should be discounted at rate commensurate w/its risk 1. consider firm’s WACC as hurdle 2. consider project’s risk level b/c it will change overall risk level of firm IX. Efficient Mrkt Hypothesis -Chapter 13 1. efficient mrkts -those in which current mrkt prices reflect available info a. implications 1. positive NPV opportunities can’t exist a. info is reflected immediately in price so that investor does not have adequate time to trade on info to make profit b. inside traders should not be able to profit 2. financial mgrs cannot time issues of stocks & bonds • try to issue when stocks are overpriced to create value for current stockholders, wait if underpriced 15 • try to buy when underpriced a. empirical issue 3. firm can sell as many stocks & bonds w/out fear of depressing price a. firms will receive fair value for its securities b. empirical issue 4. stock & bond mrkts can’t be affected by firms artificially increasing earnings a. accounting methods should not affect stock price if: 1. provide sufficient info 2. mrkt must be efficient in strong form 5. unclear what amt of control is optimal in achieving mrkt efficiency or other objectives 2. capital-financing decisions a. how much debt & equity to sell b. what types of debt & equity to sell c. to create positive NPV in capital-financing 1. fool investors • if mrkt is efficient, can’t create value via this 2. reduce costs or increase subsidies 3. create new security • more capital-expenditure opportunities w/positive NPV than such capital-financing opportunities 3. different types of efficiency • report of past performances affects mrkt price through expectation of future cash flows b/c past performance affects expectation of future cash flows a. weak form -info on past prices • today price = last price + expected return + random error 1. theoretic justification -price of stock in well traded mrkt represents discounted PV of expected cash flows that consists of the known & unknown, therefore fluctuations of price is a function of the unknown a. random walk -price cannot be predicted based upon any known factors but changes b/c of randomness, previous price unrelated to future price 2. technical analysis -efforts to predict future from patterns of past price movemts • no good if mrkt is weak form efficient b/c this info is already taken into account by mrkt 3. serial correlation -correlation btwn current return on security & return on same over later period a. positive coefficient -toward continuation 1. higher than average return to be followed by higher than average return, lower than average return to be followed by lower than average return b. negative coefficient -toward reversal 1. higher than average return to be followed by lower than average return & vice versa c. significantly high positive & negative coefficient indicates mrkt inefficiencies • not the case in real life 4. empirical evidence -beyond 15min. evidence is strong, w/in 15min. it is not a. limitations 1. w/in this 15min., there is some connection btwn past movemt & current price 2. neural networks have been used to find patterns w/in this time period that show steady increase & then sudden drop → sufficiently lg investors trade based on this info & profit in excess of transaction costs • these investors taking advantage of such inefficiencies actually make mrkt more efficient b/c eliminates such inefficiencies b. contrary opinions/evidence 1. people try to find patterns in prices b/c they see patterns in randomness b/c they don’t know what randomness looks like, Harry Roberts 16 b. semi-strong form -prices reflect (incorporate) all publicly available info 1. implications a. fundamental analysis of data of co. & that of mrkt is useless b. prices reflect underlying value c. financial mgrs cannot time stock & bond sales d. can sell as many shares w/out depressing price 1. mrkt has unlimited ability to absorb lg blocks of stock, Scholes e. it makes no difference form or place of info disclosure b/c mrkt sees through form & place of disclosure 1. accounting choice irrelevant as long as: a. enough info provided in annl report b. mrkt must be semi-strong efficient, use all accounting info in determining mrkt price 2. switch from accelerated to straightline depreciation irrelevant, Kaplan 3. deferral method of accounting for investmt tax credit to flow through method irrelevant, Kaplan 4. pooling method compared to purchase method of mergers & acquisitions irrelevant, Hong, Kaplan 5. stock priced increased for firms switching to LIFO method of cost inventory b/c changing forms actually decreased tax liability → real effect on cash flow, Biddle f. should be the case that mrkt is only affected at time of disclosure g. only required info are: 1. report of info 2. report of method of info reporting 3. report of integrity of report h. regulation -evidence tends to support that regulation is necessary to ensure integrity of info released to mrkt • this form of efficiency does not say that regulation is irrelevant b/c mrkt does not uncover untruths but treats all info as true • some argue that this form of efficiency implies that regulation is unnecessary a. criticisms 1. not everything has a mrkt 2. empirical evidence lacking that mrkts takes into account all info a. only empirical evidence has been annly reports, quarterly reports, depreciation, purchasing vs. pooling interest 3. don’t show that there would be disclosure absent regulation • amt of control optimal in achieving mrkt efficiency or other objectives unclear 2. evidence tends to support this form most strongly a. event studies -statistical studies examining whether release of info influences returns on other days 1. news tends to leak out & be reflected in stock prices before offical release 2. Fama, French cumulative abnormal return study of stock splits -found abnormally high returns around time of stock split announcemt, suggested that stock split released info to mrkt of future dividend increases, value increase 3. ie, stock prices drop on date of announcemt of CEO death 4. IPO firms experienced no abnormal returns in 5yrs following IPO showing that stocks were correctly priced at time of issuance, Ibbotson • abnormal return = actual return that day -mrkt return on same day 1. look for abnormal return -high or low 17 2. normal return is determined by looking at CAPM -stock in portfolio w/corresponding risk, expected return before & after event b. mutual funds -comparing performance of them w/mrkt 1. about half underperform & outperform mrkt c. common misconceptions 1. dart throwing -hypothesis just saying that on average investor will not be able to achieve abnormal or excess return b/c price that firm obtains from sale of its shares reflects true value of that stock given info available about it 2. price movemt -consistent w/hypothesis b/c price fluctuations is way mrkt adjusts to new info 3. stockholder disinterest -stock can be expected to be price efficiently as long as significant # of traders use publicly available info d. contrary evidence that mrkt may not be efficient 1. stocks w/sm mrkt capitalizations outperform stocks w/lg mrkt capitalizations a. just compensation of extra risk of sm stocks 2. temporal anomalies -stocks perform better certain time during yr & wk a. insufficient significance b/c differences not exceed transaction costs 3. low price to earning ratio stocks outperform higher ones on average 8% a. bk tries to explain away significance by saying that unusual returns are due to biases in commercial databases 4. found that IPO & SEO (seasoned equity offerings) co. has lower annl returns that other non-issuing co. w/similar capitalizations by 7-8%, showing that co. offered when overpriced, Loughran -mgrs can time their issuances & repurchases a. suggest perhaps that mgrs may also repurchase when stocks are undervalued 5. some evidence that there is a price-pressure effect -selling lots of stock will depress price of that stock e. limitations 1. difficult to identify event day b/c info tends to leak out 2. difficult to identify cause of fluctuation of stock prices -could be caused by normal fluctuations in mrkt or by other factors or by combination of these 3. applies to only those co. heavily traded on stock mrkts (NYSE, AMSE, NASDAQ) & not to those not traded 4. empirical studies don’t examine effect of ex ante regulation on ex post disclosure → doesn’t consider argumt that regulations are part of what makes mrkt efficient f. criticism 1. shouldn’t assume that all there is to be known is known 2. moral criticism c. strong form -prices reflect all info public & private 1. implication -nondisclosed info will make it into mrkt place so it will be of no benefit to learn nondisclosed info ealier than next person 2. empirical evidence -not support this form of efficiency a. insider traders still profit (buy when good news, sell when bad news) on info not yet made available to public or at least leaked out X. Options & Corporate Finance -Chapter 21 1. options -K arrangemts giving owner right to buy or sell an asset at fixed price anytime on or before given date a. traded on organized exchanges b. ie, options on corporate bonds & stocks 18 c. terms 1. exercising option 2. striking or exercise price 3. expiration date 4. American option -can be exercised at anytime up to expiration date 5. European option -can only be exercised on expiration date 6. pure stock -pure equity, non-leveraged firm a. graph of payout -x-axis stock price, y-axis payout, 45 degree up left to right b. generally common stock c. don’t really exist b/c assumes firm has no debt d. w/debt, graph is same line shifted down b/c has to pay out debt first 7. pure bond -risk-free bond, pure discount bond a. graph of payout -straight horizontal line b. face amt is going to be strike price c. term is going to be same as term of option 8. combinations a. preferred stock -payout is combination of payout of stock & bond b. bond convertible into stock -payout is combination of payout of stock, call & put options 1. value of bond w/convertibility -at least value of stock + value of bond paying interest + less risk 2. exercising option a. call -buying stock for bond b. put -selling bond for stock c. derivatives -where value of 1 thing depends on value of something else 1. currency futures K -in purchase K w/paymt in different currency in future, can buy call or put option, seller of option is risk taker of fluctuation of currency mrkt a. hedges -eliminates/reduces risk b. stradles 2. interest rate transactions 3. complications a. when other borrowing or multiple parties involved 2. call options -right to buy asset at fixed price during particular time period a. usually on stocks & bonds b. all such K specify that exercise price & # of shares to be adjusted for stock splits & stock dividends 1. exercise price -original divided by split 2. # of shares -original multiplied by split c. value of call option at expiration -depends on mrkt price of underlying stock at expiration 1. in the $ when mrkt price is greater than strike price 2. out of the $ when mrkt price is less than strike price -worthless • no such thing as negative value 3. at the $ when mrkt price is strike price 4. graph -hockey stick, x-axis value of common stock at expiration, y-axis value of call at expiration • buying stock -same as buying call option on stock w/strike price of 0 1. graph -x-axis stock price, y-axis value of stock, 45 degree line sloping up 3. put options -right to sell asset at fixed price during particular time period a. value of put option at expiration 1. in the $ when mrkt price is greater than strike price 2. out of the $ when mrkt price is less than strike price 3. at the $ when mrkt price is strike price 4. graph -flipped around mirror image of call option graph 4. selling options 19 a. call option -obligation for seller to sell holder stocks • if seller doesn’t own stocks, then have to purchase then on mrkt & then sell to holder 1. when mrkt price is greater than strike price -seller is out difference btwn 2 2. when mrkt price is less than strike price -seller doesn’t lose or gain anything b/c option won’t be exercised 3. graph -x-axis shre price at expiration, y-axis value of seller’s position at expiration, mirror image down of hockey stick b. put option -obligation for seller to buy holder’s stocks 1. when mrkt price is greater than strike price -seller doesn’t lose or gain anything b/c option won’t be exercised 2. when mrkt price is less than strike price -seller is out difference btwn 2 3. graph -reverse mirror image of call option graph for seller 5. combination of options a. buying put option & simultaneously buying stock 1. if mrkt price is less than strike price, decline in mrkt price of shares will be exactly offset by rise in value of put 2. graph is same as selling call • put call parity: value of stock + value of put + value of call = PV of strike price at risk free rate a. put can be described as a call b. call can be described as a put b. one strategy in options mrkt may offset another strategy resulting in riskless return 6. valuing options before expiration a. bound of value of call 1. low -difference btwn mrkt price & strike price 2. high -mrkt price 3. graph -x-axis value of common stock before expiration, y-axis value of call prior to expiration, diagonal block a. curve upward -greater marginal incremental value at higher stock prices than at lower b. 2 aspects of value of call option 1. loan value -allows one to keep money (difference in stock price & strike price) & invest it in meanwhile, gives you right to stock although not to use of stock in interim a. as interest rate goes up, loan value is greater b. as term increases, loan value is greater c. value of this portion of call option = PV (stock price -strike price) d. call option would still have this value even though strike price is same as future stock price e. call option has 0 value if stock price is also 0 2. bargain purchase value -value of call option increases as value of underlying asset goes up a. call option is worth at least difference btwn stock price & strike price + loan value b. stock price represents PV of stock’s expected cash flows 1. if today’s stock price increases, means that expectation of future cash flows is that it will go up, as well as its future stock price c. value of call option depends on 5 factors 1. stock price -call’s value increases when mrkt price inceases a. call’s value increases more when mrkt price is high than when mrkt price is low 2. exercise price -call’s value decreases when strike price is higher 3. risk-free interest rate -delayed paymt for exercising call is more valuable when interest rates are high a. deferring paymt for call is less valuable when interest rates are lower 4. expiration date -call’s value increases when expiration date is farther off • doesn’t matter if option is only exercisable at end or during term b/c American options are effectively generally exercised at end of term 20 a. exception -if stock pays dividend b. other limitations 1. applies only to options & underlying assets that are freely transferrable 2. empirical studies have only studied short-term options -90 days or less 5. variance of stock -call’s value increases when variability of underlying asset increases a. graph -x axis stock price, y axis probability, standard deviation bell curve 1. option is buying right side of curve 2. riskier stock means fatter, flatter curve -means portion under option is actually greater a. greater chance that there will be a better return w/option b. regardless of how low stock may fall b/c if stock price is = or lower than strike price, already out of the $ c. increase in value of call option due to increase in stock’s risk is greater than decrease in stock’s return b. call option buyers are risk seekers -playing risk on stock price • payout is hockey stick • can figure out value/price via put/call parity formula d. value of put option 1. stock price -put’s value decreases when mrkt price increases 2. exercise price -put’s value is higher when higher strike price than when lower strike price 3. interest rate -put’s value is lower when interest rate is high a. PV of strike price is lower when interest rate is high 4. expiration date -put’s value increases when expiration date is farther off 5. variability of stock -put’s value increases when variability of stock increases • payout is mirror image of hockey stick • can figure out value/price via put/call parity formula d. value & price not the same for options like stocks (price fluctuates around certain # that tends to indicate its value) 1. movemt of price erratic so difficult to deduce value of option 7. option pricing formula -Black-Scholes a. intro 1. option -riskier than stocks 2. implication -buying call & stock will eliminate risk 3. CAPM doesn’t apply here b. 2-state option model 1. borrowing to finance stock purchase duplicates risk of call a. duplicating amt -amt borrowed to make future payoffs from buying stock & borrowing, the same as future payoffs from buying call on stock b. call price = cost of buying shares -borrowing $ at certain % 2. advantage -can take into account certain events, ie, dividends, stock splits 3. disadvantage -not clear model but just algorithm c. Black-Scholes model -not responsible for it on exam 1. applies to infinitesimal time periods a. so if want to test, have to test instantaneously 2. formula is function of 5 factors -left out formula b/c overly complicated, all objective factors a. current stock price b. strike price of call c. continuous risk-free return (annualized) d. variance per yr of return on stock • may not be accurate • includes its idiosyncratic risk & not its portfolio risk a. on day to day basis e. time in yrs to expiration date 21 • also probability that standardized, normally distributed random variable will be < or = to d 3. assumptions a. no penalties or restrictions on short selling b. transaction costs & taxes are 0 c. option is European d. stock pays no dividend e. stock price is continuous f. mrkt operates continuously g. short-term interest rate is known & constant h. stock price is lognormally distributed 4. objective -values option via cumulative probabilities that option will finish in or out of the $ based on stock variability & all those other factors a. valid only as long as factors don’t change 1. change in variability of stock will cause greater (%) change in value of option d. model validity 1. work better than CAPM, APT 2. just about establishing relationship btwn stock price & value of option (given by probabilities & math) 3. evidence that it works (accurate) & not just that people believe it works -self-correcting, would be possible to profit by arbitrage otherwise 8. stocks & bonds as options a. in terms of call option -underlying asset is firm 1. stockholders -call option holders w/strike price of that amt paid to bondholders (debt creditors) a. saying that stockholders would buy firm from bondholders if firm cash flow was above amt paid to bondholders & not if below that amt 2. bondholders -owner of firm, seller of call option 3. graph of stock payout -x-axis net assets of leveraged firm (assets -liabilities), y-axis stock payout (uses mrkt values) a. 45 degree angle up, but don’t see straight line to left of 0 b. stock can be equivalent to call option on assets of firm 1. if assets > liabilities, will exercise call by continuing to own firm (will get their dividend) 2. if assets < liabilities, will not exercise but just walk away (will get nothing but turn over firm to debtholders) • really a covered put + call option • poor analogy b/c what bondholder would sell to stockholder at this price, bondholder has not sold anything to stockholder -about funneling firm cash flow from bondholder (set amt) to stockholder (remainder) b. in terms of put option 1. stockholders -own firm & owe set amt (which happens to be strike price) to bondholders, holder of put 2. bondholder -seller of put (has to buy firm for fixed price) a. if assets > liabilities, will get amt of debt b. if assets < liabilities, will get assets • don’t have absolute right to debt but liabilities less put (put 0 when assets sufficient) 3. graph -straight line w/bend downward to left, same perameters as graph above c. sum 1. value of call on firm = value of firm + value of put on firm -value of default-free bond a. left -stockholder position in terms of call option b. right -stockholder position in terms of put option 2. value of firm -value of call on firm = value of default-free bond -value of put on firm 22 a. left -bondholder’s position in terms of call options b. right -bondholder’s position in terms of put options 3. essentially -options w/0 strike price 4. suggestion contrary to CAPM -shareholder value may go up as risk of firm goes up b/c of this option value b/c starts to look less like stock & more like option, ie, leveraged buyouts (increasing amt of leaverage) a. CAPM -as debt goes up, β/risk goes up, stock price decreases → not necessarily b/c high tech stocks are high risk b. APT -may take risk of debt into account in inflation & difference in long-term & short-term interest rates 5. implications to corporate law -debtholders can’t vote • still have to be studied d. loan guarantees • value of default-free bond = value of risky bond + value of put option a. govt is assuming obligation cost equal to value of put option (right to sell) 1. if risky bonds are guaranteed a. bondholders are benefiters & not stockholders b/c not liable anyways for default 2. if new debt is being issued & guaranteed a. existing stockholders benefit b/c were able to issue debt at low interest rate b. old bondholders also gain b/c firm’s value increases 9. capital-structure policy & options -investing policy a. selecting high risk projects instead of low risk -stock is call option 1. stockholders benefit at expense of bondholders -bondholders suffer $ for $ when lower than bond obligation 2. value of call increases as stock is more volatile -here value of stock increases as firm is more volatile 3. value of risky bond = value of stock -value of call on firm b. milking firm meaning paying out all in anticipation of financial distress -put option 1. hurts bondholders 2. put option -reflects ability of stockholders to sell firm to bondholders in exchange for bondholders’ promised paymt 3. value of put increases as value of underlying asset falls -firm value falls when dividends are paid out, put value on firm increases • value of risky bonds = value of riskless bonds -value of put option a. value of risky bond decreases when value of put option increases c. delay investmt is also option 1. ie, purchase land, invest more for oil drill -purchasing land is call option • NPVanalysis ignores flexibility real firms have -decision tree analysis helps close gap d. PV of cash flows undervalues investmts b/c inherent call & put options not taken into account 1. baseline isn’t straight in real life but decision tree 2. call option -can create more cash flow than just what diagrammed, although may require an initial capital outlay 3. put option -not requiring as big an initial outlay as indicated b/c have option to scrap & sell • but difficult to make concrete projections that far into future • buying puts & calls against itself