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ey Chapter 8 Shares and Their Valuation LEARNING OBJECTIVES After studying this chapter, college students ought to be capable to: • Determine a number of the extra essential rights that include inventory possession and outline the next phrases: proxy, proxy struggle, takeover, and preemptive proper. • Briefly clarify why labeled inventory is perhaps utilized by an organization and what founders’ shares are. • Differentiate between carefully held and publicly owned companies and checklist the three distinct varieties of inventory market transactions. Decide the worth of a share of frequent inventory when: (1) dividends are anticipated to develop at some fixed price, (2) dividends are anticipated to stay fixed, and (Three) dividends are anticipated to develop at some super-normal, or nonconstant, progress price. • Calculate the anticipated price of return on a relentless progress inventory. • Apply the full firm (company worth) mannequin to worth a agency in conditions when the agency doesn’t pay dividends or is privately held. • Clarify why a inventory’s intrinsic worth may differ between the full firm mannequin and the dividend progress mannequin. Clarify the next phrases: equilibrium, marginal investor, and Environment friendly Markets Speculation (EMH); distinguish among the many three ranges of market effectivity; briefly clarify the implications of the EMH on monetary selections; and focus on the outcomes of empirical research on market effectivity and the implication of behavioral finance on these outcomes. • Learn and perceive the inventory market web page given within the day by day newspaper. • Clarify the explanations for investing in worldwide shares and determine the “bets” an investor is making when he does make investments abroad. Outline most well-liked inventory, decide the worth of a share of most well-liked inventory, or given its worth, calculate its anticipated return. 1. LECTURE SUGGESTIONS This chapter supplies essential and helpful data on frequent and most well-liked shares. Furthermore, the valuation of shares reinforces the ideas coated in each Chapters 6 and seven, so Chapter 8 extends and reinforces these chapters. We start our lecture with a dialogue of the traits of frequent shares, after which we focus on how shares are valued available in the market and the way inventory costs are reported within the press. We conclude the lecture with a dialogue of most well-liked shares.

The small print of what we cowl, and the best way we cowl it, could be seen by scanning Blueprints Chapter 8. For different solutions in regards to the lecture, please see the “Lecture Options” in Chapter 2, the place we describe how we conduct our lessons. DAYS ON CHAPTER: Three OF 58 DAYS (50-minute intervals) ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1True. The worth of a share of inventory is the PV of its anticipated future dividends. If the 2 traders anticipate the identical future dividend stream, they usually agree on the inventory’s riskiness, then they need to attain comparable conclusions as to the inventory’s worth. -2A perpetual bond is much like a no-growth inventory and to a share of most well-liked inventory within the following methods: 1. All three derive their values from a collection of money inflows–coupon funds from the perpetual bond, and dividends from each varieties of inventory. 2. All three are assumed to have indefinite lives with no maturity worth (M) for the perpetual bond and no capital beneficial properties yield for the shares. 8-3Yes. If an organization decides to extend its payout ratio, then the dividend yield element will rise, however the anticipated long-term capital beneficial properties yield will decline. 8-4No. The right equation has D1 within the numerator and a minus signal within the denominator. -5a. The common investor in a listed agency will not be actually fascinated about sustaining his proportionate share of possession and management. If he wished to extend his possession, he may merely purchase extra inventory on the open market. Consequently, most traders should not involved with whether or not new shares are bought straight (at about market costs) or by rights choices. Nevertheless, if a rights providing is getting used to impact a inventory break up, or whether it is getting used to scale back the underwriting value of a difficulty (by substantial underpricing), the preemptive proper might be useful to the agency and to its stockholders. . The preemptive proper is clearly essential to the stockholders of carefully held companies whose house owners are fascinated about sustaining their relative management positions. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 8-1D0 = $1. 50; g1-Three = 5%; gn = 10%; D1 by D5 = ? D1 = D0(1 + g1) = $1. 50(1. 05) = $1. 5750. D2 = D0(1 + g1)(1 + g2) = $1. 50(1. 05)2 = $1. 6538. D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1. 50(1. 05)Three = $1. 7364. D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1. 50(1. 05)Three(1. 10) = $1. 9101. D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1. 50(1. 05)Three(1. 10)2 = $2. 1011. 8-2D1 = $Zero. 50; g = 7%; ks = 15%; [pic] = ? [pic] -3P0 = $20; D0 = $1. 00; g = 10%; [pic] = ? ; ks = ? [pic] = P0(1 + g) = $20(1. 10) = $22. ks= [pic] + g = [pic] + Zero. 10 = [pic] + Zero. 10 = 15. 50%. ks = 15. 50%. 8-4Dp = $5. 00; Vp = $60; kp = ? kp = [pic] = [pic] = 8. 33%. 8-5a. The terminal, or horizon, date is the date when the expansion price turns into fixed. This happens on the finish of 12 months 2. b. Zero 1 2 Three | | | | 1. 25 1. 50 1. 80 1. 89 37. 80 = [pic] The horizon, or terminal, worth is the worth on the horizon date of all dividends anticipated thereafter. On this drawback it’s calculated as follows: pic] c. The agency’s intrinsic worth is calculated because the sum of the current worth of all dividends in the course of the supernormal progress interval plus the current worth of the terminal worth. Utilizing your monetary calculator, enter the next inputs: CF0 = Zero, CF1 = 1. 50, CF2 = 1. 80 + 37. 80 = 39. 60, I = 10, after which remedy for NPV = $34. 09. 6. The agency’s free money circulate is predicted to develop at a relentless price, therefore we are able to apply a relentless progress formulation to find out the full worth of the agency. Agency Worth = FCF1/(WACC – g) Agency Worth = $150,000,000/(Zero. 10 – Zero. 05) Agency Worth = $Three,000,000,000.

To seek out the worth of an fairness declare upon the corporate (share of inventory), we should subtract out the market worth of debt and most well-liked inventory. This agency occurs to be fully fairness funded, and this step is pointless. Therefore, to search out the worth of a share of inventory, we divide fairness worth (or on this case, agency worth) by the variety of shares excellent. Fairness Worth per share = Fairness Worth/Shares excellent Fairness Worth per share = $Three,000,000,000/50,000,000 Fairness Worth per share = $60. Every share of frequent inventory is price $60, based on the company valuation mannequin. 8-7a. Zero 1 2 Three four | | | | Three,000,000 6,000,000 10,000,000 15,000,000 Utilizing a monetary calculator, enter the next inputs: CF0 = Zero; CF1 = 3000000; CF2 = 6000000; CF3 = 10000000; CF4 = 15000000; I = 12; after which remedy for NPV = $24,112,308. b. The agency’s terminal worth is calculated as follows: [pic] c. The agency’s whole worth is calculated as follows: Zero 1 2 Three four 5 | | | | | | Three,000,000 6,000,000 10,000,000 15,000,000 16,Zero50,000

PV = ? 321,000,000 = [pic] Utilizing your monetary calculator, enter the next inputs: CF0 = Zero; CF1 = 3000000; CF2 = 6000000; CF3 = 10000000; CF4 = 15000000 + 321000000 = 336000000; I = 12; after which remedy for NPV = $228,113,612. d. To seek out Barrett’s inventory value, you might want to first discover the worth of its fairness. The worth of Barrett’s fairness is the same as the worth of the full agency much less the market worth of its debt and most well-liked inventory. Complete agency worth$228,113,612 Market worth, debt + most well-liked 60,000,000 (given in drawback) Market worth of fairness$168,113,612

Barrett’s value per share is calculated as: [pic] 8-8FCF = EBIT(1 – T) + Depreciation – [pic] – ([pic] = $500,000,000 + $100,000,000 – $200,000,000 – $Zero = $400,000,000. Agency worth = [pic] = [pic] = [pic] = $10,000,000,000. That is the full agency worth. Now discover the market worth of its fairness. MVTotal= MVEquity + MVDebt $10,000,000,000= MVEquity + $Three,000,000,000 MVEquity= $7,000,000,000. That is the market worth of all of the fairness. Divide by the variety of shares to search out the value per share. $7,000,000,000/200,000,000 = $35. 00. 8-9a. Terminal worth = [pic] = [pic]= $713. 33 million. . Zero 1 2 Three four | | | | | -20 30 40 42. 80 ($ 17. 70) 23. 49 522. 10 753. 33 $527. 89 Utilizing a monetary calculator, enter the next inputs: CF0 = Zero; CF1 = -20; CF2 = 30; CF3 = 753. 33; I = 13; after which remedy for NPV = $527. 89 million. c. Complete valuet=Zero = $527. 89 million. Worth of frequent fairness = $527. 89 – $100 = $427. 89 million. Value per share = [pic] = $42. 79. 8-10The issue asks you to find out the worth of [pic], given the next info: D1 = $2, b = Zero. 9, kRF = 5. %, RPM = 6%, and P0 = $25. Proceed as follows: Step 1:Calculate the required price of return: ks = kRF + (kM – kRF)b = 5. 6% + (6%)Zero. 9 = 11%. Step 2:Use the fixed progress price formulation to calculate g: [pic] Step Three:Calculate [pic]: [pic] = P0(1 + g)Three = $25(1. 03)Three = $27. 3182 ( $27. 32. Alternatively, you can calculate D4 after which use the fixed progress price formulation to resolve for [pic]: D4 = D1(1 + g)Three = $2. 00(1. 03)Three = $2. 1855. [pic] = $2. 1855/(Zero. 11 – Zero. 03) = $27. 3182 ( $27. 32. 8-11Vp = Dp/kp; subsequently, kp = Dp/Vp. a. kp = $8/$60 = 13. Three%. b. kp = $8/$80 = 10. Zero%. c. p = $8/$100 = 8. Zero%. d. kp = $8/$140 = 5. 7%. 8-12[pic] 8-13a. ki = kRF + (kM – kRF)bi. kC = 9% + (13% – 9%)Zero. four = 10. 6%. kD = 9% + (13% – 9%)(-Zero. 5) = 7%. Observe that kD is beneath the risk-free price. However since this inventory is like an insurance coverage coverage as a result of it “pays off” when one thing dangerous occurs (the market falls), the low return will not be unreasonable. b. On this state of affairs, the anticipated price of return is as follows: [pic] = D1/P0 + g = $1. 50/$25 + four% = 10%. Nevertheless, the required price of return is 10. 6 p.c. Buyers will search to promote the inventory, dropping its value to the next: pic] At this level, [pic], and the inventory will likely be in equilibrium. 8-14Calculate the dividend money flows and place them on a time line. Additionally, calculate the inventory value on the finish of the supernormal progress interval, and embody it, together with the dividend to be paid at t = 5, as CF5. Then, enter the money flows as proven on the time line into the money circulate register, enter the required price of return as I = 15, after which discover the worth of the inventory utilizing the NPV calculation. You should definitely enter CF0 = Zero, or else your reply will likely be incorrect. D0 = Zero; D1 = Zero; D2 = Zero; D3 = 1. Zero; D4 = 1. 00(1. 5) = 1. 5; D5 = 1. 00(1. 5)2 = 2. 25; D6 = 1. 00(1. 5)2(1. 08) = $2. 43. [pic] = ? Zero 1 2 Three four 5 6 | | | | | | | 1. 00 1. 50 2. 25 2. 43 Zero. 658 +34. 71 = Zero. 858 18. 378 36. 96 $19. 894 = [pic] [pic] = D6/([pic] – g) = $2. 43/(Zero. 15 – Zero. 08) = $34. 71. That is the inventory value on the finish of 12 months 5.

CF0 = Zero; CF1-2 = Zero; CF3 = 1. Zero; CF4 = 1. 5; CF5 = 36. 96; I = 15%. With these money flows within the CFLO register, press NPV to get the worth of the inventory in the present day: NPV = $19. 89. 8-15a. The popular inventory pays $8 yearly in dividends. Subsequently, its nominal price of return can be: Nominal price of return = $8/$80 = 10%. Or alternatively, you can decide the safety’s periodic return and multiply by four. Periodic price of return = $2/$80 = 2. 5%. Nominal price of return = 2. 5% ( four = 10%. b. EAR = (1 + NOM/four)four – 1 EAR = (1 + Zero. 10/four)four – 1 EAR = Zero. 103813 = 10. 3813%. -16The worth of any asset is the current worth of all future money flows anticipated to be generated from the asset. Therefore, if we are able to discover the current worth of the dividends in the course of the interval previous long-run fixed progress and subtract that whole from the present inventory value, the remaining worth can be the current worth of the money flows to be obtained in the course of the interval of long-run fixed progress. D1 = $2. 00 ( (1. 25)1 = $2. 50PV(D1) = $2. 50/(1. 12)1= $2. 2321 D2 = $2. 00 ( (1. 25)2 = $Three. 125PV(D2) = $Three. 125/(1. 12)2= $2. 4913 D3 = $2. 00 ( (1. 25)Three = $Three. 90625PV(D3) = $Three. 0625/(1. 12)Three= $2. 7804 ( PV(D1 to D3)= $7. 5038 Subsequently, the PV of the remaining dividends is: $58. 8800 – $7. 5038 = $51. 3762. Compounding this worth ahead to 12 months Three, we discover that the worth of all dividends obtained throughout fixed progress is $72. 18. [$51. 3762(1. 12)3 = $72. 18. ] Making use of the fixed progress formulation, we are able to remedy for the fixed progress price: [pic]= D3(1 + g)/(ks – g) $72. 1807= $Three. 90625(1 + g)/(Zero. 12 – g) $8. 6616 – $72. 18g= $Three. 90625 + $Three. 90625g $four. 7554= $76. 08625g Zero. 0625= g 6. 25%= g. 8-17First, remedy for the present value. P0 = D1/(ks – g) P0 = $Zero. 50/(Zero. 2 – Zero. 07) P0 = $10. 00. If the inventory is in a relentless progress state, the fixed dividend progress price can also be the capital beneficial properties yield for the inventory and the inventory value progress price. Therefore, to search out the value of the inventory 4 years from in the present day: [pic] = P0(1 + g)four [pic] = $10. 00(1. 07)four [pic] = $13. 10796 ? $13. 11. [pic] 8-18a. [pic] b. [pic] 8-19 Zero 1 2 Three four | | | | | D0 = 2. 00 D1 D2 D3 D4 g = 5% [pic] a. D1 = $2(1. 05) = $2. 10; D2 = $2(1. 05)2 = $2. 21; D3 = $2(1. 5)Three = $2. 32. b. Financial Calculator Resolution: Enter Zero, 2. 10, 2. 21, and a couple of. 32 into the money circulate register, enter I = 12, PV = ? PV = $5. 29. c. Financial Calculator Resolution: Enter Zero, Zero, Zero, and 34. 73 into the money circulate register, I = 12, PV = ? PV = $24. 72. d. $24. 72 + $5. 29 = $30. 01 = Most value you need to pay for the inventory. e. [pic] f. No. The worth of the inventory will not be dependent upon the holding interval. The worth calculated in Elements a by d is the worth for a Three-year holding interval. It is the same as the worth calculated in Half e apart from a small rounding error.

Every other holding interval would produce the identical worth of [pic]; that’s, [pic] = $30. 00. 8-20a. 1. [pic] 2. [pic] = $2/Zero. 15 = $13. 33. Three. [pic] four. [pic] b. 1. [pic] = $2. 30/Zero = Undefined. 2. [pic] = $2. 40/(-Zero. 05) = -$48, which is nonsense. These outcomes present that the formulation doesn’t make sense if the required price of return is the same as or lower than the anticipated progress price. c. No. 8-21The reply relies on when one works the issue. We used the February Three, 2003, challenge of The Wall Avenue Journal: a. $16. 81 to $36. 72. b. Present dividend = $Zero. 75. Dividend yield = $Zero. 75/$19. 8 ( Three. 9%. You may wish to use ($Zero. 75)(1 + g)/$19. 48, with g estimated someway. c. The $19. 48 shut was up $Zero. 98 from the day past’s shut. d. The return on the inventory consists of a dividend yield of about Three. 9 p.c plus some capital beneficial properties yield. We’d anticipate the full price of return on inventory to be within the 10 to 12 p.c vary. 8-22a. Finish of 12 months: 02 03 04 05 06 07 08 | | | | | | | D0 = 1. 75 D1 D2 D3 D4 D5 D6 Dt= D0(1 + g)t D2003= $1. 75(1. 15)1 = $2. 01. D2004= $1. 5(1. 15)2 = $1. 75(1. 3225) = $2. 31. D2005= $1. 75(1. 15)Three = $1. 75(1. 5209) = $2. 66. D2006= $1. 75(1. 15)four = $1. 75(1. 7490) = $Three. 06. D2007= $1. 75(1. 15)5 = $1. 75(2. Zero114) = $Three. 52. b. Step 1: PV of dividends = [pic]. PV D2003 = $2. 01/(1. 12)= $1. 79 PV D2004 = $2. 31/(1. 12)2= $1. 84 PV D2005 = $2. 66/(1. 12)Three= $1. 89 PV D2006 = $Three. 06/(1. 12)four= $1. 94 PV D2007 = $Three. 52/(1. 12)5= $2. 00 PV of dividends= $9. 46 Step 2: [pic] That is the value of the inventory 5 years from now. The PV of this value, discounted again 5 years, is as follows: PV of [pic] = $52. 80/(1. 12)5 = $29. 6. Step Three: The value of the inventory in the present day is as follows: [pic]= PV dividends Years 2003-2007 + PV of [pic] = $9. 46 + $29. 96 = $39. 42. This drawback is also solved by substituting the right values into the next equation: [pic]. Calculator resolution: Enter Zero, 2. 01, 2. 31, 2. 66, Three. 06, 56. 32 (Three. 52 + 52. 80) into the money circulate register, enter I = 12, PV = ? PV = $39. 43. c. 2003 D1/P0 = $2. 01/$39. 43= 5. 10% Capital beneficial properties yield= 6. 90* Anticipated whole return= 12. 00% 2008 D6/P5 = $Three. 70/$52. 80= 7. 00% Capital beneficial properties yield= 5. 00 Anticipated whole return= 12. 00% We all know that ks is 12 p.c, and the dividend yield is 5. 10 p.c; subsequently, the capital beneficial properties yield should be 6. 90 p.c. The details to notice listed here are as follows: 1. The whole yield is all the time 12 p.c (apart from rounding errors). 2. The capital beneficial properties yield begins comparatively excessive, then declines because the supernormal progress interval approaches its finish. The dividend yield rises. Three. After 12/31/07, the inventory will develop at a 5 p.c price. The dividend yield will equal 7 p.c, the capital beneficial properties yield will equal 5 p.c, and the full return will likely be 12 p.c. d.

Folks in excessive earnings tax brackets will likely be extra inclined to buy “progress” shares to take the capital beneficial properties and thus delay the fee of taxes till a later date. The agency’s inventory is “mature” on the finish of 2007. e. For the reason that agency’s supernormal and regular progress charges are decrease, the dividends and, therefore, the current worth of the inventory value will likely be decrease. The whole return from the inventory will nonetheless be 12 p.c, however the dividend yield will likely be bigger and the capital beneficial properties yield will likely be smaller than they have been with the unique progress charges. This outcome happens as a result of we assume the identical final dividend however a a lot decrease present inventory value. . Because the required return will increase, the value of the inventory goes down, however each the capital beneficial properties and dividend yields improve initially. In fact, the long-term capital beneficial properties yield continues to be four p.c, so the long-term dividend yield is 10 p.c. 8-23a. Half 1: Graphical illustration of the issue: Supernormal Regular progress progress Zero 1 2 Three ( | | | | ••• | D0 D1 (D2 + [pic]) D3 D( PVD1

PVD2 [pic] P0 D1 = D0(1 + gs) = $1. 6(1. 20) = $1. 92. D2 = D0(1 + gs)2 = $1. 60(1. 20)2 = $2. 304. [pic] [pic]= PV(D1) + PV(D2) + PV([pic]) = [pic] = $1. 92/1. 10 + $2. 304/(1. 10)2 + $61. 06/(1. 10)2 = $54. 11. Financial Calculator resolution: Enter Zero, 1. 92, 63. 364(2. 304 + 61. 06) into the money circulate register, enter I = 10, PV = ? PV = $54. 11. Half 2: Anticipated dividend yield: D1/P0 = $1. 92/$54. 11 = Three. 55%. Capital beneficial properties yield: First, discover [pic], which equals the sum of the current values of D2 and [pic] discounted for one yr. [pic] Financial Calculator resolution: Enter Zero, 63. 364(2. 304 + 61. 6) into the money circulate register, enter I = 10, PV = ? PV = $57. 60. Second, discover the capital beneficial properties yield: [pic] Dividend yield = Three. 55% Capital beneficial properties yield = 6. 45 10. 00% = ks. b. As a result of longer interval of supernormal progress, the worth of the inventory will likely be greater for annually. Though the full return will stay the identical, ks = 10%, the distribution between dividend yield and capital beneficial properties yield will differ: The dividend yield will begin off decrease and the capital beneficial properties yield will begin off greater for the 5-year supernormal progress situation, relative to the 2-year supernormal progress state.

The dividend yield will improve and the capital beneficial properties yield will decline over the 5-year interval till dividend yield = four% and capital beneficial properties yield = 6%. c. All through the supernormal progress interval, the full yield will likely be 10 p.c, however the dividend yield is comparatively low in the course of the early years of the supernormal progress interval and the capital beneficial properties yield is comparatively excessive. As we close to the top of the supernormal progress interval, the capital beneficial properties yield declines and the dividend yield rises. After the supernormal progress interval has ended, the capital beneficial properties yield will equal gn = 6%.

The whole yield should equal ks = 10%, so the dividend yield should equal 10% – 6% = four%. d. Some traders want money dividends (retired folks), whereas others would favor progress. Additionally, traders should pay taxes annually on the dividends obtained in the course of the yr, whereas taxes on capital beneficial properties could be delayed till the achieve is definitely realized. 8-24a. ks = kRF + (kM – kRF)b = 11% + (14% – 11%)1. 5 = 15. 5%. [pic] = D1/(ks – g) = $2. 25/(Zero. 155 – Zero. 05) = $21. 43. b. ks = 9% + (12% – 9%)1. 5 = 13. 5%. [pic] = $2. 25/(Zero. 135 – Zero. 05) = $26. 47. c. ks = 9% + (11% – 9%)1. 5 = 12. Zero%. [pic] = $2. 25/(Zero. 12 – Zero. 5) = $32. 14. d. New knowledge given: kRF = 9%; kM = 11%; g = 6%, b = 1. Three. ks = kRF + (kM – kRF)b = 9% + (11% – 9%)1. Three = 11. 6%. [pic] = D1/(ks – g) = $2. 27/(Zero. 116 – Zero. 06) = $40. 54. 8-25a. Previous ks = kRF + (kM – kRF)b = 9% + (Three%)1. 2 = 12. 6%. New ks = 9% + (Three%)Zero. 9 = 11. 7%. Previous value: [pic] New value: [pic] For the reason that new value is decrease than the outdated value, the growth in client merchandise ought to be rejected. The lower in danger will not be adequate to offset the decline in profitability and the lowered progress price. b. POld = $38. 21. PNew = [pic]. Fixing for ks now we have the next: $38. 1= [pic] $2. 10= $38. 21(ks) – $1. 9105 $four. 0105= $38. 21(ks) ks= Zero. 10496. Fixing for b: 10. 496% = 9% + Three%(b) 1. 496% = Three%(b) b = Zero. 49865. Test: ks = 9% + (Three%)Zero. 49865 = 10. 496%. [pic] = [pic] = $38. 21. Subsequently, provided that administration’s evaluation concludes that danger could be lowered to b = Zero. 49865, or roughly Zero. 5, ought to the brand new coverage be implement. SPREADSHEET PROBLEM 8-26The detailed resolution for the spreadsheet drawback is accessible each on the teacher’s useful resource CD-ROM and on the teacher’s facet of South-Western’s website, http://brigham. swlearning. com. INTEGRATED CASE

Mutual of Chicago Insurance coverage Firm Inventory Valuation 8-27ROBERT BALIK AND CAROL KIEFER ARE SENIOR VICE-PRESIDENTS OF THE MUTUAL OF CHICAGO INSURANCE COMPANY. THEY ARE CO-DIRECTORS OF THE COMPANY’S PENSION FUND MANAGEMENT DIVISION, WITH BALIK HAVING RESPONSIBILITY FOR FIXED INCOME SECURITIES (PRIMARILY BONDS) AND KIEFER BEING RESPONSIBLE FOR EQUITY INVESTMENTS. A MAJOR NEW CLIENT, THE CALIFORNIA LEAGUE OF CITIES, HAS REQUESTED THAT MUTUAL OF CHICAGO PRESENT AN INVESTMENT SEMINAR TO THE MAYORS OF THE REPRESENTED CITIES, AND BALIK AND KIEFER, WHO WILL MAKE THE ACTUAL PRESENTATION, HAVE ASKED YOU TO HELP THEM.

TO ILLUSTRATE THE COMMON STOCK VALUATION PROCESS, BALIK AND KIEFER HAVE ASKED YOU TO ANALYZE THE BON TEMPS COMPANY, AN EMPLOYMENT AGENCY THAT SUPPLIES WORD PROCESSOR OPERATORS AND COMPUTER PROGRAMMERS TO BUSINESSES WITH TEMPORARILY HEAVY WORKLOADS. YOU ARE TO ANSWER THE FOLLOWING QUESTIONS. A. DESCRIBE BRIEFLY THE LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS. ANSWER:[SHOW S8-1 THROUGH S8-5 HERE. ] THE COMMON STOCKHOLDERS ARE THE OWNERS OF A CORPORATION, AND AS SUCH THEY HAVE CERTAIN RIGHTS AND PRIVILEGES AS DESCRIBED BELOW. 1. OWNERSHIP IMPLIES CONTROL.

THUS, A FIRM’S COMMON STOCKHOLDERS HAVE THE RIGHT TO ELECT ITS FIRM’S DIRECTORS, WHO IN TURN ELECT THE OFFICERS WHO MANAGE THE BUSINESS. 2. COMMON STOCKHOLDERS OFTEN HAVE THE RIGHT, CALLED THE PREEMPTIVE RIGHT, TO PURCHASE ANY ADDITIONAL SHARES SOLD BY THE FIRM. IN SOME STATES, THE PREEMPTIVE RIGHT IS AUTOMATICALLY INCLUDED IN EVERY CORPORATE CHARTER; IN OTHERS, IT IS NECESSARY TO INSERT IT SPECIFICALLY INTO THE CHARTER. B. 1. WRITE OUT A FORMULA THAT CAN BE USED TO VALUE ANY STOCK, REGARDLESS OF ITS DIVIDEND PATTERN. ANSWER:[SHOW S8-6 HERE. ] THE VALUE OF ANY STOCK IS THE PRESENT VALUE OF ITS EXPECTED DIVIDEND STREAM: [pic] = [pic]

HOWEVER, SOME STOCKS HAVE DIVIDEND GROWTH PATTERNS THAT ALLOW THEM TO BE VALUED USING SHORT-CUT FORMULAS. B. 2. WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT GROWTH STOCKS VALUED? ANSWER:[SHOW S8-7 AND S8-8 HERE. ] A CONSTANT GROWTH STOCK IS ONE WHOSE DIVIDENDS ARE EXPECTED TO GROW AT A CONSTANT RATE FOREVER. “CONSTANT GROWTH” MEANS THAT THE BEST ESTIMATE OF THE FUTURE GROWTH RATE IS SOME CONSTANT NUMBER, NOT THAT WE REALLY EXPECT GROWTH TO BE THE SAME EACH AND EVERY YEAR. MANY COMPANIES HAVE DIVIDENDS THAT ARE EXPECTED TO GROW STEADILY INTO THE FORESEEABLE FUTURE, AND SUCH COMPANIES ARE VALUED AS CONSTANT GROWTH STOCKS.

FOR A CONSTANT GROWTH STOCK: D1 = D0(1 + g), D2 = D1(1 + g) = D0(1 + g)2, AND SO ON. WITH THIS REGULAR DIVIDEND PATTERN, THE GENERAL STOCK VALUATION MODEL CAN BE SIMPLIFIED TO THE FOLLOWING VERY IMPORTANT EQUATION: [pic] = [pic] = [pic]. THIS IS THE WELL-KNOWN “GORDON,” OR “CONSTANT-GROWTH” MODEL FOR VALUING STOCKS. HERE D1 IS THE NEXT EXPECTED DIVIDEND, WHICH IS ASSUMED TO BE PAID 1 YEAR FROM NOW, kS IS THE REQUIRED RATE OF RETURN ON THE STOCK, AND g IS THE CONSTANT GROWTH RATE. B. Three. WHAT HAPPENS IF A COMPANY HAS A CONSTANT g THAT EXCEEDS ITS ks? WILL MANY STOCKS HAVE EXPECTED g > ks IN THE SHORT RUN (THAT IS, FOR THE NEXT FEW YEARS)?

IN THE LONG RUN (THAT IS, FOREVER)? ANSWER:[SHOW S8-9 HERE. ] THE MODEL IS DERIVED MATHEMATICALLY, AND THE DERIVATION REQUIRES THAT ks > g. IF g IS GREATER THAN ks, THE MODEL GIVES A NEGATIVE STOCK PRICE, WHICH IS NONSENSICAL. THE MODEL SIMPLY CANNOT BE USED UNLESS (1) ks > g, (2) g IS EXPECTED TO BE CONSTANT, AND (Three) g CAN REASONABLY BE EXPECTED TO CONTINUE INDEFINITELY. STOCKS MAY HAVE PERIODS OF SUPERNORMAL GROWTH, WHERE gS > ks; HOWEVER, THIS GROWTH RATE CANNOT BE SUSTAINED INDEFINITELY. IN THE LONG-RUN, g < ks. C. ASSUME THAT BON TEMPS HAS A BETA COEFFICIENT OF 1. , THAT THE RISK-FREE RATE (THE YIELD ON T-BONDS) IS 7 PERCENT, AND THAT THE REQUIRED RATE OF RETURN ON THE MARKET IS 12 PERCENT. WHAT IS THE REQUIRED RATE OF RETURN ON THE FIRM’S STOCK? ANSWER:[SHOW S8-10 HERE. ] HERE WE USE THE SML TO CALCULATE BON TEMPS’ REQUIRED RATE OF RETURN: ks= kRF + (kM – kRF)bBon Temps = 7% + (12% – 7%)(1. 2) = 7% + (5%)(1. 2) = 7% + 6% = 13%. D. ASSUME THAT BON TEMPS IS A CONSTANT GROWTH COMPANY WHOSE LAST DIVIDEND (D0, WHICH WAS PAID YESTERDAY) WAS $2. 00 AND WHOSE DIVIDEND IS EXPECTED TO GROW INDEFINITELY AT A 6 PERCENT RATE. 1.

WHAT IS THE FIRM’S EXPECTED DIVIDEND STREAM OVER THE NEXT Three YEARS? ANSWER:[SHOW S8-11 HERE. ] BON TEMPS IS A CONSTANT GROWTH STOCK, AND ITS DIVIDEND IS EXPECTED TO GROW AT A CONSTANT RATE OF 6 PERCENT PER YEAR. EXPRESSED AS A TIME LINE, WE HAVE THE FOLLOWING SETUP. JUST ENTER 2 IN YOUR CALCULATOR; THEN KEEP MULTIPLYING BY 1 + g = 1. 06 TO GET D1, D2, AND D3: Zero 1 2 Three | | | | D0 = 2. 00 2. 12 2. 247 2. 382 1. 88 1. 76 1. 65 . . . D. 2. WHAT IS THE FIRM’S CURRENT STOCK PRICE? ANSWER:[SHOW S8-12 HERE. WE COULD EXTEND THE TIME LINE ON OUT FOREVER, FIND THE VALUE OF BON TEMPS’ DIVIDENDS FOR EVERY YEAR ON OUT INTO THE FUTURE, AND THEN THE PV OF EACH DIVIDEND DISCOUNTED AT k = 13%. FOR EXAMPLE, THE PV OF D1 IS $1. 8761; THE PV OF D2 IS $1. 7599; AND SO FORTH. NOTE THAT THE DIVIDEND PAYMENTS INCREASE WITH TIME, BUT AS LONG AS ks > g, THE PRESENT VALUES DECREASE WITH TIME. IF WE EXTENDED THE GRAPH ON OUT FOREVER AND THEN SUMMED THE PVs OF THE DIVIDENDS, WE WOULD HAVE THE VALUE OF THE STOCK. HOWEVER, SINCE THE STOCK IS GROWING AT A CONSTANT RATE, ITS VALUE CAN BE ESTIMATED USING THE CONSTANT GROWTH MODEL: pic] = [pic] = [pic] = [pic] = $30. 29. D. Three. WHAT IS THE STOCK’S EXPECTED VALUE ONE YEAR FROM NOW? ANSWER:[SHOW S8-13 HERE. ] AFTER ONE YEAR, D1 WILL HAVE BEEN PAID, SO THE EXPECTED DIVIDEND STREAM WILL THEN BE D2, D3, D4, AND SO ON. THUS, THE EXPECTED VALUE ONE YEAR FROM NOW IS $32. 10: [pic] = [pic] = [pic] = [pic] = $32. 10. D. four. WHAT ARE THE EXPECTED DIVIDEND YIELD, THE CAPITAL GAINS YIELD, AND THE TOTAL RETURN DURING THE FIRST YEAR? ANSWER:[SHOW S8-14 HERE. ] THE EXPECTED DIVIDEND YIELD IN ANY YEAR n IS DIVIDEND YIELD = [pic], WHILE THE EXPECTED CAPITAL GAINS YIELD IS

CAPITAL GAINS YIELD = [pic] = ok – [pic]. THUS, THE DIVIDEND YIELD IN THE FIRST YEAR IS 7 PERCENT, WHILE THE CAPITAL GAINS YIELD IS 6 PERCENT: TOTAL RETURN = 13. Zero% DIVIDEND YIELD = $2. 12/$30. 29 = 7. Zero% CAPITAL GAINS YIELD = 6. Zero% E. NOW ASSUME THAT THE STOCK IS CURRENTLY SELLING AT $30. 29. WHAT IS THE EXPECTED RATE OF RETURN ON THE STOCK? ANSWER:THE CONSTANT GROWTH MODEL CAN BE REARRANGED TO THIS FORM: [pic] = [pic]. HERE THE CURRENT PRICE OF THE STOCK IS KNOWN, AND WE SOLVE FOR THE EXPECTED RETURN. FOR BON TEMPS: pic] = $2. 12/$30. 29 + Zero. Zero60 = Zero. Zero70 + Zero. Zero60 = 13%. F. WHAT WOULD THE STOCK PRICE BE IF ITS DIVIDENDS WERE EXPECTED TO HAVE ZERO GROWTH? ANSWER:[SHOW S8-15 HERE. ] IF BON TEMPS’ DIVIDENDS WERE NOT EXPECTED TO GROW AT ALL, THEN ITS DIVIDEND STREAM WOULD BE A PERPETUITY. PERPETUITIES ARE VALUED AS SHOWN BELOW: Zero 1 2 Three | | | | 2. 00 2. 00 2. 00 1. 77 1. 57 1. 39 . . . P0 = 15. 38 P0 = D/kS = $2. 00/Zero. 13 = $15. 38. NOTE THAT IF A PREFERRED STOCK IS A PERPETUITY, IT MAY BE VALUED WITH THIS FORMULA. G.

NOW ASSUME THAT BON TEMPS IS EXPECTED TO EXPERIENCE SUPERNORMAL GROWTH OF 30 PERCENT FOR THE NEXT Three YEARS, THEN TO RETURN TO ITS LONG-RUN CONSTANT GROWTH RATE OF 6 PERCENT. WHAT IS THE STOCK’S VALUE UNDER THESE CONDITIONS? WHAT IS ITS EXPECTED DIVIDEND YIELD AND CAPITAL GAINS YIELD IN YEAR 1? YEAR four? ANSWER:[SHOW S8-16 THROUGH S8-18 HERE. ] BON TEMPS IS NO LONGER A CONSTANT GROWTH STOCK, SO THE CONSTANT GROWTH MODEL IS NOT APPLICABLE. NOTE, HOWEVER, THAT THE STOCK IS EXPECTED TO BECOME A CONSTANT GROWTH STOCK IN Three YEARS. THUS, IT HAS A NONCONSTANT GROWTH PERIOD FOLLOWED BY CONSTANT GROWTH.

THE EASIEST WAY TO VALUE SUCH NONCONSTANT GROWTH STOCKS IS TO SET THE SITUATION UP ON A TIME LINE AS SHOWN BELOW: Zero 1 2 Three four | | | | | 2. 600 Three. 380 four. 394 four. 65764 2. 301 2. 647 Three. Zero45 46. 114 54. 107 SIMPLY ENTER $2 AND MULTIPLY BY (1. 30) TO GET D1 = $2. 60; MULTIPLY THAT RESULT BY 1. Three TO GET D2 = $Three. 38, AND SO FORTH. THEN RECOGNIZE THAT AFTER YEAR Three, BON TEMPS BECOMES A CONSTANT GROWTH STOCK, AND AT THAT POINT [pic] CAN BE FOUND USING THE CONSTANT GROWTH MODEL. pic] IS THE PRESENT VALUE AS OF t = Three OF THE DIVIDENDS IN YEAR four AND BEYOND AND IS ALSO CALLED THE TERMINAL VALUE. WITH THE CASH FLOWS FOR D1, D2, D3, AND [pic] SHOWN ON THE TIME LINE, WE DISCOUNT EACH VALUE BACK TO YEAR Zero, AND THE SUM OF THESE FOUR PVs IS THE VALUE OF THE STOCK TODAY, P0 = $54. 107. THE DIVIDEND YIELD IN YEAR 1 IS four. 80 PERCENT, AND THE CAPITAL GAINS YIELD IS 8. 2 PERCENT: DIVIDEND YIELD = [pic] = Zero. 0480 = four. 8%. CAPITAL GAINS YIELD = 13. 00% – four. 8% = 8. 2%. DURING THE NONCONSTANT GROWTH PERIOD, THE DIVIDEND YIELDS AND CAPITAL GAINS YIELDS ARE NOT CONSTANT, AND THE CAPITAL GAINS YIELD DOES NOT EQUAL g.

HOWEVER, AFTER YEAR Three, THE STOCK BECOMES A CONSTANT GROWTH STOCK, WITH g = CAPITAL GAINS YIELD = 6. Zero% AND DIVIDEND YIELD = 13. Zero% – 6. Zero% = 7. Zero%. H. SUPPOSE BON TEMPS IS EXPECTED TO EXPERIENCE ZERO GROWTH DURING THE FIRST Three YEARS AND THEN TO RESUME ITS STEADY-STATE GROWTH OF 6 PERCENT IN THE FOURTH YEAR. WHAT IS THE STOCK’S VALUE NOW? WHAT IS ITS EXPECTED DIVIDEND YIELD AND ITS CAPITAL GAINS YIELD IN YEAR 1? YEAR four? ANSWER:[SHOW S8-19 AND S8-20 HERE. ] NOW WE HAVE THIS SITUATION: Zero 1 2 Three four | | | | | 2. 00 2. Zero 2. 00 2. 00 2. 12 1. 77 1. 57 1. 39 20. 99 25. 72 = [pic] DURING YEAR 1: DIVIDEND YIELD = [pic] = Zero. 0778 = 7. 78%. CAPITAL GAINS YIELD = 13. 00% – 7. 78% = 5. 22%. AGAIN, IN YEAR four BON TEMPS BECOMES A CONSTANT GROWTH STOCK; HENCE g = CAPITAL GAINS YIELD = 6. Zero% AND DIVIDEND YIELD = 7. Zero%. I. FINALLY, ASSUME THAT BON TEMPS’ EARNINGS AND DIVIDENDS ARE EXPECTED TO DECLINE BY A CONSTANT 6 PERCENT PER YEAR, THAT IS, g = -6%. WHY WOULD ANYONE BE WILLING TO BUY SUCH A STOCK, AND AT WHAT PRICE SHOULD IT SELL? WHAT WOULD BE THE DIVIDEND YIELD AND CAPITAL GAINS YIELD IN EACH YEAR?

ANSWER:[SHOW S8-21 AND S8-22 HERE. ] THE COMPANY IS EARNING SOMETHING AND PAYING SOME DIVIDENDS, SO IT CLEARLY HAS A VALUE GREATER THAN ZERO. THAT VALUE CAN BE FOUND WITH THE CONSTANT GROWTH FORMULA, BUT WHERE g IS NEGATIVE: [pic] = [pic] = [pic] = [pic] = [pic] = $9. 89. SINCE IT IS A CONSTANT GROWTH STOCK: g = CAPITAL GAINS YIELD = -6. Zero%, HENCE: DIVIDEND YIELD = 13. Zero% – (-6. Zero%) = 19. Zero%. AS A CHECK: DIVIDEND YIELD = [pic] = Zero. 190 = 19. Zero%. THE DIVIDEND AND CAPITAL GAINS YIELDS ARE CONSTANT OVER TIME, BUT A HIGH (19. Zero PERCENT) DIVIDEND YIELD IS NEEDED TO OFFSET THE NEGATIVE CAPITAL GAINS YIELD.

J. BON TEMPS EMBARKS ON AN AGGRESSIVE EXPANSION THAT REQUIRES ADDITIONAL CAPITAL. MANAGEMENT DECIDES TO FINANCE THE EXPANSION BY BORROWING $40 MILLION AND BY HALTING DIVIDEND PAYMENTS TO INCREASE RETAINED EARNINGS. THE PROJECTED FREE CASH FLOWS FOR THE NEXT THREE YEARS ARE -$5 MILLION, $10 MILLION, AND $20 MILLION. AFTER THE THIRD YEAR, FREE CASH FLOW IS PROJECTED TO GROW AT A CONSTANT 6 PERCENT. THE OVERALL COST OF CAPITAL IS 10 PERCENT. WHAT IS BON TEMPS’ TOTAL VALUE? IF IT HAS 10 MILLION SHARES OF STOCK AND $40 MILLION TOTAL DEBT, WHAT IS THE PRICE PER SHARE? ANSWER:[SHOW S8-23 THROUGH S8-28 HERE. 0 1 2 3 4 | | | | | -5 10 20 21. 20 $ -4. 545 8. 264 15. 026 398. 197 $416. 942 = TOTAL VALUE VALUE OF EQUITY = TOTAL VALUE – DEBT = $416. 94 – $40 = $376. 94 MILLION. PRICE PER SHARE = $376. 94/10 = $37. 69. K. WHAT DOES MARKET EQUILIBRIUM MEAN? ANSWER:[SHOW S8-29 AND S8-30 HERE. ] EQUILIBRIUM MEANS STABLE, NO TENDENCY TO CHANGE. MARKET EQUILIBRIUM MEANS THAT PRICES ARE STABLE–AT ITS CURRENT PRICE, THERE IS NO GENERAL TENDENCY FOR PEOPLE TO WANT TO BUY OR TO SELL A SECURITY THAT IS IN EQUILIBRIUM.

ALSO, WHEN EQUILIBRIUM EXISTS, THE EXPECTED RATE OF RETURN WILL BE EQUAL TO THE REQUIRED RATE OF RETURN: [pic] = D1/P0 + g = ok = kRF + (kM – kRF)b. L. IF EQUILIBRIUM DOES NOT EXIST, HOW WILL IT BE ESTABLISHED? ANSWER:[SHOW S8-31 AND S8-32 HERE. ] SECURITIES WILL BE BOUGHT AND SOLD UNTIL THE EQUILIBRIUM PRICE IS ESTABLISHED. M. WHAT IS THE EFFICIENT MARKETS HYPOTHESIS, WHAT ARE ITS THREE FORMS, AND WHAT ARE ITS IMPLICATIONS? ANSWER:[SHOW S8-33 THROUGH S8-37 HERE. ] THE EMH IN GENERAL IS THE HYPOTHESIS THAT SECURITIES ARE NORMALLY IN EQUILIBRIUM AND ARE “PRICED FAIRLY,” MAKING IT IMPOSSIBLE TO “BEAT THE MARKET. WEAK-FORM EFFICIENCY SAYS THAT INVESTORS CANNOT PROFIT FROM LOOKING AT PAST MOVEMENTS IN STOCK PRICES–THE FACT THAT STOCKS WENT DOWN FOR THE LAST FEW DAYS IS NO REASON TO THINK THAT THEY WILL GO UP (OR DOWN) IN THE FUTURE. THIS FORM HAS BEEN PROVEN PRETTY WELL BY EMPIRICAL TESTS, EVEN THOUGH PEOPLE STILL EMPLOY “TECHNICAL ANALYSIS. ” SEMISTRONG-FORM EFFICIENCY SAYS THAT ALL PUBLICLY AVAILABLE INFORMATION IS REFLECTED IN STOCK PRICES, HENCE THAT IT WON’T DO MUCH GOOD TO PORE OVER ANNUAL REPORTS TRYING TO FIND UNDERVALUED STOCKS.

THIS ONE IS (WE THINK) LARGELY TRUE, BUT SUPERIOR ANALYSTS CAN STILL OBTAIN AND PROCESS NEW INFORMATION FAST ENOUGH TO GAIN A SMALL ADVANTAGE. STRONG-FORM EFFICIENCY SAYS THAT ALL INFORMATION, EVEN INSIDE INFORMATION, IS EMBEDDED IN STOCK PRICES. THIS FORM DOES NOT HOLD–INSIDERS KNOW MORE, AND COULD TAKE ADVANTAGE OF THAT INFORMATION TO MAKE ABNORMAL PROFITS IN THE MARKETS. TRADING ON THE BASIS OF INSIDER INFORMATION IS ILLEGAL. N. PHYFE COMPANY RECENTLY ISSUED PREFERRED STOCK. IT PAYS AN ANNUAL DIVIDEND OF $5, AND THE ISSUE PRICE WAS $50 PER SHARE. WHAT IS THE EXPECTED RETURN TO AN INVESTOR ON THIS PREFERRED STOCK?

ANSWER:[SHOW S8-38 AND S8-39 HERE. ] [pic]= [pic] = [pic] = 10%. ———————– ks = 15% gn = 6% ( 1/(1. 15)Three ( 1/(1. 13)Three ( 1/(1. 13)2 ( 1/1. 13 gs = 50% gn = 8% [pic] ks = 12% gs = 15% gn = 5% WACC = 10% [pic] = 30. 29 = [pic] g = Zero% g = Zero% g = Zero% gn = 6% ks = 13% [pic] = $66. 54 = [pic] gs = 30% gs = 30% gs = 30% gn = 6% ks = 13% g = Zero% ks = 13% g = 6% ks = 13% ks = 10% gs = 20% gs = 20% gn = 5% WACC = 12% WACC = 12% gn = 7% [pic] WACC = 13% gn = 7% 530 = [pic] ( 1/(1. 15)four ( 1/(1. 15)5 ks = 12% ( 1/1. 13 ( 1/(1. 13)2 ( 1/(1. 13)Three ( 1/(1. 13)2 ( 1/(1. 13)2 ( 1/1. 13 ( 1/(1. 13)2 ( 1/(1. 13)Three ( 1/(1. 13)Three ( 1/1. 13 ( 1/1. 13 (%89

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