lecture 13&14

lecture 13&14 - Ciecmre 12 __:.::m Portfolio's...

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Unformatted text preview: Ciecmre 12 __:.::m Portfolio's Standard Deviation l Lecture 13 l w W :> We will now find a formula that characterizes the riskireturn trade-off for a single asset or portfolio. (Note: The correlation coefficient is not provided. You will need to calculate the standard deviation of the Portfolio using the same method you used for Kroger and Microsoft.) Reminder: Diversification 2 Investing in more than one security that are not perfectly positively correlated to reduce risk. How does this correct standard d ' ' _ _ evration com are to an i - dewahon based on a weighted average? P ncorrectly calculated standard portfoho . a $.71 “fir . it?” fly, {__ K, .1 RISK 0' IR?- . A? . _ emu“, a weighted average of the two h'mhyeotoodwééifiéaiiom # of randomly selected securities | I (I: - Richard T Bliss. Babson University V . and Terry D. Nixon, Miami Universin e - Richard T. Bliss. 8W. 3"”; and Terry D. Nixon, Minn“ FIN 301 AB - Fal12011 FIN 301 AB - Fall 2011 101 100 .- I Lecture 13 ._ Lecture 13 3*. Risk in the CAPM Ca' IAssetPricin M el Why the drop? Two types of risk: - Diversifiabie risk (aka company—specific or unsystematic risk) Question: On average, what is the minimum 6 that we can reach through randomly addin stocks to a ortfolio? see fi ure 8-6, . 272 n q , _ __ 9 p ( 9 p ) mm wwlw 0 Market risk (aka nondiversifiabie or systematic risk) , i’°r*icoii'0 list 6‘0 dines r15 4M Portfolio WWW “T flocks 7“ 0 Wigiio i-tmmuggg Market risk cannot be diversified awa _ ms" 0 Every stock has both kinds of risk, i.e. Total Risk (0) = Firm-specific risk + Market Risk = diversifiable risk + nondsversifiable risk # of randomly selected securities The standard deviations We have computed measure rota; risk, What is the simplest way to reduce total risk? Question: Per the CAPM, which risk does the market assume we are taking? Given this assumption, what risk will the market reward us for taking? Random 1 stock portfolio from NYSE: 5,, = (See figure 8-6, p. 272) Random 4 stock portfolio from NYSE' a _ . p _ © . Richard T. Bliss, Babson University and Terry D. Nixon, Miami University a - Richard T. Bliss. BM Wwfijiz and Terry D. Nixon, MW“ U“ . 103 FIN 301 AB - Fall 2011 FIN 301 AB - Fall 2011 —_—_————_— “M I. :m How can we measure market risk? [ Lecture 13 . . - Historical rate of return On common stock H—-————W- Beta=b=B—> Note: Just because every investor is subject to nondiversifiable risk does not mean that they should all earn the same rate of return. Some stocks are more sensitive to the _ effects of nondiversifiable risk than others. For example, a change in interest rates Will affect a bank (in all probability) more than a grocery store. Historical rate Of return on Market index Where do ‘3 comef o 9 1. Let's plot some historic returns for a stock against the market. 2. Let's fit a line to these plotted points. 3- mint—Fa— WMQQKEBEQ What is the beta ([3) of the market? 7 . 4“ l lit-l7. WWW}; Ylfili Elfwtwg “he I-I—SLJLF. J Q - Richard T. Bliss. Babson University and Ten)! D. Nixon1 Miami University e-axmrsumWMn - Mm- -. deu-ry 1). Norm 195 FIN 301 AB - Fall 2011 cm am A B — Fal12011 .,,,m Lecturers ' fl What do some different 0‘s tell us, on an approximate basis, about expected returnsfor Question: If we have betas for individual assets, how do we find a beta for a portfolio of 355915? assets? _ (Jr (i-rr B ~ 0 h’" J094*- l J Com uti Portfolio ‘3 Remember that to earn the riskireturn profile predicted by the CAPM, we must hold a 0 =1 {m 2 wimp m] 44mg diversified portfolio. Why? ' ’ W3. a (I j r. , '\ t I » t _ . LVM [Nu (1330* (FA YELNuWrieCi Jpn; W ‘ngk 97 mi ipfll'ywlpm 36C unit] I Lat; L5 0 I“? q \' r . ‘ n . . 29? t) Ii 3 ilfiiilflluiZ-Yél iii—{HQ “3K- [3 :05 V1 the. no "1 ‘ it Wle 501 ' + 32 “at or “E milikei [S Q P a To measure the market risk of our portfolio, we need to calculate portfolio betas. B = 40 Mr» is i'~ ‘t , .- . . The beta for a portfolio is simply alweighted averagerPf the hates 0f the indwidual assets ,JQ, um 30 4“ mule/1 i9ij flout in the portfono' NLRB—ff”! [3 = 2.0 Jr ‘ .- "Wf ‘w talc-‘1tori-atria iid - rs. -”‘€*“m#hh” ' N o] , “ii-twp _ . flp—ZIBJ'WI .l'=l Whatdowe useforweights? H‘E- {E‘C’xtiw [7’i0PCr‘rim {11>} invested in 901311 was Example: You have a portfoiio with $1,000 in Treasury bills and $1,500 in a diversified mutual fund that has a B of 1.2. What is the B of your portfolio? VJ (000 ({- T' Bi” ‘j I A. : ' - I") _ JCL‘ (3.1591; 2 . __ ,_ :2 1 V boo a “F 5' '0 MT. . b 1800 i E , Po ‘ a . 4— I _ L” (as) ' kw“) - 71?. fi-RichardT.BIi&s,BabsonUnivcrsity _ _ alarm o. Nixon. Miami Univusity e - Richard T. Bliss. Bmww'": andT .N' . FIN 301 AB — Fall 2011 “W” m" it: 10? FIN 301 as - Fall 2011 106 FIN 301 AB -1'-'all 2011'! | Lecture 13 ' l WELL; ___. ‘M Example: AJ! Money Management has an equity fund consisting of the following stools: Stock Market Value “Be—ta ATG $100,000 iii 0:; re m g 1.10 TGW $50,000 2...». .. g, 1.20 owe $75,000 , 0.75 wow $125,000 0.30 CFD $150,000 1.40 f What is the portfolio beta? $510,003 First compute the weights: were2 [CG/9w : . 2 WTGW: §O/ gOQ :.| WGWG: jig/:03 ‘2 _15 WWW: ' "Ly/9043 ; lg WCFD=150/gm _ 7 N l flPZZfliwl : i:l 2. ' l. 5 ~ Wt“-t)+_1>(.19;-1,1s:iei1.30111 - I Why are we doing this? midi-'1 at! -- " . h \ OlMl WE market Parfiu‘o HULL1 if . r a “mare 1010...: his] ‘i—QJY e - Rim 7 Bliss. BM” “,3 and Terry D. Nixon. M :-;'. 1m TAB-:11 9‘ mp Lecture—13 in our portfolio. Think about this graphically: Required rate Of return To draw SML (security market line): 1. Put beta on the x-axis and required rate of return on the y—axrs 2, Risk—free rate must be on the y—axis (no risk). 3. Where does the market portfolio go? 4. Connect points from (2) and (3). SML in equation form: SMLI to: '30 +154 _j‘1_:--..u 1_ ,7, InlCAPM setting, our risk premium is only based upon the amount of nondiversifiable risk m, L4,? I ‘. r. «9...! beta 110 Mafia-Gk you. —____ inll‘gifi Frflrmuml "" ray] 18 i (8.8) ,4}! 1" ‘ '11 l j {-71 E, Ti—‘aa‘lx 1:3 (titanium i G - Richa'd T. Bliss, Babson University and Terry D. Nixon. Miami University 1,39 FIN 301 AB - Fall 2011 in Words: Example: You can buy a bond that matures in one—year fg$§§5 today. In one year the . . _ bond pays back $1,000. If the risk—free rate is 5% and the'bond'sfi is 0.8, what must the Tam" “— 7'5“ 9'22 *1 md'uafs‘ifi‘met expected market return be? \‘H’we C“. 1L { u W“ U 5 j __ , '3" We Jr Flak WW1“ * - ‘i -‘ ‘3 CA Pill hr 1 g” I rinRF+[rM_rRF]fli lav/rt The SML lets us compute the required return for any asset i, if we have an estimate oifi (beta for stock I} and values for rRF (the nominal risk-free rate) and rm (return on a market portfolio). It is a linear relationship between ri and risk as measured by Bi. n ‘ ‘J M Where would you get an estimate oand rM? 7‘ K ‘3 Q Firm 7, or \I T- Bill LEW-L i, ‘i it Question: How would changes in expected inflation affect the SML? what is the expected return from purchasing Magna sfbtw ‘ 6; W“ W Mm ] ! Clnmfit ' = —_ c ‘ 1 i% 1—; r1 RF + [rM rRF] fii Required rate 3 *F “l Hi; Vivi-law T Of return 7:- IJ ‘4 15' ~"Ul‘ + L 773‘" 435') “is : 3'32’i. *\ / i 1 have _-;iti;.-';thdd ii.“- mm El P ' - . . ractrce. If Magna 3 ii felts to 1.10, what is your new expected return? strains M was], "#38966: inf‘kiim 1- increase bl 170 WWW. RT- T’filiyw “it WW i 0 ‘ beta 9 - Richani T. Bliss, Babson University and Terry D. Nixon, Miami University FIN 301 AB - Fall 2011 111 FIN 301A,B — Fai12011 1m 25! __ "'_ Z77 Afum THE COST 1%) OF CAPITAL - the cost ofdebt H - the cost of equity Y5 - the cost of preferred stock [9 What is the firm’s cost of capital? 4th tr (mile (my: The Cost of Debt 1%1 W3 +911“ hwc‘h w cost of debt, rd, for a bond is the current yield~to-maturity (YTM) yield-to-maturity- 'l’ne wm {yum mind ' . it Mt wetting 19%“an alt Meet t OF, ’ atrium) (after-tax\cost of debt = YTM X (1 - tax rate) = rd 2: (1 - T) where T = the firm’s marginal tax rate example, we'll demonstrate the for the firm. FIN 301 AB - Fall 2011 11‘} by PMS“: °~ SQWHQ M “filing O-RichudT.B|iSS.w sermonmflm Lecture 14 Example: A firm has a choice of either issuing bonds (debt) or selling equity to raise $500,000. If the firm issues $500,000 worth of bonds (assume they are W budpiitbf‘mw e , they wilt have a 3214: coupon payment rate resulting in the payment of $5 ,000 TTM. to; ($50 .000 x .10) in interest each year. Let's look at the resulting income statements: With Equity With Bond (no bonds issued) EBIT $200,000 $200,000 -| (0 ) £50,000 )/ EBT 200,000 150,000 —T (34%) new, EAT [32.000 3 a ’Ohuiolenls Question: How much did the coupon payments really cost the firm? ‘ Q It Pom $90, 00 Higifrn as“; - gig—D :. plat: =5U/ GYM Mode 3 5,000 \5 0‘7"" J ‘J l U -381): old: 2 Lb '. Want CIR f Example: SRP Ltd. has bonds outstanding which mature in one year. The bonds have a $1,000 faci—iil‘fvalue and their coupon rate is 3.2 % with annual interest payments. The bonds are currenfly p{iced at $1 ,017. If the firm’s tax rate is 36%, what are the before and after-tax costs of debt? What are the band’s cash flows? t——-—-————-————-—————-~—l U011) 12:50 ; YTM formula: 31‘? E 1 (32 50 LU: ll? ' H 31-30 k - A __.__._—————— “'"t-‘fia'k tot : 7 M l 7 at 31f ; PK} :— A: i H YTM= 1131.30 flan 7m: .uziv: H.392 © - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University 113 FIN 3D1-A,B — Fall 2011 @ _ El Practice: What is the YTM of a $1,000 face value bond which has three years to After-tax cost of debt = id X (1 ‘ ‘ _ . maturity, pays annual interest at a 13.5% coupon rate, and is currently priced at .iigij U45) $988.50? ; fl 1" (Note: Don’t confuse the bond's coupon rate with its YTM.) -_ 7,171. _ _ [El/lfiSgi Example: A $1,000 per bond with a co pon rate of 10% (paid semi-annually) has a or - current market price of $1,100 and matures in six years. What is its YTM? ) D l l ELINEZ l TM '50 3° Hm) ti [curlSe 3° go ‘ i I ___H_.._..__..__q_m Price = PV of future CF’s discounted at the YTM 3?. =7 My) gg ‘ I I. Tim \1 ' [too '50 (H [1) logo - P ‘ k x (“will Jr Ulr 11%)“ “AW/Lg" timtumr ,LW '00 ‘3 _.——-—'—"—..L'L ' l *“l lizsoIfF—F—H J' iii-2) HMS Two ways to comgute YTMs: Trial and error or with a financial calculator. Example: A bond “a? ?2 years to maturity and a face value of $1,000. The coupon rate is 9.75%. Bonds of Similar risk and maturity are currently yielding 11%. What will the price of the bond be? 1 i1 TIMELINE: W ‘l on; Wl-S i000 Price = PV of future CF's discounted at the YTM " r 5% f The Cost of Common E ui % a li- ml .m _ _ _ . ‘15 . L T} i “ f—i——— The cost of common equity capital IS more difficult to determine. Why? k J “Jr I L N O fiw-Wflmegd mama-9% “‘3 fiaflmuwfifi 4140.246: l Jr v.»- nefln #3 mm gestalt-iris“: -. “iii S: S - Constant Dividend Growth Model 1' a“ M {W A‘HQ‘W‘T' “Wt-is ° The Security Market Line (SML) mom i - Bond Yield plus Risk Premium | © - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University 115 FIN 301.A.B — Fall 2011 cm 1111 A u - Fall arm The Constant Growth el How can we use this to determine the cost of equity? pvl '=”F'>'MTM m - g). i stock price at time 0 is equal to [)1 I (rs — 9) if constant growth (9) starts immediately. Let's now make the following changes in terminology: m,t = po when; p0 = Garment stock vaiue (price) Which of these variables do we have? PMTr+1= D1 where D1 = Dividend (one period after the start of constant growth) D! = Do 3" (1 + 9f r = rs where rs = cost (required return) of common stock Wm“ “my. ohm. We can also look up Po, the finn’s current stock price. 30. fiesmlxtmg {D a is Con M So rearranging: PFDUUS ‘9) —4 - earva ififfi§ififlfiél. or, T “"\ d» 1/ T 1 . , dividend yield + expected dividend growth rate 1A rlladrg J it: 3 vice Yoke : i . . Example: Quarter Stores dividend growth rate is 2.5% and this. is expected to last for the foreseeable future. The current annual dividend, Do, is=$0.60 per share. it the stock price is currently@ what is the expected egu/ityrehtm, rs, forQuarter Stores? C0337 in Mll- ,* “01‘s. , «__,‘,fi 1,. il -l, . rs =§i(D1 {Po Q ‘ INK! V “304' ’93?“ A'Uuiei‘dx? D1= JGC-Ll-Cl-B) Po: 2/9 9: Icy: : lols’ therefore, m—sl’l+‘fl;:wfiomszsasfl t‘l i 1- s - Richard T. Bliss. Babson University and Terry D. Nixon, Miami University 9 - Richmd 1‘. Bliss. and Terry D. thw ; Fm 301 A13 _ F33 2011 11? FIN 301 AB - Fall 2011 _ m Example: Simpson Photo's current stock price is $29.50. One year ago, the firm paida dividend of $1.51 and just yesterday paid a dividend of $1.60. if this trend in percentage growth of dividends continues into the foreseeable future, what Is Simpson's cost of equity? +90: mice :35". rs= (D1/Po)+9= (Wiggle mg) «i may 2.1m :7.“ M. We know Pu. but where do D1 and 9 come from? \ MM , W 15\ Lb 0‘ 1%,: [‘io_13i _ ,r—-—-" '..'. L5 ‘ [Si ’0qu 0 i “L l-ioU‘QSoib)l The Cost of Commgn Eguig using the SML What if we don‘t have a firm that pays dividends? (many do not) {1\C%Ccm~VO-TJ!£$ Mi weird-{ith our} Aiulgimig Enter the SML and the CAPM. Recali “at til“ WW I ' '/"‘\ r3 = rm: + \(rM -— rap,- __—. K / \ r \ w a sir i _ i - ~ .1 Problems: 1‘: R Di 1“ WWW .l dim; i—N' Q “lame. T - Etta Assuming we can resolve thes e SML? Issues how do we compute the cost of equfiY “s'ngme FM 301 AB - Fait 2011 - - [Elissa-W! e Richa'd and Terry D. NW“- Leciure 14 119 Example: Potash Inc. has an estimated beta (B) of 1.2. The current yield on Treasury bills is 4.6% and the expected return on the S&P 500 for the coming year is 12.7%. What is Potash’s cost of equity? who mm.“ r5=rRF+ (rM—rRFm : .Ot-nc 4t— (“3] .(j-(Lii L. 1‘, his take chad Waiter lime. El Practice: Lonestar Industries is currently selling for $17.75lshare- The firm just paid a dividend of $1 .2513hare, and this is expected to grow at a constant rate of 4%. What is Lonestar’s cost of equ ? ’ v-'l_c i _ {A El Practice: BLT Industriest'ichurrentiy priced at $10 per share. The stock pays no dividend, but you estimate that its price will increase to $12 per share in one year. If the risk—free rate is 7% and the expected return on the S&P 500 is 16%. what is BLT's estimated beta (5)? T1 Lia? t Lisa“ is?) («5; l ; Uii’k‘lb “Guest 11:91:; 1 2‘”! glad/EVIL?” -—-“ ,IDJ mm wire-“’5 «M G) - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University 119 FIN 301 A,B - Falt 2011 Megs: ' ' lusRiskPremium At times, the previous two approaches are not feasible andlor do not result in realistic resuits for calculating the cost of equity. Though subjective, the bond yield plus risk premium approach can result in an acceptable approximation. Remember: the risk return relationship indicates that the cost of equity must exceed the cost of debt for a given firm. To arrive at a cost of equity using this method, add a subjective risk premium (our text suggests 3 to 5%) to a firm’s cost of debt. r {4/ an; cancer-j f l - .l. L’ Lari} r3 = Bond yield + Risk premium is yin l”; TVA-*7- i i, mi. :lO'i gamma: We are familiar with the formula for valuing preferred stock (essentially a perpetuity). I“: a; Value of Preferred Stock = Vi: = (0.; I rp) BL (Note This! r W -- W: 51' - 0m?” 3 assumes meal drvrdend payments.) K?!“ J Why are we familiar with this? What's the value of a perpetuity? | {1" p‘inr-i‘l J Rearrange: o-Richardtslissw e j; and TenyD.Nixm.M ' .;‘_"' FIN 301 AB - Felt 2011 ' “We ‘4 _ .. Example: TSR has preferred stock with a par value of $50!share. Preferred dividends are set at a constant rate of 10% of the preferred stock's par value with the next dividend being paid exactly one year from today. if TSR’s ef rred stock is currently selling at a price of $40i'share in the market. what is the cost of preferred stock for TSR? I - rpm“--. .lr‘. ro] .‘ r (-i F: . s A i A l i. : 7 if”? lie . I W l Push“: {No-ta: Par value of preferred stock is not the same—asthe preferredstockg, market. value” L (price per share). Par value of preferred stock (1) represents the maximum amount collectible by preferred stockholders in the case of bankruptcy. and (2) dividends are often stated as a fixed percentage of par value. Practice: SPI issues preferred stock with a par value of STSIshare. Dividends are set at 5% of the par value. This preferred stock will sell for $60!share to the pubtic, Calculate the cost of this preferred stock. (JUL l" {6112* L {Li-{i .rif“.."' w.w_ugu Note: We will account for flotation costs as fia’ii’iir the prbiéérs herein costs. Vite-wilt M not increase'thé'cest of capital as they discuss on p. 349. fi - Riotde Bliss. Bataan University and Terry D. Nixon, Misni University 12‘! RN 301 AB - Fall 2011 ...
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This note was uploaded on 04/04/2012 for the course FIN 301 taught by Professor Schaeff during the Fall '08 term at Miami University.

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lecture 13&14 - Ciecmre 12 __:.::m Portfolio's...

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