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by: Arno Leuschke


Arno Leuschke
GPA 3.66

S. Parendo

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S. Parendo
Class Notes
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This 57 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 134A at University of California Santa Barbara taught by S. Parendo in Fall. Since its upload, it has received 82 views. For similar materials see /class/227154/econ-134a-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.




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Date Created: 10/22/15
More on the SML and Ch 12 SML and Weighted Average Cost of Capital Econ 134A Page 1 Spring 05 Previously we obtained the CAPM WI SML al39ket portfolio R rf er 1 The SML gives the positive relationship between risk and expected return Risk is given by beta Econ 134A Page 2 Spring 05 I 31333 Suppose there is a stock A You are given its Beta and its expected return this is graphically represented on the right Is security A priced correctly Overpriced Underpriced Remember rW Econ 134A Page 3 Spring 05 Its overpriced R Security A is overpriced SML since there is a stock B 13 M m that will lie on the SML If and give the required 39 39 quot A return Investors will Rr Choose B over A i B 39gt 395 gt Econ 134A Page 4 Spring 05 Fw My 7 z j gm3r g u lJju u Lubem A stock has a beta of 18 A security analyst who specializes in studying this stock expects its return to be 18 percent Suppose the riskfree rate is 5 percent and the expected market risk premium is 8 percent Is the analyst pessimistic or optimistic about this stock relative to the market s expectations Econ 134A Page 5 Spring 05 l l l L J l J L J L l l J l l l A portfolio that combines the riskfree asset and the market portfolio has an expected return of 25 percent and a standard deviation of4 percent The riskfree rate is 5 percent and the expected return on the market portfolio is 20 percent Assume the capitalassetpricing model holds What expected rate of return would a security earn if it had a 05 correlation with the market portfolio and a standard deviation of 2 percent Econ 134A Page 6 Spring 05 Problems with CAPM Problem 1 CAPM assumes homogeneous expectations This implies that one of CAPM s biggest assumptions is that noone had valuable information and they think nobody else does either Econ 134A Page 7 Spring 05 Second problem There are other problems with Beta For example Betas may vary over time example last month Betas are affected by a company s change in technology product line etc Econ 134A Page 8 Spring 05 r7771 5 w q F mm WW7 a pm r quot quoti s U3 I39 J Julie L01 LieW Laltsgmgsl yy Empirical evidence on CAPM ls Beta dead See Appendix to Ch10 CAPM predicts that highbeta stocks have high expected returns this is what SML line shows Empirical tests which use historical data on stocks do not always show that this positive relationship is correct Econ 134A Page 9 Spring 05 7 J 4 A 9147 no r7 div3 r glnr qu V g quoti iy JirA 7 J1N i i V Ni 1 VizUM gCJJULLUMQ LKrlyjLL LU LJ my f a 1 i was 1751 1 U L21 1 0 s y p w Juice U Connecting CAPM with NPV CAPM will give us the discount rate Discount the eXQected cash flows using this riskadjusted discount rate NPV 2 5 CL C2 1REIEYW Where C7 is the expected return from the risky investment Econ 134A Page 10 Spring 05 How do we get this discount rate Find an asset of comparable risk and use the market to determine the risk 3 and then apply CAPM E er er Econ 134A Page 1 1 Spring 05 Firms can change the beta of their equity by changing their DebtEquity ratio Unlevered 25 Levered Half Levered Econ 134A Page 12 Spring 05 Unlevered firm This firm has just equity issued it carries no debt This firm s assets equals its value in equity stock market cap Thus the beta on this firm is assets 2 equity Econ 134A Page 13 Spring 05 Levered firms These firms have both equity stock and debt bonds The firm s total value is the sum of the value of the stocks and bonds Equity equ y Debt debt DebtEqu1ty DebtEqu1ty assets 2 Econ 134A Page 14 Spring 05 How can we use this D DE assets 2 debt equity E D C ui o O DE 3 q ty DE E DE equity Rearranging DE equity 2 assets D asses 1 E Econ 134A Page 15 Spring 05 Now let s look at a firm s cost of financing investments for which it uses both debt and equ y Notation B Bonds or debt 8 Stock or equity rS the return to equity what the firm pays to its shareholders rB the cost of debt what the firm pays to its creditors Econ 134A Page 16 Spring 05 WA CCaverage of required returns WACC is the weighted average of the required returns rS and r3 It is the overall cost of capital for a firm FWACC I rs B rB1 TC SB SB Econ 134A Page 17 Spring 05 Alternative Investment Criterion Econ 134A Page 1 Spring 05 Previously In Chapters 4 and 5 we studied NPV Rule accept if NPVgt0 Positive characteristics of the NPV rule Time value of money Uses forecasted project cash flows Riskadjusted discount rate NPV is additive Econ 134A Page 2 Spring 05 Alternative Investment Criteria We will examine Payback and Discounted Payback Profitability Index Internal Rate of Return Econ 134A Page 3 Spring 05 l l J l Payback Period The time it takes to recover the initial investment Payback Period Rule A particular cutoff date say 2 years is selected All investment projects that have payback periods of 2 years or less are accepted The rest are rejected Econ 134A Page 4 Spring 05 Ev mn iwvr w 6 m7 gleam EWm W 323 W r WarJ bum UUL DQUJ k3 kw U Q34 Lilng u f km JGyg Period 1 2 3 4 NPV10 PByrs Pro 1 2o 10 10 100 7249 2 Pro 2 2o 10 1o 0 264 2 Proj 3 2o 0 2o 0 347 2 Which one to choose Any problems with Payback Period Econ 134A Page 5 Spring 05 a 1 Lquot 4 f7 1 A F A A 1 I A I7 F L 7 391 4quot 3 l a x h 4 4 l l l l l l l l J l l l J l Discount all cash flows Apply Payback period rule Period 1 2 3 4 NPV10 PB Pro 1 20 10 10 100 7249 2 20 9 09 826 75 13 gt2 Pro 2 20 10 10 264 2 909 826 gt2 Proj 3 20 0 20 347 2 0 1653 gt2 Pro 4 20 15 15 603 2133 1364 1240 2 Econ 134A Page 6 Spring 05 rlijmyrw WW c 173 2 m i ir Q JSm b ALLA11 k9 J L i L L J l J l J i 0 1 2 3 4 Pro A 2300 600 750 800 1000 Pro B 2300 1100 950 500 450 What is the NPV of the two projects What is the payback period for projects A and B What is the discounted payback period Econ 134A Page 7 Spring 05 I PV of In ows PV of Out ows Pl Rule Accept all projects with Pl gt 1 Popular in NonPro t Management Period 1 2 3 NPV12 Pl Project 1 2o 70 10 505 352 Project 2 1o 15 40 352 452 Project 3 1o 5 50 254 275 Econ 134A Page 8 Spring 05 Numerator is PV of inflows Denominator is PV of costs If fraction is greater than one that means numerator is greater than denominator so NPV is positive Problem scale is not considered Econ 134A Page 9 Spring 05 m The IRR is the discount rate that equates a project s NPV to Zero The IRR is defined exclusively in terms of an asset s cost and its cash flows IRR RULE Accept an investmentproject if the opportunity cost of capital discount rate is less than the IRR Econ 134A Page 10 Spring 05 Example A project with an Initial Investment of 4000 and Cash flows at time 12 of 2000 and 4000 respectively 2000 4000 i0 1 2 4DDG 2000 4000 0 NPV 4000 1 IRR 1 IRR2 RR 28 Econ 134A Page 11 Spring 05 Graphically NPV Discount Rate When the discount rate is less than IRR NPV is positive so we accept the project This graph assumes we have an initial cash out ow followed by cash inflows in the future Spring 05 Econ 134A Page 7 1391 Example II An investment costs 125 and produces cash inflows of 15 per year in perpetuity What is the IRR of this investment Econ 134A Page 13 Spring 05 Problems with IRR Hard to calculate Since it may involve solving a polynomial the best way is often trial and error lnvestinq vs financinq Investing COltO and C1 02 gt0 Accept the project if rlt IRR Financing COgtO and C1 C2 lt0 Accept the project if rgt IRR Econ 134A Page 14 Spring 05 Financing graph NPV Financing iscoum D Rate Econ 1341 P392715 Spnng 3905 an Meme em m Can have multiple lRRs If cash flows Change signs more than once for example CO 100 0150 0260 C3 30 0445 then we will have more than one IRR In general of IRRs equals of times the sign changes Discount Rate Accept Econ 734A Pager l6 Sprlng 3905 Example Calculate the IRR for an investment with the following cash flows Project 792 1780 1000 Econ 134A Page 17 Spring 05 Problems III The Scale Problem Small project with high IRR is preferred to large project with lower IRR but the latter may have higher PV No way to compare mutually exclusive projects Incremental cash flows can be used Econ 134A Page 18 Spring 05 E 7m quot3977 F quot73 quot L g l I Wsz L u LLBm lb 1 l L l L C0 C1 NPV 25 IRR Small Budget 10m 40m 22m 300 Large Budget 25m 65m 27m 160 Incremental Cash C C flows from choosing 0 1 large instead of 251015 654025 small budget Page 19 Spring 05 Econ 134A Incremental RR 25 1IRR 15 Incremental IRR6667 NPV of Incremental cash flow 25 1 25 6667 gt25 discount rate and NPV is positive so we accept the large budget Econ 134A Page 20 Spring 05 MampM Proposition II Conclusion of Ch 15 Econ 134A Page 1 Spring 05 MampM Prop II Previously we obtained setting Tc0 RWACC S RS B RB SB SB MampM Proposition I the value of the firm remains constant We also showed the WACC remains constant in the previous lecture Econ 134A Page 2 Spring 05 If RO is the cost of capital of a unlevered firm then R0 RWACC for any debt to equity ratio Starting with R0 RWACC S RS B RB SB SB Solving for RS we get MampM Prop It RszRo Ro RB Econ 134A Page 3 Spring 05 MampM Graph RO is the cost of capital to an unlevered firm and RS and RB are the cost of equity and cost of debt respectively Note that the cost of equity rises to keep the weighted average cost of capital constant Econ 134A Cost of Capital r Page 4 Debt to Equity Ratio BIS Spring 05 MampM II with Taxes What if we add in taxes lots of algebra B R5 R0 1 TCR0 RB The intuition here is that the necessary return on the equity increases slower than without taxes Econ 134A Page 5 Spring 05 Graph of MampM II with Taxes Cost of Capital r This is the graph of MampM II with taxes lt5 With financial distress RB we get a U shape Debt to Equity Ratio BIS Econ 134A Page 6 Spring 05 Evidence for MampM Propositions 1 US DV debt to value ratio are fairly low Comparing across countries US 45 1989 Japan 81 UK 56 Germany 61 France 63 2 Across industries DE ratios have different values but within industries the ratios are comparable Steel industry DE 1665 Pharmaceutical industry DE 0079 Econ 134A Page 7 Spring 05 Summary M amp M Proposition 1 VL VU Without taxes VL VU T 13 with taxes M amp M Proposition 11 B R5 R0 R0 RB Without taxes R5 R0 g R0 RB1 Tc with taxes Econ 134A Page 8 Spring 05 F a 7 m Tam 7 n 47 z 7 l 79 yr gt quot3 lgj D J jl quotH MD LJ f 39 39 L f c U A C3 11 T a L1 L51 nll l g gu Lubbuya l l l L j l J L J L l l J l l l Gibson Inc expects perpetual EBIT of 1 2 million per year The firm s pretax cost of debt is 8 per annum and its annual interest expense is 200000 Company analysts estimate that the unlevered cost of Gibson s equity is 12 percent Gibson is subject to 35 corporate tax rate a What is the value of this firm b If there are no costs of financial distress of bankruptcy what percentage of the firm s capital structure would be financed by debt C Is the conclusion in b applicable to the real world Econ 134A Page 9 Spring 05 x7 7 m f l 1 7r m l h w l 977 7 7quot wind 7 atquot ll M y ll 1 m is l willyVJ h I i 4 39 J L L iguuutgraucy l l l L j l J L J L l l J l l l Green Manufacturing Inc plans to announce that it will issue 2 million of perpetual debt and use the proceeds to repurchase common stock The bonds will have a 6 annual coupon rate Green is currently an all equity firm worth 10 million with 500000 shares of stock outstanding After the sale of the bonds Green will maintain the new capital structure indefinitely Green currently generates annual pretax earnings of 1 5 million This level of earnings is expected to remain constant The corporate tax rate is 40 Econ 134A Page 10 Spring 05 l l l L J l J L J L l l J l l l a What is the expected return on Green s equity before the announcement of the debt issue b Construct Green s marketvalue balance sheet before the announcement of the debt issue What is the price per share of the firm s equity c Construct the sheet after the announcement d What is the price per share immediately after the announcement of the debt issue e How many shares will be repurchased How many shares remain after the repurchase f Construct the balance sheet after restructuring What is Greens price per share after restructuring g What is the required return on equity after restructuring Econ 134A Page 11 Spring 05 l l l l l l l l J l l l J l l l An option confers the right but not the obligation to make a transaction The buyer will have the option to do as they wish Options can be written on stocks bonds commodities foreign currency and metals and more The discussion here will focus on stocks as the underlying asset Econ 134A Page 12 Spring 05 J l l l l l J l J l l J l l l An option can be used to control a larger number of shares than an investor could normally purchase We ll see a put option will allow the purchaser to lock in a profit think of a farmer selling grain so this is a form of insurance The price of an option will always be positive Econ 134A Page 13 Spring 05 14D VH4 N A L74 quotmmw E sL MM 117 a J l u rfuglg l l l l l l l l J l l l J l l l Strike price The price at which the exchange will occur Expiry The date by which the exchange must take place the option is no longer valid after English Option exercised only on the expiration date American Option exercised on or before the expiration date Econ 134A Page 14 Spring 05 l l J l Call Option Grants the holder purchaser the right to buy the asset at the strike price Put Option Grants the holder the right to sell the asset at the strike price In the Money The option if exercised at current prices has a positive value Out of the Money just the opposite of in the money Econ 134A Page 15 Spring 05 Valuing Options at expiration Base decision on Stock price If it s above buy at strike price X sell at market price PS Profit is PSX If it s below It s best to let the option expire unexercised Thus the value of the option is vcltPsgt max PSx 0 Econ 134A Page 16 Spring 05 Graphically Value of Call Value of stock Strike price The option is worthless until the stock s price is at least the strike price and then increases exactly as fast as the stock s value increases Econ i34A Page 17 Spring 05 The value of the call to the seller Strike Price Stock Price Value of selling a Call Ecnn 734A Page 7 18 Sprmg 05 Value of a put Ifthe price P8 is higherthan X no transaction will take place but if the price is lower the option will be exercised The profit is thus VP maxX PSO Value of Put Strike price Econ 134A Page 19 Spring 05 Portfolio insurance Suppose we own a stock but buy a put on that stock At the expiration date the payoff from the combination will be the sum of the two payoffs Value of stock and Put v smke prlce Econ 134A Page 20 Spring 05


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