Introduction to Finance
Introduction to Finance UGBA 103
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ask me Flu51 Da metha TotalL Retww I Total Return Dividend Income Total Gain or loss I Can all three terms be negative I Example Suppose you purchased a stock for 50 Over the next year its price goes down to 40 but the stock paid a dividend of 5 What is the total return I The following year the price goes to 60 and the rm pays a 10 dividend Now what is the return RWVV UMW Returny I When you sell a stock you realize the total return If you do not sell it the return is unrealized Does this make any difference I Having a dollar in cash is no different to owning a stock that sells for 1 Amie I Many bad investment decisions are made because people do not understand this point For example I My father who happens to be a doctor I Dollar cost averaging 10me 726th I Discount rates are usually specified in percentage terms ie in terms of per invested I Some Definitions Dividend Yield Pt Capital Gain t I Percentage Return Dividend Yield Capital Gain I Why I 5 HoldMLgRetww I If all dividends are reinvested then the holding period return is 1R1gtlt1R2gtltgtlt1RN quotEmpie I You buy a stock for 10 At the end of the first year it pays a dividend of 1 and sells for 11 At the end of the second year it pays the same dividend but now the price is 105 What is the percentage return over the first year How about over the second year Finally what about over the two years I What you do with dividends matters RealReturms I The real return is the holding period return or nominal return minus the inflation rate I In theory this what investors actually get so this is really what they care about I Is there anything wrong with this theory I How do you measure the inflation rate I Expected vrs Realized I In ation rate differs across individuals I The CPI consumer price index the generally accepted measure of realized in ation is upwardly biased 8 HMtOVLwdPerforwwmwof 100 1925 2005 mauon oun 39 3901 8244228 Treasury BHIS Corpovate Bonds 1 UUD UUU smausiecks 2347U5 Wu d Pontoho IDU UEID 1U UDU Value of Investment 14IZDU 3100 10 r l v r l v l 1925 1935 1945 1955 1955 1975 1985 1995 2005 Yequot VowW I One measure but not the only measure of spread I Definition R1 2R2E2quot RNE2 N l EEEJ I Where Stovndayd Dw afuow I The Standard Deviation is the square root of the variance Standard Deviation I Variance Example I The return of common stocks from 19501954 was 3171 2402 1837 99 What is the Variance and Standard Deviation of this sample WWW Trudeo BatwePw ifme Trudeo Batwaew RmowndRatww RMOWRPIWW I Large Portfohos of Stocks I Let39s add individual stocks to the pxcture VWW M a Wyof gym NormaL DWElmfww I 15t d dD t 826 I For one distribution the vanance s the aquot 6 em quot A l f I Z Standard Deviations 9544 on y measure 0 the spread I mmh d su but o 5 57 I 3 Standard Deviations 9974u I Why is this the Case7 7910me 075W NormaL Darthme I Fact The only distribution which satisfies I Variance Exists I Sums of rv39s distributed under this distribution are also distributed under this distribution is the Normal Distribution I Why are these properties desirable What about the actual Medmfuow of returny I Unfortunately returns are not normally distributed they have quotfat tailsquot I However normals are not a bad approximation I mpth Thought Expth A very rich uncle of yours has recently passed away He made his fortlme in Las Vegas and so has gambling in his blood You and nine of your relatives are currently in your late uncle39s lawyers of ce getting ready for the reading of the will The terms of the will is as follows The lawyer is to throw ten dice one for each relative If any die comes up between two and five that relative inherits 1 million Otherwise he or she gets nothing While you are still taking this news in one of your relatives suggests throwing all ten dice separately for each relative The same rule would apply to the average of the 10 dice The lawyer thinks about this and agrees to give any relative the choice of either mechanism What would you do WWW bytha WWW17m oftha MWWOflO WWWW I Is there a short cut I For 2 independent random variables X and Y what is the mean of X Y SWMWd I What about aX bY where a and b are constants ELXb17aELbEEaXbY I What about aX bY cZ where c is constant and Z a random variable ELXbi7cZab17cZ 21 Iy bwew wtoufform vowW100 I For 2 independent random variables X and Y what is the variance of XY twp WI J Gfoj SWMWd I What about aX bY where a and b are constants 2 2 2 2 VMEXbY1aGXbGy I What about aX bY cZ where c is constant and Z an independant random variable varEzXbYcZa26 b26 c2z2 WWWIO 014300 I What is the mean I What is the variance I What about the standard deviation I What is the approximate probability of the average being between 2 and 5 NormaL DOWdruwa I 1 Standard Deviation 6826 I 2 Standard Deviations 95 44 I 3 Standard Deviations 9974 L CoxMW I Definition For two random variables X and Y eg return on IBM and the return on APPLE covX Y Xn Y I Intuitively measures the amount one stock goes up down when another stock goes up down lb Correlawa c0rrXY covX Y VarX varY m A w ovav more ampth W WWW I Another rich uncle has died this one is a stock broker All his wealth is equally invested in 10 companies His will specifies that you and your relatives can do one of two things Either each one of you can take all the shares of one company or you can all agree to take the same fraction ie number of shares of each company Either way on your 60th birthday you will be entitled to sell the stock plus the reinvested dividends Before that date you cannot sell or consume the dividends What should you do 18 Dace wry Stocky I What is the most important difference between the dice example and the stock example I The dice are independent and therefore have zero covarlance I Stocks are correlated with each other and so will not in general have zero covariance I The net result is that you cannot get rid of all the risk in the stock example 19 S uAmway of what we know mfow I Dice Experiment much better to role 10 dice than just one I Why I By analogy it is better to invest in many stocllts rather that just one I But unlike dice stocllts I not independent they are usually positively correlated I are not identical I How does this change the story I Not by much 50 190dequ I The expected return of a portfolio is simply the weighted average of the expected returns of its constituent securities I So for a portfolio of N securities N N N E ExtI ExtEM ExtIi i1 i1 i1 where xi is the fraction of wealth invested in stock 1 31 UmW VowLance I The variance of a portfolio is NOT simply the weighted average of the variances of the constituent securities I For two stocllts varlgzbI7J a2 var j 2ab covbTI7Jb2 varl 0120392ab5er b26j 412039 2abpxy039xcsy b26j What Dzthe generaL WW N N N N var2xiRi 2x36 22 2 xixjoij i1 i1 i1 ji1 all variance terms all covariance terms Avwflww Way to Lookatth 1501me var RP CovRPRP CovRP2xiRi inCovRPR inopoiCorrRPRi I Divide both sides by SDRP SD RP6P 2xi6iCorrRPI 34 0thou05twndourdx I Since the standard deviation is simply the square root of the variance it will also not be a weighted average of standard deviations of the constituent securities I There is one exception what is it I When pl then varlr1bl7jazo39 2ablt5xoy b2ltsj 1chr boy alt535boy ArtExample I Say there at two stocks with the same expected return One has a standard deviation of 1 and the other has a standard deviation of 2 and they have a covariance of 1 3 I Would you ever hold the second stock I What is the standard deviation of a portfolio which is 75 the of the first stock and 25 of the second 5b I As long as the correlation is below 1 the standard deviation of a portfolio is always less then the weighted average standard deviation of its constituent securities I This is one of the most important concepts in this course OK but what ftha stocky hatya WW expected raftWM I You can still diversify I Take two stocks with the same expected standard deviation but different expected returns ie 30 5 Stock B Expected 20 Return E k A 10 Stoc 5 10 15 20 1 Standard Deviation Would you ever hold stock A 58 Exampler I Stock A has a expected return of 10 and B of 5 Their standard deviations are both 15 and their correlation coefficient is 5 What is the expected return and standard deviation of a 50 50 combination of the two stocks What ofyow wowted W other Vat WW I Weight the two stocllts differently Embed Retum 12 10 8 6 4 2 Standard Ikviatim 5 10 15 20 25 What WWW adi eVemt correlawa ooa o emty Ef cient Frontier Expected Return 2 4 6 8 1O 12 14 16 St and ard Deviation 41 What fa1e ocky had WW wopeoted returny wva vaV mwey Efficient Etontier Expected Return 4 6 8 10 Standard Deviation Au chtLeotwa I Topic I POItfolio Choice I Chapter 11 Today Lecturep CathaJStIWe 0w aPerfeot Mowth Eff d39OfTaMy ask me Vahwng owv A M I Conceptually there are two ways you can get the value of an asset 1 Calculate the value of what the asset provides I E g compute the present value of the expected cash ows 2 Calculate the value on all claims to the asset I E g compute the value of a company by adding up all the claims investors have on the company s cash ows Whom WWW oarpqumycamflowsr I Equity holders I Debt holders I So one way to value a corporation is to add up the value of all debt and equity outstanding I Does the ratio of debt to equity affect the value of the corporation 3Lamp M l r I r I M I I I I Value of a firm is the sum of its debt and equity I Does the ratio of debt to equity affect firm value I NO That would be like saying the price you pay for a house depends on how big your mortgage is I Aside This result sounds obvious but that is only because of how I presented it Before MM people did not see this simple argument Example 7 I Consider two rms that are identical in every way except that their capital structures are different One is unlevered and has equity worth 1000 The other rm has 500 in debt with a 10 interest rate What is the value of the levered rm and why Swwvmowy I If the two rms do not have the same value arbitrage profits are possible I MMI is therefore based on the absence of arbitrage however I individuals must have the same access to capital as the firm Why is this not an unrealistic assumption Margin loans 39 Any organization will do I you need two identical firms FCF to Equ I FCF to equity is just the FCF that equity holder are entitled to that is it is I FCF to Equity FCF Net Borrowing I So if the firm is paying interest on existing debt and not borrowing any additional funds the FCF to equity is just the FCF minus interest expense Example Conservative Ties has no debt in its capital structure The CFO Mr Cal Under rad is considering an equit buy back finance by debt He claims he can there y raise the return to equit holders The firm is currentl worth 8 million 400000 shares at 20 share T e idea is to issue 4 million in debt at an interest rate of 10 Cal supports his contention by working out the expected return on equity under three scenarios that are e ually likely return on assets of 5 15 and 25 ie that the firm has FCF of 400000 12 million and 2 million Example WW I Is his analysis correct I The analysis is correct but the stockholders are no better off I Under the new capital structure the equity is riskier so it must earn a higher return FCF to Equity wvwler the two cap Ltod Wrwotwey Advantage to Equity Holders of Debt FCF to Equity Disadvantage to Equity Holders of Debt Swwvmowyr I Whatever financial leverage the rm does the stockholders can do themselves Since they could do it but Chose not to it cannot make them better off I The reason equity has a higher return is that it is riskier WeightedAwa COWOf CathwL WACC I The cost of capital is another name for the discount rate or expected return I The WACC is the overall expected return of the firm as a whole I To see why think of the rm as a portfolio consisting of D fraction of value in debt and E fraction of value in equity then Rwacc LRD i E DE DE RaftWW 0w Equity for 0v LWWQOL Filmw I MMI implies that the WACC must be the same no matter the amount of leverage I Think what would happen if the firm only has one investor who holds all the debt and equity I Let RU be the WACC of an all equity or unlevered firm I The WACC of a levered rm is given by D E R DE D DE RE RaftWW 0w Equity com 01 I Multiplying both sides by DE E D E D TRU ERD RE I Rearranging terms D RE 2 RU ERU RD Mod gtmm MilletII No TM D RE 2 RU ERU RD I The required return on equity is a linear function of the firm39s debt to equity ratio I The higher the debt to equity ratio the higher the return on equity How doyowoaladafe w I w I 7 I I If the debt is risklessthen it should earn the 7 riskless rate D E U E U D I If it is risky then it is like any other risky asset in principle you can use a model like the CAPM I Problem Payoffs are highly nonlinear so simple covariances are unlikely to work ISo CompbwngWBeta of 13ny coMW tWVBQW 200 I Recall that the beta of a call option is Ix s FirmAssetsz BC 150 7 x I In this case equity is a call on the firms I assets A so substituting we get Value 5E AE A I Letting the assets of the firm equal the sum of debt and equity ADE and simplifying Equity Required 50 e I Debt Payment 0 5 0 100 150 260 D Firm AssetValue 6E A 1 E 6A 19 20 BetWOWvmdWwy I Of course the beta the firm is the same thing as the beta of equity of an unlevered firm I So if we start with an unlevered firm and add debt then the beta of equity will Change as follows D E A 1 E U I when the debt is riskless A 1 why 21 BetaWWWDM I Beta of debt is equal to the beta of a portfolio 7 that is long the firms assets and short a call option equity so A a Em I But the beta of the firm is the unlevered beta and ADE so Ul E D D U E 150 Value Q 50 0 200 Risk Free Bond 7 Less Put Optionl e i 9 r 6 50 Required Debt Payment 100 Firm Asset Value Debt 150 RWWDdwme mm AMXW Maw Firm Assets iLess Equity Call Option 200 BetmtRWDeM I Now substituting in the beta of equity HM D E 5D D I Simplifying 51921 A lt1gt5U I when debt is riskless A 1 E DEgt 3U Beta9951 WWIW s e The15W WW I When the firm pays taxes you can think of the government as just another clairnant Equity Beta when ED 2 O I Thus there are now three claims on the firm 2390 I Equity holders 3 15 I Debt holders 10 I IRS 05 7 BD 00 39 00 05 10 15 20 25 30 35 DebttoEquity Ratio 26 WCWWWT e WQWkMTM gm I Thus the quirk is that interest payment on debt occurs on a before tax basis whereas as dividends are paid on an after tax basis I To see the general effect assume that Earnings Before Interest and Taxes EBlT is constant in perpetuity 27 28 AllEquity Farm1x I Earnings after taxes for the all equity firm are EBIT1 Tc I Assume earnings after taxes are equal to FCF Then because there are no bondholders this is also the total cash ow paid out after taxes LWWQOI Filmw I First interest is paid to the bond holders on a pretax basis RD D I Thus remaining income is E B I T RD D I The remaining cash ow after taxes to equity holders is EB IT RDD1 Tc I Total FCF cash ows available to pay out to debt and equity after taxes EBIT RDD1 1 RDD EBIT1 TcRDDTc oftheFCF I Unlevered Firm EBIT1 Tc I Levered Firm EBIT1 TcRDDTc I Thus the levered firm pays out higher cash ows to its investors The difference RDDTC is the extra cash ow going to equity holders that is not going to the government This is the tax shield I Clearly the cash ow to investors depends in this case on the debt to equity ratio 31 Valwe af ne TwoShLelol WIWW WlevelofWWWaM I The extra cash ow to equity holders is TCRDD I Applying the perpetuity formulae provides the present value of this cash ow RDDI TCD D I Why do we discount at RD I This is the difference in value between an unlevered and a levered firm Nwotteotwa I Effect of Taxes I Other Market Imperfections I Reading I Chapter 16 Infaro t afoyam Bondy DWMLdtwwv Altwnafwe IVWMWRMW The 39VLeZdtoMatWtyquot I The yield to maturity is the single rate that sets the present value of the bond payments equal to the current price I So it is the IRR of an investment in the bond that is held to maturity I The yield on a par bond is the coupon so it is like an interest rate adjusted quotcouponquot I In the US for semi annual bonds it is generally not equal to the EAR because it is quoted on the same basis as the coupon rate ie it is like an APR 7 Yield Example I The treasury has a 10 year bond outstanding with a coupon of 7 It is now 4 years 6 months old It is currently selling for 98 What is its yieldto maturity I What is the yield if the price is 101 WYLeldvae I Each and every bond the US Treasury issues is traded in over the counter markets some issues are more liquid then others Thus every issue has a price and so every issue has a yield I The collection of all these yields is plotted on a curve with the maturity of the issue on the X axis and the yield on the y axis this curve is called the yield curve4 OWWRWBOW I What is an on the run bond I Why are the yields of Off the run and on the run bonds different Oct06 47 Oct05 7 Oct00 1mo 3mo 6mo 1yr 2yr 3yr 5yr 7yr 10yr 20yr 30yr Concept quwm Another Concept QWLOW I Is it quotfairquot to compare the yield of a bill I What do people use the yield curve for with a bond I To find out What he rislltless rate is at each I No because maturity l bonds pay coupons bills 10 not I So the yields represent returns for different maturity instruments I But is this what the curve really tells us WSpot STRIP chd RelafwaetWeewtlwSpof Curve and Covamv Yield Curvey I One of the first derivative securities was From the 0110ng SP0t the Strip yield curve calculate the Maturity 1 2 3 4 yield of a 4 year annual 5 0t Rate 35 4 45 474 I Strips are pure d1scount treasur1es With Pay 3 coupon bond p Repeat with a 65 rnatur1t1es longer than a year coupon bond I How is the coupon paying yield curve related to the spot yield curve 4 YW BovaYLeZdy Other Yieldme Coupon 0 3 65 80 70 i 60 YTM 474 4723 4696 50 40 30 20 i US Treasury Maturity 1 2 3 4 10 IBM 00 t t l l x x Yield Spot Rate 35 4 45 474 Years to Mammy CorporataBmwl RatW I Rating agencies rate each bond issue I Two most well known are Moody39s and Standard and Poors C orporovte Yield C we 1200 7 1000 7 800 7 f 2 2 6000 7 gt 0 400 7 Us Industrizls AAA US Industrizls A1 200 7 7 USIndusmals B13133 7 US CableBdcst B 000 1 1 1 1 1 1 0 5 10 15 20 25 30 35 Ye ars to Maturity meoLpaJBQVLdy I Tax exemption implies that the yields can be lower than Treasury yields I Also rated by the agencies MMLLoipalledvaa 60 50 7 40 7 30 7 Yield 20 7 Us Treasury Yield Curve 10 7 Municipal Yields AAA 7 Municipal Yields A 00 1 1 1 1 1 1 0 5 10 15 20 25 30 35 Years to Maturity I mama 10m Bondy I There are different kinds I Local Bonds in a foreign country I Bonds issued locally but by a foreign entity I Eurobonds bonds issued in a foreign country but in a local currency Gar eldCurve 60 50 i 40 7 30 7 Yield 20 i US Treasury Yield 10 i Gilt Yield 00 l l l l l l 0 5 10 15 20 25 30 Years to Maturity 35 FOVWMdRatey I The rate you contract today for some time in the future I eg the 3 month rate 6 months from now Darivng FOVWOW OZ Ratey FromthaSpof Curve I You can use the LOP to derive forward rates from the spot yield curve I Lets begin by just considering 1 year forward rates that is the rate on an investment for 1 year ForwardRafa Exam11919 I If the yield on a 2 year rislltless pure discount bond is 10 EAR and the yield on a 1 year riskless bond is 9 EAR what is the 1 year forward rate for 1 year from now 507Mwa I There are two ways to risklesst invest for two years I Purchase a 2 year pure discount bond I Purchase a 1 year pure discount bond and take out a1 year forward contract I By the Law of One Price both strategies my cost the same Swa Forwawd Contract I Even if the forward contract is not traded you can create them yourself from the spot rates Let39s see how to do this in the first forward rate example I If the yield on a 2 year riskless pure discount bond is 10 EAR and the yield on a 1 year riskless bond is 9 EAR what is the 1 year forward rate for 1 year from now MWMWAW I Only the material covered until this point will be on Wednesday s midterm I That is the material in Chapters 13458 IntmeRafaofRe WW I Sometimes you know expected cash flows and the PV and you would like to know what discount rate sets them equal I You can also think of this as the return of the investment IRR I The internal rate of return IRR is the discount rate that sets the net present value of an investment opportunity equal to zero I For a bond this rate is known as the yield to maturity IMMWRMM I Thus far I have only spoken about the NPV Rule But other rules exist I Keep in mind that any rule that disagrees with the NPV rule does not take the investment for which the benefits exceeds the costs m t Dow39y walromat I Don is thinking of opening a laundromat Each new machine costs 500 Don has been informed that at full capacity each machine will generate 150 per year However machines require maintenance so to keep the machines in working order Don must spend a fraction of this on maintenance As might be expected this maintenance cost increases as the machines age Don expects to do no maintenance in the first year but after that he expects his net cashflow to decrease by 20 each year in perpetuity I What is the IRR of a washing machine IRR Rule I What do you think the rule is Accept the project if its IRR is greater than the discount rate Reject the project if its IRR is less than the discount rate I What should Don do What Lgthe NPV ofDmv39y LWWOmatmaWwwofr I Does the NPV Rule always give the same answer as the IRR rule 30 IRR and WW Vate WW I The difference between the IRR and the discount rate is the amount your estimate of the discount rate can be off without changing the investment decision L Voblemxyw tl vIRR I Negative investments lead to the wrong conclusion I Negative cashflows lead to multiple lRRs For mutttally We project I Timing Matters I Scale Matters I We will use examples to illustrate each problem Negatwa I VIAWWI Mr Mankiw an economist at Harvard recently accepted the following deal to write an introductory economics text He took an up front payment of 1000000 and was expected to deliver a completed text within three years Mankiw gures that based on his consulting rates his disutility from writing and the amount of time that he will spend it will cost him 500000 a year to complete the book ie for this amount he is indifferent between writing and not writing the book If current interest rates are 10 based on the IRR method what should he have done What about the NPV method NPV 7waqu DealL NPV 100000 200000 300000 400000 200000 100000 Discount Rate 40 Multiple WW I Assume that the deal also includes royalties that are expected to be 20000 a year in perpetuity once the book is completed Now what should he do chtteotwa IMidterm Exam I Lecture in a Week I Alternative Investment Rules I Reading I Chapter 6 Today Ledwe DowW Pol13W CathaJBudge ng w Leverage What happwtotlwstookx plaice WI WI 0v OVAW WPade I In perfect markets I No change on all except the ex dividend date I What happens on the ex dividend date I why I What effects could change this I Taxes I Bankruptcy Costs ArtExample The Cash Cow Corporation has no growth opportunities but generates 10000 yr for certain in er etuity Currenth this is all paid out as 1 d1vidend on the 1 0 0 shares outstan ing One stockholder suggests that it would be value enhancing to pay extra dividends on each dividend date by selling an extra 00 shares each year and paying out the proceeds immediately as dividends In a perfect market if the riskless rate is 10 is he right To answer this uestion lets just consider a one time decision to pay a extra divi end by issulng stock I V39me of 00dede Policy I To first order ie in the absence of taxes dividend policy is irrelevant it cannot affect firm value I The reason is any investor can change dividend policy by either selling or buying more shares I Since dividend policy is a financial decision this is really just and example of MM Based on this point when might dividend policy matter Al Example I The Nothing Corporation has no assets or growth opportunities It nevertheless wants to pay a dividend Thus it has decided to issue stock and pay out the proceeds as a dividend Assuming a at personal tax rate of 34 would anybody invest in this stock AWExomlpla I Cash Out Corp is about to pay a dividend of 1 share Its current stock price is 50 If the marginal investor39s highest marginal tax rate is 39 and capital gains are taxed at a at 28 what will the stock price drop be to prevent tax arbitrage Swenggv Lottery BOW I Interest on these bonds are tax free However the capital gain loss is taxed I So you can deduct the capital loss against income and take the interest payment tax free I How much should the price drop if the marginal tax on capital gains is 54 EmpWLoaLRawlty I The great thing about Sweden if you are an empiricist not so great if you live there is that all income tax returns are public information I So you can actually test this Here are the imputed and actual taxes over two regimes I Actual 54 Imputed 537 5 I Actual 21 Imputed 223 49 D WW POW with TW onWas MWmO yDWdedHustory I Until the Bush tax cuts dividends were taxed as I Let39s see Mcrosoft39s Histor1 personal income I Because personal income is usually taxed at higher rate than capital gains it was not optimal for a firm to issue dividends I Instead firms should let shareholders manufacture their own dividends by selling stock or firms repurchase stock themselves I Today things are reversed I Perhaps that is why Microsoft started paying dividends 9 Capitaldewava Laverage COEOfCOLp tal I Didn39t we already do capital budgeting I Recall that the cost of capital is the return Yes but on a marketed investment opportunity of I We pulled the cost of capital out of thin air Similar riSk I We ignored the effect of leverage I You can use the CAPM to calculate the cost of capital using stock prices What happeny L f baprojeot than yaw are WWW by lava60L I Leverage changes the risk of equity so if you are using an equity beta in evaluating the project you have to make sure that it re ects the leverage I Leverage has tax consequences so you need to take those into account WACC MedLodz I The concept I Discount the PCP of the project at the appropriate discount rate I We will show that the appropriate discount rate is the WACC I Why don39t we always use this method I Because it is complicated to implement if the firm does not maintain a target debt equity ratio Lets see 5 a how dayow go about W I There are 3 well known methods I WACC I APV I FTE I We don39t have time to cover all three in detail so we will concentrate on WACC and briefly cover APV and FTE WACC wi m T W E D r r r l T wacc DEE DED c I How do you know this is the right discount rate DuctNORMAL What we WlWe I The return on the claims to the assets must equal the return generated by the assets themselves E01rED01rD FCF1 TchD0 VlL I Rearranging terms Eo1rEDo1rD1 1 FCF1 Vf 17 WACC gt0de I Dividing both sides by Eq Da and sianljfying L Hi Do Johm E0 D0 E0 Do E0 D0 m I Substituting and Rearranging terms provides FCF VL VOL E0D0 1 1 1 rWACC I NOTE Holds no matter what leverage policy the rm adopts 18 Why thew do we want to W ax tomget debt eqMLQ ratio I Because the WACC is constant with a target debt equity ratio E D r r r l T W DE E DE D WACC MedLodz I Discount the FCFs using the WACC to provide an estimate of the value of the project Exampie Avoo I New product with a 4 year life I Expected annual sales 60MM year I Manufacturing Costs 25 MM year I Operating expenses 9MM year I Development I RampD and Marketing 667MM I Capital Investment 24MM I NO Working Capital implications I Corporate tax rate of 40 507Mwa I Step 1 I Calculate the PCP I Step 2 I Determine the target D E ratio I Step 3 I Calculate the WACC I Step 4 I Calculate the NPV J A may Leverage Assets Liabilities Cost Of Capital Cash 20 Debt 320 Debt 6 Existing Assets 600 Eguitx 300 EqUitY 10 Total Liabilities Total Assets 620 amp Equity 620 Avocr y WACC E D rwucc rE ED ED 300 300 rD1Tc 1006 601 40 600 68 00 What Lftheprqjecf 0w WW to the farm7 I In this case you need to infer the WACC of the project from the WACC of the firm I Can we just use the same formula with the new values for E and D I NO 1 Why I We proceed by first calculating the unlevered cost of capital Utalayered WACC I In a NORMAL market U T ErE DrD V rU V r Where VT is the market value of all future tax shields I When the firm maintains a target debt equity ratio 71 ry so ErE DrD V VT rU E DrU I Substituting and rearranging terms gives UWWGOL WACC wL vov taAgetdeb tequig radio ED ED I The same expression as the frictionless case Now we Waitethe Coytof Equity Capital I Simply rearrange terms D rE ED ED rU EDErE DrD ED D rE rU rD E E rU rD D D rUErU ErD Coyfoquw fy CapitalL wailvow tauget debt equity Val LO I 80 D rE rU EUU rD I Assuming you know the cost of capital of debt you can use this equation to get the return on equity and calculate the new WACC using the project leverage Example I Suppose AVCO decides to finance the project with all equity What is the NPV I What if Avco uses 75 debt financing assume that with this level of debt financing the cost of debt capital will be 7 Avoo yUVIlawed WACC I Unlevered WACC r ir ED E ED D 300 300 100 V 60 V 8 V 600 600 rU Avccr yWACC with 75 Debt I Equity Cost of Capital D rE rUErU rD 88 711 IWACC E D 1 1 rm EDrE EDrD c 25 75 110 y 70 7 1 40 59lty 100 100 chtgLeotttrra I Topic I Finish Capital Budgeting with Leverage I Discuss the Ideko Case I Reading I Chapter 18