Chapter 10 Stocks and Their Valuation ANSWERS TO ENDOFCHAPTER QUESTIONS


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1 Chapter Stoc and Their Valuation ANSWERS TO ENOFCHAPTER QUESTIONS  a. A proxy i a document giving one peron the authority to act for another, typically the power to vote hare of common toc. If earning are poor and tocholder are diatified, an outide group may olicit the proxie in an effort to overthrow management and tae control of the buine, nown a a proxy fight. A taeover i an action whereby a peron or group ucceed in outing a firm management and taing control of the company. b. The preemptive right give the current hareholder the right to purchae any new hare iued in proportion to their current holding. The preemptive right may or may not be required by tate law. When granted, the preemptive right enable current owner to maintain their proportionate hare of ownerhip and control of the buine. It alo prevent the ale of hare at low price to new tocholder which would dilute the value of the previouly iued hare. c. Claified toc i ometime created by a firm to meet pecial need and circumtance. Generally, when pecial claification of toc are ued, one type i deignated Cla A, another a Cla B, and o on. Cla A might be entitled to receive dividend before dividend can be paid on Cla B toc. Cla B might have the excluive right to vote. Founder hare are toc owned by the firm founder that have ole voting right but retricted dividend for a pecified number of year. d. Some companie are o mall that their common toc are not actively traded; they are owned by only a few people, uually the companie manager. Such firm are aid to be cloely held corporation. In contrat, the toc of mot larger companie are owned by a large number of invetor, mot of whom are not active in management. Such companie are aid to be publicly owned corporation. e. The overthecounter (OTC) maret i the networ of dealer that provide for trading in unlited ecuritie. An organized ecurity exchange i a formal organization, having a tangible phyical location, that facilitate trading in deignated ( lited ) ecuritie. The two major U.S. ecurity exchange are the New Yor Stoc Exchange (NYSE) and the American Stoc Exchange (AMEX). f. The econdary maret deal with trading in previouly iued, or Harcourt, Inc. item and derived item copy right by Harcourt, Inc. Anwer and Solution: 
2 outtanding, hare of etablihed, publicly owned companie. The company receive no new money when ale are made in the econdary maret. The primary maret handle additional hare old by etablihed, publicly owned companie. Companie can raie additional capital by elling in thi maret. g. Going public i the act of elling toc to the public at large by a cloely held corporation or it principal tocholder, and thi maret i often termed the initial public offering (IPO) maret. h. Intrinic value ( Pˆ) i the preent value of the expected future cah flow. The maret price (P ) i the price at which an aet can be old. i. The required rate of return on common toc, denoted by, i the minimum acceptable rate of return conidering both it riine and the return available on other invetment. The expected rate of return, denoted by ˆ, i the rate of return expected on a toc given it current price and expected future cah flow. If the toc i in equilibrium, the required rate of return will equal the expected rate of return. The realized (actual) rate of return, denoted by, i the rate of return that wa actually realized at the end of ome holding period. Although expected and required rate of return mut alway be poitive, realized rate of return over ome period may be negative. j. The capital gain yield reult from changing price and i calculated a (P  P )/P, where P i the beginningofperiod price and P i the endofperiod price. For a contant growth toc, the capital gain yield i g, the contant growth rate. The dividend yield on a toc can be defined a either the endofperiod dividend divided by the beginningofperiod price, or the ratio of the current dividend to the current price. Valuation formula ue the former definition. The expected total return, or expected rate of return, i the expected capital gain yield plu the expected dividend yield on a toc. The expected total return on a bond i the yield to maturity.. A zero growth toc ha contant earning and dividend; thu, the expected dividend payment i fixed, jut a a bond coupon payment. Since the company i preumed to continue operation indefinitely, the dividend tream i a perpetuity. A perpetuity i a ecurity on which the principal never ha to be repaid. l. Normal, or contant, growth occur when a firm earning and dividend grow at ome contant rate forever. One category of noncontant growth toc i a upernormal growth toc which ha one or more year of growth above that of the economy a a whole, but at ome point the growth rate will fall to the normal rate. Thi occur, generally, a part of a firm normal life cycle. Anwer and Solution:  Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
3 l. Equilibrium i the condition under which the expected return on a ecurity i jut equal to it required return, ˆ, and the price i table. n. The Efficient Maret Hypothei (EMH) tate () that toc are alway in equilibrium and () that it i impoible for an invetor to conitently beat the maret. In eence, the theory hold that the price of a toc will adjut almot immediately in repone to any new development. In other word, the EMH aume that all important information regarding a toc i reflected in the price of that toc. Financial theorit generally define three form of maret efficiency: weaform, emitrongform, and trongform. Weaform efficiency aume that all information contained in pat price movement i fully reflected in current maret price. Thu, information about recent trend in a toc price i of no ue in electing a toc. Semitrongform efficiency tate that current maret price reflect all publicly available information. Therefore, the only way to gain abnormal return on a toc i to poe inide information about the company toc. Strongform efficiency aume that all information pertaining to a toc, whether public or inide information, i reflected in current maret price. Thu, no invetor would be able to earn abnormal return in the toc maret. o. Preferred toc i a hybridit i imilar to bond in ome repect and to common toc in other repect. Preferred dividend are imilar to interet payment on bond in that they are fixed in amount and generally mut be paid before common toc dividend can be paid. If the preferred dividend i not earned, the director can omit it without throwing the company into banruptcy. So, although preferred toc ha a fixed payment lie bond, a failure to mae thi payment will not lead to banruptcy. Mot preferred toc entitle their owner to regular fixed dividend payment.  True. The value of a hare of toc i the PV of it expected future dividend. If the two invetor expect the ame future dividend tream, and they agree on the toc riine, then they hould reach imilar concluion a to the toc value. 3 A perpetual bond i imilar to a nogrowth toc and to a hare of preferred toc in the following way:. All three derive their value from a erie of cah inflowcoupon payment from the perpetual bond, and dividend from both type of toc.. All three are aumed to have indefinite live with no maturity value (M) for the perpetual bond and no capital gain yield for the toc. Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  3
4 4 Ye. If a company decide to increae it payout ratio, then the dividend yield component will rie, but the expected longterm capital gain yield will decline. 5 No. The correct equation ha in the numerator and a minu ign in the denominator. 6 a. The average invetor in a lited firm i not really intereted in maintaining hi proportionate hare of ownerhip and control. If he wanted to increae hi ownerhip, he could imply buy more toc on the open maret. Conequently, mot invetor are not concerned with whether new hare are old directly (at about maret price) or through right offering. However, if a right offering i being ued to effect a toc plit, or if it i being ued to reduce the underwriting cot of an iue (by ubtantial underpricing), the preemptive right may well be beneficial to the firm and to it tocholder. b. The preemptive right i clearly important to the tocholder of cloely held firm whoe owner are intereted in maintaining their relative control poition. Anwer and Solution:  4 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
5 SOLUTIONS TO ENOFCHAPTER PROBLEMS  $.5; g 3 5%; g n %; through 5? ( + g ) $.5(.5) $.575. ( + g )( + g ) $.5(.5) $ ( + g )( + g )( + g 3 ) $.5(.5) 3 $ ( + g )( + g )( + g 3 )( + g n ) $.5(.5) 3 (.) $.9. 5 ( + g )( + g )( + g 3 )( + g n ) $.5(.5) 3 (.) $..  $.5; g 7%; 5%; Pˆ? Pˆ g $ $ P $; $.; g %; Pˆ?; ˆ? Pˆ P ( + g) $(.) $. ˆ P $. $ + g $.(.) $ %. ˆ 5.5%. 4 p $5.; V p $6; p? p v p p $5. $ % Pˆ Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  5
6 Step : Calculate the required rate of return on the toc: RF + ( M  RF )b 7.5% + (4%)..3%. Step : Calculate the expected dividend: $. $.(.) $.4 $.(.) $.88 3 $.88(.7) $3.8 Step 3: Calculate the PV of the expected dividend: PV iv $.4/(.3) + $.88/(.3) $.4 + $.8 $4.4. Step 4: Calculate Pˆ : Pˆ 3 /(  g) $3.8/(.3 .7) $58.. Step 5: Calculate the PV of Pˆ : PV $58./(.3) $46.8. Step 6: Sum the PV to obtain the toc price: Pˆ $4.4 + $46.8 $5.5. Alternatively, uing a financial calculator, input the following: CF, CF.4, and CF 6.99 ( ) and then enter I.3 to olve for NPV $ The problem a you to determine the contant growth rate, given the following fact: P $8, $4, and 4%. Ue the contant growth rate formula to calculate g: ˆ P + g $ g $ 8 g.9 9%. 7 The problem a you to determine the value of 3 Pˆ, given the following fact: $, b.9, RF 5.6%, RP M 6%, and P $5. Proceed a follow: Anwer and Solution:  6 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
7 Step : Calculate the required rate of return: RF + ( M  RF )b 5.6% + (6%).9 %. Step : Ue the contant growth rate formula to calculate g: ˆ P + g $. + g $ 5 g.3 3%. Step 3: Calculate Pˆ 3 : Pˆ P 3 ( + g) 3 $5(.3) 3 $7.38 $7.3. Alternatively, you could calculate 4 and then ue the contant growth rate formula to olve for Pˆ 3 : 4 ( + g) 3 $.(.3) 3 $.855. Pˆ $.855/(. .3) $7.388 $ V p p / p ; therefore, p p /V p. a. p $8/$6 3.3%. b. p $8/$8 %. c. p $8/$ 8%. d. p $8/$4 5.7%. 9 Pˆ g ( + g) g $ 5[ + (.5)].5 (.5)] $ 5(.95) $4.75. $ a. i RF + ( M  RF )b i. C 9% + (3%  9%).4.6%. 9% + (3%  9%).5 7%. Note that i below the rifree rate. But ince thi toc i lie an inurance policy becaue it pay off when omething bad happen (the maret fall), the low return i not unreaonable. b. In thi ituation, the expected rate of return i a follow: ˆ C /P + g $.5/$5 + 4% %. Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  7
8 However, the required rate of return i.6 percent. Invetor will ee to ell the toc, dropping it price to the following: Pˆ C $ $.73. At thi point, ˆ C equilibrium. $.5 $ %.6%, and the toc will be in  $, S 7% + 6% 3%, g 5%, g 5%, g n 6% % g 5% g 5% g 6% /(.3 .6) $5.3  Calculate the dividend tream and place them on a time line. Alo, calculate the price of the toc at the end of the upernormal growth period, and include it, along with the dividend to be paid at t 5, a CF 5. Then, enter the cah flow a hown on the time line into the cah flow regiter, enter the required rate of return a I 5, and then find the value of the toc uing the NPV calculation. Be ure to enter CF, or ele your anwer will be incorrect. ;,, 3. 4.(.5).5; 5.(.5).5; 6.(.5) (.8) $.43. Pˆ? % g 5% g 8% $9.89 Pˆ Pˆ 5 6 /(  g).43/(.5 .8) Thi i the price of the toc at the end of Year 5. CF ; CF  ; CF 3.; CF 4.5; CF ; I 5%. With thee cah flow in the CFLO regiter, pre NPV to get the value of the toc today: NPV $9.89. Anwer and Solution:  8 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
9 3 a. V p p p $.8 $5. b. V p $. $ g 5%. 3 4 Pˆ a. $(.5) $.. $(.5) $.. 3 $(.5) 3 $.3. b. PV $.(.899) + $.(.797) + $.3(.78) $ Calculator olution: Input,.,., and.3 into the cah flow regiter, input I, PV? PV $5.9. c. $34.73(.78) $4.7. Calculator olution: Input,,, and into the cah flow regiter, I, PV? PV $4.7. d. $4.7 + $5.9 $3. Maximum price you hould pay for the toc. e. Pˆ ( + g) g g $...5 $3.. f. The value of the toc i not dependent upon the holding period. The value calculated in Part a through d i the value for a 3year holding period. It i equal to the value calculated in Part e except for a mall rounding error. Any other holding period would produce the ame value of Pˆ ; that i, Pˆ $ a. g $.449/$ %. Calculator olution: Input N, PV .7, PMT, FV.449, I? I 7.%. b. $.7/$.4 5%. c. ˆ /P + g $.7/$.4 + 7% 5% + 7% %. Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  9
10 6 a.. Pˆ $ (.5) $.9. $9.5.. Pˆ $/.5 $ Pˆ $ (.5).5.5 $.. $.. 4. Pˆ $ (.).5. $..5 $44.. b.. Pˆ $.3/ Undefined.. Pˆ $.4/(.5) $48, which i nonene. Thee reult how that the formula doe not mae ene if the required rate of return i equal to or le than the expected growth rate. c. No. 7 The anwer depend on when one wor the problem. We ued the June 6,, Wall Street Journal: a. $33½ to $6. b. Current dividend $.88. ividend yield $.88/$ %. You might want to ue an expected dividend yield of ($.88)( + g)/$ , with g etimated omehow. c. The $ cloe wa up 5 / 8 from the previou day cloe. d. The return on the toc conit of a dividend yield of about.6 percent plu ome capital gain yield. We would expect the total rate of return on toc to be in the to percent range. Anwer and Solution:  Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
11 8 a. End of Year: % g 5% g 5% t ( + g) t $.75(.5) $.. 3 $.75(.5) $.75(.35) $.3. 4 $.75(.5) 3 $.75(.59) $ $.75(.5) 4 $.75(.749) $ $.75(.5) 5 $.75(.4) $3.5. b. Step PV of dividend t ( 5 t t + ) PV $.(PVIF %, ) $.(.899) $.79 PV 3 $.3(PVIF %, ) $.3(.797) $.84 PV 4 $.66(PVIF %,3 ) $.66(.78) $.89 PV 5 $3.6(PVIF %,4 ) $3.6(.6355) $.94 PV 6 $3.5(PVIF %,5 ) $3.5(.5674) $. PV of dividend $9.46 Step. Pˆ 6 7 g n 6(+ gn) g n $ 3.5(.5)..5 $3.7.7 $5.8. Thi i the price of the toc 5 year from now. The PV of thi price, dicounted bac 5 year, i a follow: PV of Pˆ 6 $5.8(PVIF %,5 ) $5.8(.5674) $9.96. Step 3 The price of the toc today i a follow: Pˆ PV dividend Year 6 + PV of Pˆ 6 $ $9.96 $39.4. Thi problem could alo be olved by ubtituting the proper value into the following equation: 5 t ( + g ) 6 Pˆ. t t ( ) gn Calculator olution: Input,.,.3,.66, 3.6, 56.3 ( ) into the cah flow regiter, input I, PV? PV $ Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution: 
12 c. /P $./$ % Capital gain yield 6.9* Expected total return.% 7 6 /P 5 $3.7/$5.8 7.% Capital gain yield 5. Expected total return.% *We now that i percent, and the dividend yield i 5. percent; therefore, the capital gain yield mut be 6.9 percent. The main point to note here are a follow:. The total yield i alway percent (except for rounding error).. The capital gain yield tart relatively high, then decline a the upernormal growth period approache it end. The dividend yield rie. 3. After /3/6, the toc will grow at a 5 percent rate. The dividend yield will equal 7 percent, the capital gain yield will equal 5 percent, and the total return will be percent. d. People in high income tax bracet will be more inclined to purchae growth toc to tae the capital gain and thu delay the payment of taxe until a later date. The firm toc i mature at the end of 3. e. Since the firm upernormal and normal growth rate are lower, the dividend and, hence, the preent value of the toc price will be lower. The total return from the toc will till be percent, but the dividend yield will be larger and the capital gain yield will be maller than they were with the original growth rate. Thi reult occur becaue we aume the ame lat dividend but a much lower current toc price. f. A the required return increae, the price of the toc goe down, but both the capital gain and dividend yield increae initially. Of coure, the longterm capital gain yield i till 4 percent, o the longterm dividend yield i percent. Anwer and Solution:  Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
13 9 a. Part. Graphical repreentation of the problem: Supernormal Normal growth growth 3 ( + Pˆ ) 3 PV PV PVPˆ P ( + g ) $.6(.) $.9. ( + g ) $.6(.) $.34. Pˆ 3 g n ( + g ) g n n $.34(.6)..6 $6.6. Pˆ PV( ) + PV( ) + PV( Pˆ ) Pˆ + + ( + ) ( + ) ( + ) $.9(.99) + $.34(.864) + $6.6(.864) $54.. Calculator olution: Input,.9, ( ) into the cah flow regiter, input I, PV? PV $54.. Part. Expected dividend yield: /P $.9/$ %. Capital gain yield: Firt, find Pˆ which equal the um of the preent value of and Pˆ, dicounted for one year. $.34 + $6.6 Pˆ (PVIF %, ) + Pˆ(PVIF %, ) (.) $57.6. Calculator olution: Input, ( ) into the cah flow regiter, input I, PV? PV $57.6. Second, find the capital gain yield: Pˆ P P $ 57.6 $54. $ %. ividend yield 3.55% Capital gain yield 6.45.%. Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  3
14 b. ue to the longer period of upernormal growth, the value of the toc will be higher for each year. Although the total return will remain the ame, %, the ditribution between dividend yield and capital gain yield will differ: The dividend yield will tart off lower and the capital gain yield will tart off higher for the 5year upernormal growth condition, relative to the year upernormal growth tate. The dividend yield will increae and the capital gain yield will decline over the 5year period until dividend yield 4% and capital gain yield 6%. c. Throughout the upernormal growth period, the total yield will be percent, but the dividend yield i relatively low during the early year of the upernormal growth period and the capital gain yield i relatively high. A we near the end of the upernormal growth period, the capital gain yield decline and the dividend yield rie. After the upernormal growth period ha ended, the capital gain yield will equal g n 6%. The total yield mut equal %, o the dividend yield mut equal %  6% 4%. d. Some invetor need cah dividend (retired people) while other would prefer growth. Alo, invetor mut pay taxe each year on the dividend received during the year, while taxe on capital gain can be delayed until the gain i actually realized.  a. RF + ( M  RF )b % + (4%  %).5 5.5%. Pˆ /(  g) $.5/( ) $.43. b. 9% + (%  9%).5 3.5%. Pˆ $.5/( ) $6.47. c. 9% + (%  9%).5.%. Pˆ $.5/(. .5) $3.4. d. New data given: RF 9%; M %; g 6%, b.3. RF + ( M  RF )b 9% + (%  9%).3.6%. Pˆ /(  g) $.7/(.6 .6) $ a. Old RF + ( M  RF )b 9% + (3%)..6%. New 9% + (3%).9.7%. Old price: Pˆ g ( + g) g $(.7) $38.. New price: Pˆ $(.5).7.5 $3.34. Since the new price i lower than the old price, the expanion in conumer product hould be rejected. The decreae in ri i not ufficient to offet the decline in profitability and the reduced Anwer and Solution:  4 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
15 growth rate. b. P Old $38.. P New $(.5)..5 Solving for we have the following: $38. $..5 $. $38.( )  $.95 $4.5 $38.( ).496. Solving for b:.496% 9% + 3%(b).496% 3%(b) b Chec: 9% + (3%) %. Pˆ $ $38.. Therefore, only if management analyi conclude that ri can be lowered to b.49865, or approximately.5, hould the new policy be put into effect. Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Anwer and Solution:  5
16 SOLUTION TO SPREASHEET PROBLEMS  The detailed olution for the problem i available both on the intructor reource CROM (in the file Solution for Ch  Build a Model.xl) and on the intructor ide of the Harcourt College Publiher web ite, 3 a. Supernormal growth rate %; normal growth rate 4% INPUT ATA: KEY OUTPUT: Supernormal growth.% Current price (P ) $3.5 Normal growth rate 4.% Price at /3/6 $4.9 Req. rate of return.% ividend yield 6.% Lat dividend ( ) $ % Supernormal period 5 year Cap. gain yield 5.78% 7 4.% Total return both yr..% MOELGENERATE ATA: Expected dividend: PV of dividend: $ $ Stoc price Stoc price at /3/6: $4.9 at //: $3.5 Yield in 7: Yield in : ividend 8.% ividend 6.% Capital Gain 4.% Capital Gain 5.78% Total.% Total.% b.. 3 percent INPUT ATA: KEY OUTPUT: Supernormal growth.% Current price (P ) $7.86 Normal growth rate 4.% Price at /3/6 $35.64 Req. rate of return 3.% ividend yield 7.3% Lat dividend ( ) $ % Supernormal period 5 year Cap. gain yield 5.97% 7 4.% Total return both yr. 3.% Solution to Spreadheet Problem:  6 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
17 . 5 percent INPUT ATA: KEY OUTPUT: Supernormal growth.% Current price (P ) $.59 Normal growth rate 4.% Price at /3/6 $9.6 Req. rate of return 5.% ividend yield 8.68% Lat dividend ( ) $.75 7.% Supernormal period 5 year Cap. gain yield 6.3% 7 4.% Total return both yr 5.% 3. percent INPUT ATA: KEY OUTPUT: Supernormal growth.% Current price (P ) $5. Normal growth rate 4.% Price at /3/6 $.5 Req. rate of return.% ividend yield.89% Lat dividend ( ) $ % Supernormal period 5 year Cap. gain yield 7.% 7 4.% Total return both yr.% Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Solution to Spreadheet Problem:  7
18 CYBERPROBLEM 4 The detailed olution for the cyberproblem i available on the intructor ide of the Harcourt College Publiher web ite: Solution to Cyberproblem:  8 Harcourt, Inc. item and derived item copyright by Harcourt, Inc.
19 Harcourt, Inc. item and derived item copyright by Harcourt, Inc. Mini Cae:  9
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