# Solutions to Problems: Chapter 7

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1 Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b. Total hae needed \$48,000,000 \$60 800,000 hae The fim equie an additional 200,000 authoized hae to aie the neceay fund at \$60 pe hae. c. Apin mut amend it copoate chate to authoize the iuance of additional hae. Pefeed dividend LG 2; Intemediate a. \$8.80 pe yea o \$2.20 pe quate. b. \$2.20. Fo a noncumulative pefeed only the latet dividend ha to be paid befoe dividend can be paid on common tock. c. \$8.80. Fo cumulative pefeed all dividend in aea mut be paid befoe dividend can be paid on common tock. In thi cae the boad mut pay the thee dividend mied plu the cuent dividend. Pefeed dividend LG 2; Intemediate A \$15.00 quate in aea plu the latet quate B \$8.80 only the latet quate C \$11.00 only the latet quate D \$25.50 quate in aea plu the latet quate E \$8.10 only the latet quate Convetible pefeed tock LG 2; Challenge a. Conveion value conveion atio tock pice 5 \$20 \$100 b. Baed on compaion of the pefeed tock pice veu the conveion value, the inveto hould convet. If conveted, the inveto ha \$100 of value veu only \$96 if he keep ownehip of the pefeed tock.

2 c. If the inveto convet to common tock he will begin eceiving \$1.00 pe hae pe yea of dividend. Conveion will geneate \$5.00 pe yea of total dividend. If the inveto keep the pefeed they will eceive \$10.00 pe yea of dividend. Thi additional \$5.00 pe yea in dividend may caue the inveto to keep the pefeed until foced to convet though ue of the call featue. Futhemoe, while common tock dividend may be cut o eliminated altogethe with no potection, pefeed dividend ae typically fixed and cumulative poviion. P7-5. Peonal finance: Common tock valuation zeo gowth: P 0 D 1 LG 4; Baic a. P 0 \$ \$20 b. P 0 \$ \$12 c. A peceived ik inceae, the equied ate of etun alo inceae, cauing the tock pice to fall. P7-6. Peonal finance: common tock valuation zeo gowth \$5.00 Value of tock when puchaed \$ \$5.00 Value of tock when old \$ Sally capital gain i \$10.42 (\$41.67 \$31.25) pe hae. Sally total capital gain i 100 \$1, P7-7. Pefeed tock valuation: PS 0 D p p a. PS 0 \$ PS 0 \$68.82 b. PS 0 \$ PS 0 \$60.95 The inveto would loe \$7.87 pe hae (\$68.82 \$60.95) becaue a the equied ate of etun on pefeed tock iue inceae above the 9.3% etun he eceive, the value of he tock decline. P7-8. Common tock value contant gowth: P 0 D 1 ( g) LG 4; Baic Fim P 0 D 1 ( g) Shae Pice A P 0 \$1.20 ( ) \$ B P 0 \$4.00 ( ) \$ C P 0 \$0.65 ( ) \$ D P 0 \$6.00 ( ) \$ E P 0 \$2.25 ( ) \$ 18.75

3 P7-9. Common tock value contant gowth a. b. D1 g P0 \$1.20 (1.05) 0.05 \$28 \$ % \$28 \$1.20 (1.10) 0.10 \$28 \$ % \$28 P7-10. Peonal finance: Common tock value contant gowth: P 0 D 1 ( g) Computation of gowth ate: N 5, PV \$2.25, FV \$2.87 Solve fo I 5% a. Value at 13% equied ate of etun: P 0 \$ \$37.75 b. Value at 10% equied ate of etun: P 0 \$ \$60.40 c. A ik inceae, the equied ate of etun inceae, cauing the hae pice to fall. P7-11. Common tock value vaiable gowth: LG 4; Challenge P 0 PV of dividend duing initial gowth peiod PV of pice of tock at end of gowth peiod. Step 1 and 2: Value of cah dividend and PV of annual dividend t D t D t 1/(1.15) t PV of Dividend 1 \$ \$ \$ \$9.05 Step 3: PV of pice of tock at end of initial gowth peiod D 3 1 \$4.98 (1 0.10) D 4 \$5.48

4 P 3 [D 4 ( g 2 )] P 3 \$5.48 ( ) P 3 \$ PV of tock at end of yea 3 N 3, I 15%, FV \$ PV \$72.04 Step 4: Sum of PV of dividend duing initial gowth peiod and PV pice of tock at end of gowth peiod P 0 \$9.05 \$72.04 P 0 \$81.09 P7-13. Common tock value vaiable gowth LG 4; Challenge a. t D t D t 1/(1.11) t PV of Dividend 1 \$ \$ \$ \$5.11 D 4 D 3 (1.05) \$2.27 (1.05) \$2.38 P 3 [D 4 ( g)] P 3 \$2.38 ( ) P 3 \$39.67 PV of tock at end of yea 3 N 3, I 11%, FV \$39.67 Solve fo PV \$29.01 PV of dividend and futue tock pice \$5.11 \$29.01 \$34.12 b. The PV of the fit 3 yea dividend i the ame a in pat a. D 4 D 3 (1.0) 2.27 P 3 [D 4 ( g)] P 3 \$ P 3 \$20.64 PV of tock at end of yea 3 N 3, I 11%, FV \$20.64 Solve fo PV \$15.09 P 0 \$5.11 \$15.09 \$20.20 c. The PV of the fit 3 yea dividend i the ame a in pat a. D 4 D 3 (1.10) 2.50 P 3 [D 4 ( g)] P 3 \$2.50 ( )

5 P 3 \$ PV of tock at end of yea 3 N 3, I 11%, FV \$ PV \$ P 0 \$5.11 \$ \$ P7-14. Peonal finance: Common tock value all gowth model LG 4; Challenge a. P 0 (CF 0 ) P 0 \$42, P 0 \$236,111 b. P 0 (CF 1 ( g)) P 0 (\$45,475 * ( ) P 0 \$413, * CF 1 \$42,500(1.07) \$45,475 c. Step 1 and 2: Value of cah dividend and PV of annual dividend t D t D t 1/(1.18) t PV of Dividend 1 \$42, \$47, \$40, , , , \$78, Step 3: PV of pice of tock at end of initial gowth peiod D 2 1 \$53,312 (1 0.07) D 3 \$57, P 2 [D 3 ( g)] P 2 \$57, ( ) P 2 \$518, PV of tock at end of yea 2 N 2, I 18%, FV \$518, Solve fo PV \$372, Step 4: Sum of PV of dividend duing initial gowth peiod and PV pice of tock at end of gowth peiod P 0 \$78, \$372, P 0 \$451, P7-16. Peonal finance: Uing the fee cah flow valuation model to pice an IPO LG 5; Challenge a. The value of the fim common tock i accomplihed in fou tep. (1) Calculate the PV of FCF fom 2017 to infinity. [\$1,100,000 (1.02)] ( ) \$1,122, \$18,700,000 (2) Add the PV of the cah flow obtained in (1) to the cah flow fo 2016.

6 FCF 2016 \$18,700,000 1,100,000 \$19,800,000 (3) Find the PV of the cah flow fo 2010 though Yea FCF 1/(1.08) t PV 2013 \$700, \$ 648, , , , , ,800, ,533,000 Value of entie company, V c \$16,641,010 (4) Calculate the value of the common tock uing Equation 7.8. V S V C V D V P V S \$16,641,010 \$2,700,000 \$1,000,000 \$12,941,010 Value pe hae \$12,941,010 1,100,000 hae \$10.76 b. Baed on thi analyi the IPO pice of the tock i ove valued by \$0.74 (\$12.50 \$11.76) and you hould not buy the tock. c. The evied value of the fim common tock i calculated in fou tep. (1) Calculate the PV of FCF fom 2017 to infinity. [\$1,100,000 (1.03)] ( ) \$1,133, \$22,660,000 (2) Add the PV of the cah flow obtained in (1) to the cah flow fo FCF 2016 \$22,660,000 1,100,000 \$23,760,000 (3) Find the PV of the cah flow fo 2010 though Yea FCF 1/(1.08) t PV 2013 \$700, \$ 648, , , , , ,760, ,463,600 Value of entie company, V c \$19,551,610 (4) Calculate the value of the common tock uing Equation 7.8. V S V C V D V P V S \$19,551,610 \$2,700,000 \$1,000,000 \$15,851,610 Value pe hae \$15,851,610 1,100,000 hae \$14.41 If the gowth ate i changed to 3% the IPO pice of the tock i unde valued by \$1.91 (\$14.41 \$12.50) and you hould buy the tock. P7-17. Book and liquidation value LG 5; Intemediate a. Book value pe hae: Book value of aet (liabilitie + pefeed tock at book value) numbe of hae outtanding

7 Book value pe hae b. Liquidation value: \$780,000 \$420,000 10,000 \$36 pe hae Cah \$40,000 Liquidation Value of Aet 722,000 Maketable Secuitie 60,000 Le: Cuent Liabilitie (160,000) Account Rec. Long-Tem Debt (180,000) (0.90 \$120,000) 108,000 Pefeed Stock (80,000) Inventoy Available fo CS \$302,000 (0.90 \$160,000) 144,000 Land and Building (1.30 \$150,000) 195,000 Machiney & Equip. (0.70 \$250,000) 175,000 Liq. Value of Aet \$722,000 Liquidation value pe hae Liquidation value of aet Numbe of hae outtanding Liquidation value pe hae \$302,000 10,000 \$30.20 pe hae c. Liquidation value i below book value pe hae and epeent the minimum value fo the fim. It i poible fo liquidation value to be geate than book value if aet ae undevalued. Geneally, they ae ovevalued on a book value bai, a i the cae hee. P7-18. Valuation with pice/eaning multiple LG 5; Baic Fim EPS P/E Stock Pice A 3.0 (6.2) \$18.60 B 4.5 (10.0) \$45.00 C 1.8 (12.6) \$22.68 D 2.4 (8.9) \$21.36 E 5.1 (15.0) \$76.50

8 P7-19. Management action and tock value: P 0 D 1 ( g) LG 6; Intemediate a. P 0 \$3.15 ( ) \$31.50 b. P 0 \$3.18 ( ) \$39.75 c. P 0 \$3.21 ( ) \$32.10 d. P 0 \$3.12 ( ) \$26.00 e. P 0 \$3.24 ( ) \$36.00 The bet altenative in tem of maximizing hae pice i b. P7-20. Integative ik and valuation and CAPM fomula LG 4, 6; Intemediate P 0 D 1 ( g) \$50 \$3.00 ( 0.09) 0.15 ik-fee ate ik pemium ik pemium ik pemium P7-21. Integative ik and valuation LG 4, 6; Challenge a. 14% 10% 4% b. N 6, PV \$1.73, FV \$2.45 Solve fo g: I 5.97% P 0 D 1 ( g) P 0 \$2.60 ( ) P 0 \$29.45 c. A deceae in the ik pemium would deceae the equied ate of etun, which in tun would inceae the pice of the tock. P7-22. Integative ik and valuation LG 4, 6; Challenge a. Etimate gowth ate: N 5, PV \$2.45, FV \$3.44 Solve fo I 7.02% D 1 (\$ ) \$3.68 P 0 \$3.68 ( ) P 0 \$52.72 b. (1) 0.14 D 1 \$3.61(\$ ) P 0 \$3.61 ( ) \$40.20 pe hae P 0

9 (2) D 1 \$3.68 P 0 \$3.68 ( ) \$61.54 pe hae P 0 Pice i a function of the cuent dividend, expected dividend gowth ate, and the ik-fee ate, and the company-pecific ik pemium. Fo Caft, the loweing of the dividend gowth ate educed futue cah flow eulting in a eduction in hae pice. The deceae in the ik pemium eflected a eduction in ik leading to an inceae in hae pice. P7-23. Ethic poblem a. Thi i a zeo-gowth dividend valuation poblem, o: P 0 D/ \$5/0.11 \$45.45 b. Uing the new dicount ate of 12% (11% 1% cedibility ik pemium), we have: P 0 D/ \$5/0.12 \$41.67 The value decline i the diffeence between pat a and b: Value decline \$41.67 \$45.45 \$3.78 The tock ell fo almot \$4 le becaue the company financial epot cannot be fully tuted. Lack of integity i een to hut tock pice becaue of the cedibility pemium.

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