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CHAPTER 8 B-CHAPTER 8STOCK VALUATIONAnswers to Concepts Review and Critical Thinking Questions The value of any investment depends on its cash flows; i., what investors will actually receive. The cash flows from a share of stock are the dividends. Investors believe the company will eventually start ...

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CHAPTER8B135

CHAPTER8 STOCKVALUATI ON Answers to Concepts Review and Critical Thinking Questions 1.

The value of any investment depends on its cash flows; i.e., what investors will actually receive. The cash flows from a share of stock are the dividends.

2.

Investors believe the company will eventually start paying dividends (or be sold to another company).

3.

In general, companies that need the cash will often forgo dividends since dividends are a cash expense. Young, growing companies with profitable investment opportunities are one example; another example is a company in financial distress. This question is examined in depth in a later chapter.

4 . Th eg e n e r a lme t ho df orv a l ui n gas ha r eo fs t oc ki st ofin dt hep r e s e ntv a l ueofa l le xp e c t e df ut ur e di vi de nds .Thedi v i d e ndgr o wt hmode lpr e s e nt e di nt het e xti sonl yv a l i d( i )i fd i vi de ndsa r ee xpe c t e d t oo c c urf or e v e r ,t ha ti s ,t hes t oc kpr o v i de sdi vi d e n dsi npe r pe t ui t y ,a nd( i i )i fac ons t a n tgr o wt hr a t e ofdi vi de ndsoc c ur sf or e v e r .A vi o l a t i onoft h efir s ta s s umpt i onmi gh tbeac ompa n yt ha ti se xpe c t e d t oc e a s eope r a t i o nsa nddi s s ol v ei t s e l fs omefini t en umbe rofy e a r sf r om no w.Th es t oc kofs uc ha c ompa n ywoul dbev a l ue db ya ppl yi n gt heg e n e r a lme t ho dofv a l ua t i one xpl a i n e di nt hi sc ha pt e r .A vi o l a t i o noft hes e c onda s s umpt i onmi ghtbeas t a r t u pfir mt h a ti s n ’ tc ur r e nt l yp a yi nga n yd i vi de nds , bu ti se xpe c t e dt oe v e nt ua l l ys t a r tma ki ngdi v i de ndpa yme nt ss omenumbe rofy e a r sf r om no w.Thi s s t o c kwoul da l s obev a l ue db yt heg e n e r a ldi vi de ndv a l ua t i onme t hode x pl a i ne di nt hi sc ha pt e r . 5.

The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances.

6.

The two components are the dividend yield and the capital gains yield. For most companies, the capital gains yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends, the dividend yields are rarely over five percent and are often much less.

7.

Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the dividend growth rate and the capital gains yield are the same.

8.

In a corporate election, you can buy votes (by buying shares), so money can be used to influence or even determine the outcome. Many would argue the same is true in political elections, but, in principle at least, no one has more than one vote.

9.

It wouldn’t seem to be. Investors who don’t like the voting features of a particular class of stock are under no obligation to buy it.

B1 36SOLUTI ONS 10. Investors buy such stock because they want it, recognizing that the shares have no voting power. Presumably, investors pay a little less for such shares than they would otherwise. 11. Presumably, the current stock value reflects the risk, timing and magnitude of all future cash flows, both short-term and long-term. If this is correct, then the statement is false. Solutions to Questions and Problems NOTE:Al le ndofc hapt e rpr obl e mswe r es ol v e dus i ngas pr e ads he e t .Manypr obl e msr e qui r emul t i pl e s t e ps .Duet os pac ean dr e ad abi l i t yc ons t r a i n t s ,whe nt he s ei nt e r me di at es t e psar ei nc l ude di nt hi s s ol ut i onsmanual ,r ou ndi n gmayappe art ohav eo c c ur r e d.Howe v e r ,t hefin a lans we rf o re ac hpr obl e mi s f o undwi t ho utr oundi ngdur i ngan ys t e pi nt hepr obl e m. Ba s i c 1 . Th ec ons t a ntdi vi de n dgr o wt hmode li s : P 1+g)/( R–g) t=Dt×( Sot hepr i c eoft hes t oc kt od a yi s : P 1+g)/( R–g)=$ 1. 40( 1. 06)/( . 12–. 0 6)=$24. 73 0=D0( Thedi vi de n da ty e a r4i st hedi vi de ndt od a yt i me st heFVI Ff ort heg r o wt hr a t ei nd i vi de ndsa ndf our y e a r s ,s o: 4 4 1+g ) /( R–g)=$1. 40( 1. 06) /( . 12–. 06 )=$29. 46 1+g)/( R–g)=D0( P 3=D3(

Wec a ndot hes a met h i n gt ofindt hedi vi de n di nYe a r16,whi c hg i v e sust hepr i c ei nYe a r15,s o: 16 16 P 1+g)/( R–g )=D0( 1+g ) /( R–g)=$ 1. 40( 1. 06) /( . 1 2–. 06)=$5 9. 27 15=D 15(

The r ei sa not he rf e a t ur eoft hec ons t a ntdi vi de ndgr o wt hmode l :Thes t oc kp r i c egr o wsa tt he di vi de ndgr o wt hr a t e .So ,i fwekno wt hes t oc kpr i c et oda y ,wec a nfindt hef u t ur ev a l u ef ora n yt i me i nt h ef ut ur ewewa n tt oc a l c ul a t et hes t oc kpr i c e . I nt hi spr obl e m,wewa ntt okno wt hes t oc kpr i c ei n t hr e ey e a r s ,a ndweha v ea l r e a d yc a l c ul a t e dt hes t oc kpr i c et od a y .Th es t oc kpr i c ei nt hr e ey e a r swi l l be : 3 3 P ( 1+g ) =$24. 73 ( 1+. 06 ) =$29. 46 3=P 0

Andt hes t o c kpr i c ei n15y e a r swi l lb e : 15 15 P 1+g) =$24. 73 ( 1+. 06) =$59 . 27 15=P 0(

2 . Wen e e dt ofindt her e q ui r e dr e t ur noft hes t o c k.Us i n gt hec on s t a ntgr o wt hmode l ,wec a ns ol v et h e e qu a t i onf orR. Doi n gs o , wefind: R=( D1/P0)+g=( $3. 1 0/$48. 00 )+. 05=11. 46%

CHAPTER8B137 3 . Th edi vi de ndyi e l di st hedi vi de ndn e xty e a rdi vi de db yt hec ur r e ntpr i c e , s ot hedi vi de ndy i e l di s : Di vi d e ndyi e l d=D1/P0=$3. 10/$48 . 00=6. 46%

B1 38SOLUTI ONS Thec a pi t a lg a i nsy i e l d ,o rpe r c e nt a g ei nc r e a s ei nt hes t oc kpr i c e ,i st hes a mea st hed i vi de ndgr o wt h r a t e , s o: Ca pi t a lg a i nsyi e l d=5 % 4 . Us i ngt hec ons t a ntgr o wt hmod e l ,wefindt hepr i c eoft hes t oc kt oda yi s : P ( R–g )=$3 . 6 0/( . 13–. 045)=$42. 35 0=D1/ 5 . Th er e qui r e dr e t ur nofas t oc ki sma deupoft wop a r t s :Thedi vi de ndyi e l da ndt hec a pi t a lg a i nsyi e l d. So, t her e qu i r e dr e t ur noft hi ss t oc ki s : R=Di vi de ndy i e l d+Ca p i t a lga i nsyi e l d=. 039+. 09=9. 90 % 6 . Wekn o wt hes t oc kha sar e qu i r e dr e t ur nof12pe r c e nt ,a ndt hed i vi de nda ndc a pi t a lga i n syi e l da r e e qu a l , s o: Di vi d e ndyi e l d=1/ 2( . 12)=. 06=Ca pi t a lg a i nsyi e l d No wwekno wbo t ht hedi vi de n dyi e l da ndc a pi t a lg a i nsyi e l d.Th edi vi de ndi ss i mpl yt hes t oc kpr i c e t i me st hedi vi de n dyi e l d ,s o: D1=. 06( $70 )=$4. 20 Thi si st hed i vi de ndne x ty e a r .Th eque s t i ona s ksf ort hedi vi de ndt hi sy e a r .Us i n gt her e l a t i ons hi p be t we e nt hedi vi de n dt hi sy e a ra ndt hed i vi de ndne xty e a r : D1=D0( 1+g) Wec a ns ol v ef ort hedi vi de ndt h a twa sj us tpa i d: D1=$4. 20( 1+. 06) D0=$4. 20/1 . 06=$3. 96 7 . Th epr i c eofa n yfina nc i a li ns t r ume nti st hePVo ft hef ut ur ec a s hflo ws .Thef u t ur edi vi de ndsoft hi s s t o c ka r ea na n nui t yf ore i gh ty e a r s , s ot hepr i c eoft hes t oc ki st hePVA, whi c hwi l lbe : P 12. 00 ( PVI F A10%,8)=$64 . 02 0=$ 8 . Th ep r i c eas ha r eo fpr e f e r r e ds t oc ki st hedi vi d e nddi vi de db yt her e q ui r e dr e t u r n.Thi si st hes a me e qu a t i ona st hec on s t a ntgr o wt hmod e l ,wi t had i vi de ndgr o wt hr a t eofz e r ope r c e n t .Re me mbe r ,mos t pr e f e r r e ds t oc kpa y safix e ddi vi de nd,s ot hegr o wt hr a t ei sz e r o .Us i n gt hi se qu a t i on ,wefindt he pr i c epe rs ha r eoft hepr e f e r r e ds t oc ki s : R=D/ P 8. 2 5/ $113=7. 30% 0 =$

CHAPTER8B139 I n t e r me di at e 9 . Th i ss t oc kha sac ons t a n tgr o wt hr a t eofdi vi de nds ,b utt her e q ui r e dr e t u r nc ha n g e st wi c e .Tofindt he v a l ueoft hes t oc kt oda y ,wewi l lbe gi nb yfindi n gt hepr i c eoft hes t oc ka tYe a r6 ,whe nbot ht he di vi de ndgr o wt hr a t ea ndt her e qui r e dr e t ur na r es t a bl ef or e v e r .Thep r i c eoft hes t o c ki nYe a r6wi l l bet h edi vi de ndi nYe a r7, d i vi de db yt her e qu i r e dr e t ur nmi nust hegr o wt hr a t ei ndi vi de nds .So : 7 7 P 1+g)/( R–g)=D0( 1+g) /( R–g)=$3. 0 0( 1. 0 5) /( . 11–. 05)=$70. 3 6 6=D6(

No w wec a nfindt hep r i c eoft hes t o c ki nYe a r3.Wene e dt ofindt hepr i c ehe r es i nc et her e q ui r e d r e t u r nc ha ng e sa tt ha tt i me .Thep r i c eoft hes t oc ki nYe a r3i st hePVoft hedi vi de ndsi nYe a r s4,5 , a nd6 ,pl ust hePVo ft hes t oc kpr i c ei nYe a r6 .Thepr i c eoft h es t o c ki nYe a r3i s : 3 6 5 4 /1. 1 4 +$70. 36/1. 143 /1. 142+$3. 00( 1. 0 5) /1 . 14+$ 3. 00( 1. 050 ) P 3. 0 0( 1. 050) 3 =$ 56. 35 P 3 =$

Fi na l l y ,wec a nfindt hepr i c eoft hes t o c kt oda y .Thepr i c et oda ywi l lb et hePV oft hedi vi de n dsi n Ye a r s1, 2, a nd3 , pl ust hePVoft hes t oc ki nYe a r3. Thepr i c eo ft hes t oc kt od a yi s : 2 2 3 3 3 P 3. 00( 1 . 050)/1. 1 6+$3. 0 0 ( 1. 050) /( 1 . 16 ) +$3 . 00 ( 1. 050) /( 1 . 16 ) +$56. 35/( 1. 16 ) 0 =$ =$43. 50

1 0.He r eweha v eas t oc kt ha tpa y snodi vi de nd sf or10y e a r s .Onc et hes t oc kbe g i nspa yi n gdi v i de nds ,i t wi l lh a v eac on s t a n tgr o wt hr a t eofdi vi de nd s .Wec a nus et hec ons t a ntgr o wt hmode la tt ha tpoi nt .I t i si mp or t a n tt or e me mbe rt ha tg e ne r a lc ons t a ntdi vi de ndgr o wt hf or mul ai s : P Dt×( 1+g ) ]/( R–g) t=[ Thi sme a nst ha ts i nc ewewi l lus et hedi vi de ndi nYe a r10,wewi l lb efindi n gt hes t oc kpr i c ei nYe a r 9.Thedi vi de n dgr o wt hmode li ss i mi l a rt ot hePVAa n dt hePV ofap e r pe t ui t y:Thee q ua t i ongi v e s y out hePVonep e r i odbe f or et hefir s tpa yme nt .So, t h epr i c eoft hes t oc ki nYe a r9wi l lbe : ( R–g)=$8. 00/( . 13–. 0 6 )=$1 14. 29 P 9=D10 / Thepr i c eoft hes t oc kt oda yi ss i mpl yt hePVoft hes t o c kp r i c ei nt h ef ut ur e . Wes i mp l ydi s c ou ntt he f ut ur es t oc kpr i c ea tt her e qui r e dr e t ur n. Thepr i c eoft hes t oc kt o da ywi l lbe : P 114. 29/1. 139=$ 38. 04 0=$ 1 1.Th epr i c eofas t o c ki st hePV oft hef ut ur edi v i de nds .Thi ss t oc ki spa y i ngf ourdi vi de n ds ,s ot h e pr i c eoft hes t o c ki st hePVoft he s edi v i de nd sus i n gt her e qu i r e dr e t ur n. Thepr i c eoft hes t oc ki s : 4 P 12/1 . 11+$15/1 . 112+$18/1 . 113+$21/1 . 1 1 =$4 9. 98 0=$

1 2.Wi t hs upe r nor ma ldi vi de nd s , wefindt hepr i c eo ft hes t oc kwhe nt hedi vi d e ndsl e v e lo ffa tac o ns t a nt gr o wt hr a t e ,a ndt he nfindt hePV oft hef ut ur es t oc kp r i c e ,pl ust hePV ofa l ldi vi de ndsdur i n gt he s upe r no r ma lgr o wt hpe r i od.Thes t oc kbe gi nsc ons t a ntgr o wt hi nYe a r4 ,s owec a nfindt hepr i c eof t hes t oc ki nYe a r3, oney e a rb e f or et hec ons t a ntdi vi de ndgr o wt hbe gi ns ,a s :

B1 40SOLUTI ONS P 1+g)/( R–g)=$ 2. 00( 1. 05 )/( . 13–. 0 5)=$2 6. 25 4=D4(

CHAPTER8B141 Thepr i c eo ft hes t oc kt od a yi st hePV oft hefir s tt hr e edi v i de nds ,p l ust hePV oft heYe a r3s t o c k pr i c e .So, t hepr i c eoft hes t oc kt oda ywi l lbe : 3 3 P 8. 00/1. 13+$6 . 00/1 . 132+$3. 00/1. 1 3 +$26. 2 5/1 . 13 =$31. 18 0=$

1 3.Wi t hs upe r nor ma ldi vi de nd s , wefindt hepr i c eo ft hes t oc kwhe nt hedi vi d e ndsl e v e lo ffa tac o ns t a nt gr o wt hr a t e ,a ndt he nfindt hePV oft hef ut ur e s s t oc kpr i c e ,pl ust hePV ofa l ldi vi de ndsdur i n gt he s upe r no r ma lgr o wt hpe r i od.Thes t oc kbe gi nsc ons t a ntgr o wt hi nYe a r4 ,s owec a nfindt hepr i c eof t hes t oc ki nYe a r3, oney e a rb e f or et hec ons t a ntdi vi de ndgr o wt hbe gi nsa s : 3 3 ( 1+g )/( R–g)=$ 2. 80( 1. 25 ) ( 1. 07)/( . 1 3–. 07)=$97. 53 P 1+g)/( R–g)=D0( 1+g ) 2 1 3 =D3(

Thepr i c eo ft hes t oc kt od a yi st hePV oft hefir s tt hr e edi v i de nds ,p l ust hePV oft heYe a r3s t o c k pr i c e .Thepr i c eoft h es t oc kt oda ywi l lbe : 2 3 P . 80( 1. 25)/1. 13+$2. 80 ( 1 . 25) /1. 132+$2. 80( 1. 25) /1. 1 33+$97 . 53/1. 133 0 =2 P 77. 90 0 =$

1 4.He r ewene e dt ofindt hedi vi de ndn e xty e a rf oras t oc ke xpe r i e n c i ngs up e r n or ma lgr o wt h.Wekno w t hes t o c kpr i c e ,t hedi vi de ndgr o wt hr a t e s ,a ndt her e qui r e dr e t ur n,bu tnott hedi vi de nd .Fi r s t ,we ne e dt or e a l i z et ha tt hedi vi de ndi nYe a r3i st hec ur r e ntdi vi de n dt i me st h eFVI F.Thedi vi de ndi n Ye a r3wi l lbe : 3 1. 30) D3=D0(

Andt hedi vi de n di nYe a r4wi l lbet hedi vi de n di nYe a r3t i me son epl ust h egr o wt hr a t e , o r : 3 ( 1 . 1 8) 1. 30) D4=D0(

Thes t oc kbe g i n sc ons t a ntgr o wt hi nYe a r4 ,s owec a nfindt hepr i c eoft hes t oc ki nYe a r4a st he di vi de ndi nYe a r5,di vi d e db yt her e qui r e dr e t ur nmi nust heg r o wt hr a t e .Th ee qua t i onf ort hepr i c e oft hes t oc ki nYe a r4i s : P 1+g)/( R–g) 4 =D4( No wwec a ns u bs t i t ut et hepr e vi ousdi vi de n di nYe a r4i nt ot hi se qua t i ona sf ol l o ws : 3 1+g2)( 1+g3)/( R–g) P 1+g 1)( 4=D0( 3 ( 1 . 1 8)( 1. 08)/( . 14–. 08)=46. 66 D0 P 1. 30) 4 =D0(

Wh e nwes ol v et hi se q ua t i on ,wefindt ha tt hes t oc kpr i c ei nYe a r4i s46 . 66t i me sa sl a r g ea st he di vi de ndt oda y .No wwene e dt ofindt h ee qua t i onf ort h es t oc kpr i c et oda y .Thes t oc kpr i c et oda yi s t hePVo ft h edi vi de ndsi nYe a r s1 ,2, 3, a nd4, pl ust hePVoft heYe a r4pr i c e .So: 2 3 3 3 4 4 P ( 1. 30 ) / 1. 14+D0( 1 . 30) / 1. 1 42+D0( 1. 30 ) / 1. 14 +D0( 1 . 30) ( 1. 18 ) / 1. 14 +46. 66D0/ 1. 1 4 0=D0 Wec a nf a c t o ro utD0i nt h ee qua t i on, a ndc o mbi net hel a s tt wot e r ms . Doi ngs o ,weg e t : 3 3 P 70. 00=D0{ 1. 30 / 1. 1 4+1. 3 02/ 1. 142+1. 30 / 1. 1 43+[ ( 1. 30) ( 1 . 18 )+46 . 66]/1 . 144} 0=$

B1 42SOLUTI ONS

CHAPTER8B143 Re duc i n gt hee q ua t i one v e nf ur t he rb ys ol vi n ga l loft het e r msi nt hebr a c e s , weg e t : $7 0=$3 3. 04D0 D0=$70. 00/$ 33 . 04=$ 2. 12 Thi si st hedi v i de ndt oda y ,s ot hepr o j e c t e ddi v i de ndf ort hen e xty e a rwi l lbe : D1=$2. 12( 1 . 30)=$2. 75 1 5.Th ec ons t a ntgr o wt h mode lc a nbea pp l i e de v e ni ft hedi vi de ndsa r ede c l i n i n gb yac on s t a nt pe r c e nt a g e , j us t ma kes u r et or e c og ni z et hen e g a t i v egr o wt h.So, t h ep r i c eoft h es t oc kt oda ywi l lbe : P 1+g)/( R–g)=$ 10. 00( 1–. 08)/[ ( . 1 1–( –. 08) ]=$48. 42 0=D0( 1 6.Wea r egi v e nt hes t oc kpr i c e ,t hedi v i de ndgr o wt hr a t e ,a ndt her e qu i r e dr e t ur n,a nda r ea s ke dt ofind t hedi vi de nd . Us i ngt hec o ns t a ntdi vi de ndgr o wt hmode l ,weg e t : P 50=D0 ( 1+g)/( R–g) 0=$ Sol v i ngt hi se qua t i onf ort h edi vi de ndgi v e sus : D0=$50( . 14–. 08)/( 1 . 0 8)=$ 2. 78 1 7.Th epr i c eofas ha r eo fpr e f e r r e ds t oc ki st hed i vi de ndpa yme n tdi v i de db yt her e qu i r e dr e t ur n.We kn o wt hedi vi de ndpa yme nti nYe a r6,s owec a nfin dt hepr i c eoft hes t oc ki nYe a r5,o ney e a rbe f or e t hefir s t di vi de ndp a yme nt .Doi n gs o, weg e t : P 9. 00/. 0 7=$12 8. 57 5=$ Thepr i c eoft hes t oc kt oda yi st hePVoft hes t oc kpr i c ei nt hef ut ur e , s ot hepr i c et oda ywi l lbe : 5 P 128. 57/( 1. 07 ) =$91. 67 0=$

1 8.Th ea nnua ldi vi de n dp a i dt os t oc khol de r si s$0. 15,a ndt hedi vi de ndyi e l di s0. 2pe r c e nt .Us i n gt he e qu a t i onf ort hedi vi de ndy i e l d: Di vi d e ndyi e l d=Di v i de nd/St oc kp r i c e Wec a npl ugt henumb e r si na n ds ol v ef ort hes t o c kpr i c e : . 0 02=$0 . 15/P 0 P 0. 15 / . 002=$75. 0 0 0=$ The“ Ne tChg”oft hes t oc ks h o wst hes t oc ki nc r e a s e db y$2 . 20ont hi sda y ,s ot hec l os i n gs t oc kpr i c e y e s t e r da ywa s : Ye s t e r da y ’ sc l os i ngpr i c e=$75. 0 0–2. 20=$72. 80

B1 44SOLUTI ONS

CHAPTER8B145 Tofindt hen e ti nc ome ,wene e dt ofin dt heEPS.Thes t oc kquot et e l l sust heP/ Er a t i of o rt hes t oc ki s 14 . Si nc ewekno wt hes t oc kpr i c ea swe l l ,wec a nus et heP/ Er a t i ot os o l v ef o rEPSa sf ol l o ws : P/ E=14=St oc kpr i c e/EPS=$75. 0 0/EPS EPS=$75 . 00/14=$5 . 357 Wekno wt ha tEPSi sj us tt h et ot a lne ti nc omedi vi de db yt henumbe rofs ha r e sout s t a nd i ng , s o : EPS=NI/Sha r e s=$5. 3 57=NI/2 5, 000, 000 NI=$5. 357 ( 25, 000, 00 0 )=$1 33, 928, 57 1 Chal l e ng e 19. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.

W: P0 = D0(1 + g) / (R – g) = $4.50(1.10)/(.15 – .10) = $99.00 Dividend yield = D1/P0 = 4.50(1.10)/99.00 = 5% Capital gains yield = .15 – .05 = 10% X:

P0 = D0(1 + g) / (R – g) = $4.50/(.15 – 0) = $30.00 Dividend yield = D1/P0 = 4.50/30.00 = 15% Capital gains yield = .15 – .15 = 0%

Y:

P0 = D0(1 + g) / (R – g) = $4.50(1 – .05)/(.15 + .05) = $21.38 Dividend yield = D1/P0 = 4.50(0.95)/21.38 = 20% Capital gains yield = .15 – .20 = – 5%

Z:

P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2)/(R – g) = $4.50(1.20)2(1.12)/(.15 – .12) = $241.92 P0 = $4.50 (1.20) / (1.15) + $4.50 (1.20)2 / (1.15)2 + $241.92 / (1.15)2 = $192.52 Dividend yield = D1/P0 = $4.50(1.20)/$192.52 = 2.8% Capital gains yield = .15 – .028 = 12.2%

B1 46SOLUTI ONS I na l lc a s e s ,t her e q ui r e dr e t ur ni s15 %,butt her e t ur ni sdi s t r i but e ddi ffe r e nt l yb e t we e nc ur r e nt i nc o mea ndc a p i t a lg a i ns .Hi ghgr o wt hs t oc k sha v ea na ppr e c i a b l ec a pi t a lga i n sc ompone n tb uta r e l a t i v e l ys ma l lc ur r e n ti n c omeyi e l d;c on v e r s e l y ,ma t ur e ,ne g a t i v e gr o wt hs t oc kspr o vi deah i gh c ur r e nti nc omebuta l s opr i c ede pr e c i a t i ono v e rt i me . 20. a.

Using the constant growth model, the price of the stock paying annual dividends will be: P0 = D0(1 + g) / (R – g) = $3.00(1.06)/(.14 – .06) = $39.75

b.

If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or: Quarterly dividend: $3.00(1.06)/4 = $0.795 To find the equivalent annual dividend, we must assume that the quarterly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock. So, the effective quarterly rate is: . 25 Effe c t i v equa r t e r l yr a t e :1. 1 4 –1=. 0333

Thee ffe c t i v ea nnu a ldi v i d e ndwi l lb et heFVA oft heq ua r t e r l ydi vi de ndp a yme nt sa tt he e ffe c t i v equa r t e r l yr e q ui r e dr e t ur n. I nt hi sc a s e , t hee ffe c t i v ea nnu a ldi vi de ndwi l lbe : Effe c t i v e D =$0. 795 ( FVI F A3.33%,4)=$3. 34 1 No w, wec a nus et hec on s t a ntgr o wt hmode lt ofindt hec ur r e nts t o c kpr i c ea s : P0=$3. 34 / ( . 14–. 06)=$41 . 78 Not et ha twec a nnots i mpl yfindt heq ua r t e r l ye ffe c t i v er e qui r e dr e t ur na ndgr o wt hr a t et ofind t hev a l ueoft hes t oc k .Thi swoul da s s umet hed i vi de ndsi nc r e a s e de a c hqua r t e r , note a c hy e a r . 2 1.He r eweha v eas t o c kwi t hs upe r nor ma lgr o wt h,butt hedi vi de n dgr o wt hc ha ng e se v e r yy e a rf ort he fir s tf o ury e a r s .Wec a nfindt hepr i c eoft hes t o c ki nYe a r3s i nc et h edi vi de ndgr o wt hr a t ei sc ons t a nt a f t e rt het hi r ddi vi d e nd .Thep r i c eoft hes t oc ki nYe a r3wi l lbet hed i vi de n di nYe a r4, di vi de db yt he r e q u i r e dr e t ur nmi nust hec ons t a ntdi vi de ndgr o wt hr a t e . So , t hepr i c ei nYe a r3wi l lb e : P 3. 50 ( 1. 2 0) ( 1. 15 ) ( 1 . 10 ) ( 1. 05)/( . 13–. 0 5)=$69. 73 3=$ Thepr i c eoft hes t ...