problems02

ABC CORP.Current stock price, P0 50Current dividend, D0 3Dividend growth rate, g 5%Cost of equity from Gordon model 11.300% - =B3*(1+B4)/B2+B4ABC CORP.当前股价, P0 50当前股利, D0 3股利增长率, g 5%戈登模型下的权益成本 11.300% - =B3*(1+B4)/B2+B4UNHEARDOF, INC.Current dividend, D0 5Anticipated dividend growth rate, g 15%Cost of equity, rE 25%Gordon model stock price 57.5 - =B2*(1+B3)/(B4-B3)UNHEARDOF, INC.当前股利, D0 5预期股利增长率, g 15%权益成本, rE 25%戈登模型股价 57.5 - =B2*(1+B3)/(B4-B3)DISMAL.COMDividend, starting in 3 years 15Growth rate 20%Cost of equity 35%Value of Dismal.com 3 years from today 15Value of Dismal.com stock 2 years from today 100Todays stock price 54.87 - =B7/(1+B4)2Explanation: At the end of 2 years, the next dividend will be15, and this dividend will grow at 20% per year.Thus theGordon model applies, and the stock price at the end of 2years will be 15/(0.35-0.20). Todays stock price is the price 2years from now discounted at the cost of equity.DISMAL.COM三年后开始股利 15增长率 20%权益成本 35%即日起三年内Dismal.com的价值 15即日起Dismal.com2年内股票价值 100当前股票价格 54.87 - =B7/(1+B4)2解释：在两年末，下一期的股利是15，这个股利将以每年20%的增长率增长。因此戈登模型使用，2年末时的股价是15/(0.35-0.20).当前的股价是从现在开始用权益成本折现的价格。CHRYSLER CORPORATION (C)YearYear-endstockpriceDividendpershareGrowthrate1986 0.401987 0.50 25.00% - =C4/C3-11988 0.50 0.00% - =C5/C4-11989 0.60 20.00% - =C6/C5-11990 0.60 0.00% - =C7/C6-11991 0.30 -50.00% - =C8/C7-11992 0.30 0.00%1993 0.33 10.00%1994 0.45 36.36%1995 1.00 122.22%1996 35.00 1.40 40.00%Compound growth, 10 yr. 13.35% - =(C13/C3)(1/10)-1Compound growth, 5 yr. 36.08% - =(C13/C8)(1/5)-1Gordon modelP0 35.00 - Ending 1996 share priceD0 1.40 - 1996 dividendrE10-yr. growth 17.88% - =B20*(1+C15)/B19+C155-yr. growth 41.53% - =B20*(1+C16)/B19+C16A B C D E1234567891011121314151617181920212223克莱斯勒汽车公司年 年末股价 每股股利 增长率1986 0.401987 0.50 25.00% - =C4/C3-11988 0.50 0.00% - =C5/C4-11989 0.60 20.00% - =C6/C5-11990 0.60 0.00% - =C7/C6-11991 0.30 -50.00% - =C8/C7-11992 0.30 0.00%1993 0.33 10.00%1994 0.45 36.36%1995 1.00 122.22%1996 35.00 1.40 40.00%连续增长率, 10 yr. 13.35% - =(C13/C3)(1/10)-1连续增长率, 5 yr. 36.08% - =(C13/C8)(1/5)-1戈登模型P0 35.00 - 1996年年底股价D0 1.40 - 1996股利rE10-yr. 增长率 17.88% - =B20*(1+C15)/B19+C155-yr. 增长率 41.53% - =B20*(1+C16)/B19+C16A B C D E1234567891011121314151617181920212223TRANSCONTINENTAL AIRWAYSCurrent stock price, P0 65.00Current dividend per share 3.00High growth rate, ghigh 23.00%Number of high-growth years, m 5Normal growth rate, gnormal 5%Cost of equity, rEusing the function twostagegordon 14.651% - =twostagegordon(B2,B3,B5,B6,B7)A B C123456789TRANSCONTINENTAL航空当前股价, P0 65.00当前每股收益 3.00高速增长率, ghigh 23.00%高增长率年数, m 5正常增长率, gnormal 5%权益成本, rE利用函数 twostagegordon 14.651% - =twostagegordon(B2,B3,B5,B6,B7)A B C123456789ABC Corp (supernormal growth)Current dividend 3.00 Dividend valuationGrowth rate g1, years 1-10 (supernormal) 15% PV of years 1-10Growth rate g2, years 11 - 10% PV of years 11 - Cost of equity 12% Share valueYear1 3.45 - =B2*(1+$B$3)2 3.97 - =B8*(1+$B$3)3 4.56 - =B9*(1+$B$3)4 5.25 - =B10*(1+$B$3)5 6.036 6.947 7.988 9.189 10.55 - =B15*(1+$B$3)10 12.14 - =B16*(1+$B$3)11 13.35 - =B17*(1+$B$4)12 14.6913 16.1514 17.7715 19.5516 21.5034.79 - =NPV(B5,B8:B17)214.92 - =B17*(1+B4)/(B5-B4)/(1+B5)10249.72 - =SUM(E3:E4)ABC 公司 (超自然 增长)当前股利 3.00 股利价值增长率g1, 第1-10年 (超正常增长) 15% 年1-10的PV值增长率g2, 年11 - 10% 年11 - 的PV值权益成本 12% 股票价值年1 3.45 - =B2*(1+$B$3)2 3.97 - =B8*(1+$B$3)3 4.56 - =B9*(1+$B$3)4 5.25 - =B10*(1+$B$3)5 6.036 6.947 7.988 9.189 10.55 - =B15*(1+$B$3)10 12.14 - =B16*(1+$B$3)11 13.35 - =B17*(1+$B$4)12 14.6913 16.1514 17.7715 19.5516 21.5034.79 - =NPV(B5,B8:B17)214.92 - =B17*(1+B4)/(B5-B4)/(1+B5)10249.72 - =SUM(E3:E4)MERCK & CO. 2000-1991Purchaseof treasurystockCashdividendsProceedsfromexercise ofstockoptionsTax Benefitsfrom exerciseof stockoptions -computedTotalequitycashflow1991 184 893 -48 -32 997 - =SUM(B3:E3)1992 863 1,064 -52 -37 1,8381993 371 1,174 -83 -31 1,4311994 705 1,434 -139 -61 1,9391995 1,571 1,540 -264 -119 2,7271996 2,493 1,729 -442 -207 3,5731997 2,573 2,040 -413 -333 3,8671998 3,626 2,253 -490 -488 4,9001999 3,582 2,590 -323 -401 5,4472000 3,545 2,798 -641 -501 5,202Growth 38.91% 13.53% 20.15% - =(F12/F3)(1/9)-1M E R C K -C a s h D iv id e n d s v e r s u s T o ta l E q u ity C a s h F lo w , 1 9 9 1 -2 0 0 0199119921993199419951996199719981999200005 0 01 , 0 0 01 , 5 0 02 , 0 0 02 , 5 0 03 , 0 0 001 , 0 0 02 , 0 0 03 , 0 0 04 , 0 0 05 , 0 0 06 , 0 0 0CashdividendsTotalequitycfC a s h d i v i d e n d s T o t a l e q u i t y c a s h f l o wA B C D E F G123456789101112131415161718192021222324252627282930313233Gordon cost of equity-TwoStageGordonModelEnd-2000 share price, P0 93.625Number of shares outstanding, end 2000Shares issued 2,968,355,365Minus treasury shares 660,756,186Number of shares 2,307,599,179Market value of equity ($million) 216,049End 2000 total equity payout 5,202High growth rate, ghigh 20.15%Number of high-growth years, m 4Normal growth rate, gnormal 6%Cost of equity, rEusing the function twostagegordon 10.113%Just for comparisonCAPMBeta 0.55risk-free rate 5.30%Market risk-premium 5%CAPM cost of equity 8.050%H I J K123456789101112131415161718192021222324252627282930313233- =K7*K3/1000000- =F12- =F14- =twostagegordon(K9,K10,K12,K13,K14)- =K22+K21*K23L123456789101112131415161718192021222324252627282930313233MERCK公司. 2000-1991库藏股回购 现金股利股权除权收入股权除权在税收上的收益总权益现金流1991 184 893 -48 -32 997 - =SUM(B3:E3)1992 863 1,064 -52 -37 1,8381993 371 1,174 -83 -31 1,4311994 705 1,434 -139 -61 1,9391995 1,571 1,540 -264 -119 2,7271996 2,493 1,729 -442 -207 3,5731997 2,573 2,040 -413 -333 3,8671998 3,626 2,253 -490 -488 4,9001999 3,582 2,590 -323 -401 5,4472000 3,545 2,798 -641 -501 5,202增长率 38.91% 13.53% 20.15% - =(F12/F3)(1/9)-1M E R C K -现 金 股 利 与 总 权 益 现 金 流 对 比 , 1 9 9 1 -2 0 0 0199119921993199419951996199719981999200005 0 01 , 0 0 01 , 5 0 02 , 0 0 02 , 5 0 03 , 0 0 001 , 0 0 02 , 0 0 03 , 0 0 04 , 0 0 05 , 0 0 06 , 0 0 0现金股利总权益现金流现 金 股 利 总 权 益 现 金 流A B C D E F G123456789101112131415161718192021222324252627282930313233戈登权益成本-两阶段戈登模型2000年末股价, P0 93.6252000年末流通股份数发行股 2,968,355,365减库藏股 660,756,186股份数 2,307,599,179权益的市场价值($百万) 216,0492000年末总权益支出 5,202高增长率, ghigh 20.15%高增长率年数, m 4正常增长率, gnormal 6%权益成本, rE利用函数twostagegordon 10.113%对比CAPMBeta 0.55无风险利率 5.30%市场风险金 5%CAPM 权益成本 8.050%H I J K123456789101112131415161718192021222324252627282930313233- =K7*K3/1000000- =F12- =F14- =twostagegordon(K9,K10,K12,K13,K14)- =K22+K21*K23L123456789101112131415161718192021222324252627282930313233bequity 1.5bdebt 0.4Risk-free, rf 6%E(rm) 15%Corporate tax rate TC 40%Capital structurePercentage of equity 40%Percentage of debt 60%Cost of equityClassic CAPM 19.50% - =B3+B1*(B4-B3)Benninga-Sarig 20.70% - =B3*(1-B5)+B1*(B4-B3*(1-B5)Cost of debtClassic CAPM 9.60% - =B3+B2*(B4-B3)Benninga-Sarig 10.56% - =B3+B2*(B4-B3*(1-B5)Weighted average cost of capital (WACC)Classic CAPM 11.26% - =B8*B12+B9*B16*(1-B5)Benninga-Sarig 12.08% - =B8*B13+B9*B17*(1-B5)bequity 1.5bdebt 0.4无风险利率 6%市场回报期望 15%税率 40%Capital structure权益比率 40%负债比率 60%Cost of equity经典CAPM 19.50% - =B3+B1*(B4-B3)Benninga-Sarig 20.70% - =B3*(1-B5)+B1*(B4-B3*(1-B5)Cost of debt经典CAPM 9.60% - =B3+B2*(B4-B3)Benninga-Sarig 10.56% - =B3+B2*(B4-B3*(1-B5)WACC经典CAPM 11.26% - =B8*B12+B9*B16*(1-B5)Benninga-Sarig 12.08% - =B8*B13+B9*B17*(1-B5)CISCO (CSCO) ANDS&P 500 PRICESJuly 2002 - June 2007Date S&P 500 CSCO3-Jul-02 911.62 13.191-Aug-02 916.07 13.823-Sep-02 815.28 10.481-Oct-02 885.76 11.181-Nov-02 936.31 14.922-Dec-02 879.82 13.102-Jan-03 855.70 13.373-Feb-03 841.15 13.983-Mar-03 848.18 12.981-Apr-03 916.92 15.001-May-03 963.59 16.412-Jun-03 974.50 16.791-Jul-03 990.31 19.491-Aug-03 1008.01 19.142-Sep-03 995.97 19.591-Oct-03 1050.71 20.933-Nov-03 1058.20 22.701-Dec-03 1111.92 24.232-Jan-04 1131.13 25.712-Feb-04 1144.94 23.161-Mar-04 1126.21 23.571-Apr-04 1107.30 20.913-May-04 1120.68 22.371-Jun-04 1140.84 23.701-Jul-04 1101.72 20.922-Aug-04 1104.24 18.761-Sep-04 1114.58 18.101-Oct-04 1130.20 19.211-Nov-04 1173.82 18.751-Dec-04 1211.92 19.323-Jan-05 1181.27 18.041-Feb-05 1203.60 17.421-Mar-05 1180.59 17.891-Apr-05 1156.85 17.272-May-05 1191.50 19.401-Jun-05 1191.33 19.081-Jul-05 1234.18 19.151-Aug-05 1220.33 17.621-Sep-05 1228.81 17.923-Oct-05 1207.01 17.451-Nov-05 1249.48 17.541-Dec-05 1248.29 17.123-Jan-06 1280.08 18.571-Feb-06 1280.66 20.24A B C123456789101112131415161718192021222324252627282930313233343536373839404142434445461-Mar-06 1294.87 21.673-Apr-06 1310.61 20.951-May-06 1270.09 19.681-Jun-06 1270.20 19.533-Jul-06 1276.66 17.881-Aug-06 1303.82 21.991-Sep-06 1335.85 22.982-Oct-06 1377.94 24.131-Nov-06 1400.63 26.911-Dec-06 1418.30 27.333-Jan-07 1438.24 26.621-Feb-07 1406.82 25.941-Mar-07 1420.86 25.532-Apr-07 1482.37 26.741-May-07 1530.62 26.921-Jun-07 1502.97 27.852-Jul-07 1519.43 27.89A B C4748495051525354555657585960616263CISCO (CSCO) a and bJuly 2002 - June 2007Alpha -0.0032 - =INTERCEPT(F13:F72,E13:E72)BetaUsing Excels slopefunction1.8465 - =SLOPE(F13:F72,E13:E72)Using Cov/VarR-squared 0.4460 - =RSQ(F13:F72,E13:E72)t-statistic for alpha -0.3711 - =tintercept(F13:F72,E13:E72)t-statistic for beta 6.8339 - =tslope(F13:F72,E13:E72)ReturnsDate S&P 500 CSCO S&P 500 CSCO3-Jul-02 911.62 13.191-Aug-02 916.07 13.82 0.49% 4.67%3-Sep-02 815.28 10.48 -11.66% -27.66%1-Oct-02 885.76 11.18 8.29% 6.47%1-Nov-02 936.31 14.92 5.55% 28.86%2-Dec-02 879.82 13.10 -6.22% -13.01%2-Jan-03 855.70 13.37 -2.78% 2.04%3-Feb-03 841.15 13.98 -1.71% 4.46%3-Mar-03 848.18 12.98 0.83% -7.42%1-Apr-03 916.92 15.00 7.79% 14.46%1-May-03 963.59 16.41 4.96% 8.98%2-Jun-03 974.50 16.79 1.13% 2.29%1-Jul-03 990.31 19.49 1.61% 14.91%1-Aug-03 1008.01 19.14 1.77% -1.81%2-Sep-03 995.97 19.59 -1.20% 2.32%1-Oct-03 1050.71 20.93 5.35% 6.62%3-Nov-03 1058.20 22.70 0.71% 8.12%1-Dec-03 1111.92 24.23 4.95% 6.52%2-Jan-04 1131.13 25.71 1.71% 5.93%2-Feb-04 1144.94 23.16 1.21% -10.45%1-Mar-04 1126.21 23.57 -1.65% 1.75%1-Apr-04 1107.30 20.91 -1.69% -11.97%3-May-04 1120.68 22.37 1.20% 6.75%1-Jun-04 1140.84 23.70 1.78% 5.78%1-Jul-04 1101.72 20.92 -3.49% -12.48%2-Aug-04 1104.24 18.76 0.23% -10.90%1-Sep-04 1114.58 18.10 0.93% -3.58%1-Oct-04 1130.20 19.21 1.39% 5.95%1-Nov-04 1173.82 18.75 3.79% -2.42%1-Dec-04 1211.92 19.32 3.19% 2.99%3-Jan-05 1181.27 18.04 -2.56% -6.85%1-Feb-05 1203.60 17.42 1.87% -3.50%1-Mar-05 1180.59 17.89 -1.93% 2.66%1-Apr-05 1156.85 17.27 -2.03% -3.53%2-May-05 1191.50 19.40 2.95% 11.63%1-Jun-05 1191.33 19.08 -0.01% -1.66%1-Jul-05 1234.18 19.15 3.53% 0.37%1-Aug-05 1220.33 17.62 -1.13% -8.33%A B C D E F123456789101112131415161718192021222324252627282930313233343536373839404142434445464748491-Sep-05 1228.81 17.92 0.69% 1.69%3-Oct-05 1207.01 17.45 -1.79% -2.66%1-Nov-05 1249.48 17.54 3.46% 0.51%1-Dec-05 1248.29 17.12 -0.10% -2.42%3-Jan-06 1280.08 18.57 2.51% 8.13%1-Feb-06 1280.66 20.24 0.05% 8.61%1-Mar-06 1294.87 21.67 1.10% 6.83%3-Apr-06 1310.61 20.95 1.21% -3.38%1-May-06 1270.09 19.68 -3.14% -6.25%1-Jun-06 1270.20 19.53 0.01% -0.77%3-Jul-06 1276.66 17.88 0.51% -8.83%1-Aug-06 1303.82 21.99 2.11% 20.69%1-Sep-06 1335.85 22.98 2.43% 4.40%2-Oct-06 1377.94 24.13 3.10% 4.88%1-Nov-06 1400.63 26.91 1.63% 10.90%1-Dec-06 1418.30 27.33 1.25% 1.55%3-Jan-07 1438.24 26.62 1.40% -2.63%1-Feb-07 1406.82 25.94 -2.21% -2.59%1-Mar-07 1420.86 25.53 0.99% -1.59%2-Apr-07 1482.37 26.74 4.24% 4.63%1-May-07 1530.62 26.92 3.20% 0.67%1-Jun-07 1502.97 27.85 -1.82% 3.40%2-Jul-07 1519.43 27.89 1.09% 0.14%A B C D E F5051525354555657585960616263646566676869707172The intercept is not significantly different from zero.The slope is highly significant.- =LN(C13/C12)R e g r e s s in g C is c o o n S & P 5 0 01 0 %5 %0 %- 5 %- 1 0 %- 1 5 %- 4 0 %- 3 0 %- 2 0 %- 1 0 %0 %1 0 %2 0 %3 0 %4 0 %y = 1 . 8 4 6 5 x - 0 . 0 0 3 2R2= 0 . 4 4 6S & P 5 0 0CiscoCISCO (CSCO) a and bJuly 2002 - June 2007G H I J K L M N12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849G H I J K L M N5051525354555657585960616263646566676869707172R e g r e s s in g C is c o o n S & P 5 0 01 0 %5 %0 %- 5 %- 1 0 %- 1 5 %- 4 0 %- 3 0 %- 2 0 %- 1 0 %0 %1 0 %2 0 %3 0 %4 0 %y = 1 . 8 4 6 5 x - 0 . 0 0 3 2R2= 0 . 4 4 6S & P 5 0 0CiscoO P Q12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849CISCO (CSCO) a and bJuly 2002 - June 2007 -0.0032 - =INTERCEPT(F13:F72,E13:E72)利用“斜率” 1.8465 - =SLOPE(F13:F72,E13:E72)利用Cov/VarR方 0.4460 - =RSQ(F13:F72,E13:E72)的T统计值 -0.3711 - =tintercept(F13:F72,E13:E72)的T统计值 6.8339 - =tslope(F13:F72,E13:E72)收益率日期 S&P 500 CSCO S&P 500 CSCO3-Jul-02 911.62 13.191-Aug-02 916.07 13.82 0.49% 4.67%3-Sep-02 815.28 10.48 -11.66% -27.66%1-Oct-02 885.76 11.18 8.29% 6.47%1-Nov-02 936.31 14.92 5.55% 28.86%2-Dec-02 879.82 13.10 -6.22% -13.01%2-Jan-03 855.70 13.37 -2.78% 2.04%3-Feb-03 841.15 13.98 -1.71% 4.46%3-Mar-03 848.18 12.98 0.83% -7.42%1-Apr-03 916.92 15.00 7.79% 14.46%1-May-03 963.59 16.41 4.96% 8.98%2-Jun-03 974.50 16.79 1.13% 2.29%1-Jul-03 990.31 19.49 1.61% 14.91%1-Aug-03 1008.01 19.14 1.77% -1.81%2-Sep-03 995.97 19.59 -1.20% 2.32%1-Oct-03 1050.71 20.93 5.35% 6.62%3-Nov-03 1058.20 22.70 0.71% 8.12%1-Dec-03 1111.92 24.23 4.95% 6.52%2-Jan-04 1131.13 25.71 1.71% 5.93%2-Feb-04 1144.94 23.16 1.21% -10.45%1-Mar-04 1126.21 23.57 -1.65% 1.75%1-Apr-04 1107.30 20.91 -1.69% -11.97%3-May-04 1120.68 22.37 1.20% 6.75%1-Jun-04 1140.84 23.70 1.78% 5.78%1-Jul-04 1101.72 20.92 -3.49% -12.48%2-Aug-04 1104.24 18.76 0.23% -10.90%1-Sep-04 1114.58 18.10 0.93% -3.58%1-Oct-04 1130.20 19.21 1.39% 5.95%1-Nov-04 1173.82 18.75 3.79% -2.42%1-Dec-04 1211.92 19.32 3.19% 2.99%3-Jan-05 1181.27 18.04 -2.56% -6.85%1-Feb-05 1203.60 17.42 1.87% -3.50%1-Mar-05 1180.59 17.89 -1.93% 2.66%1-Apr-05 1156.85 17.27 -2.03% -3.53%2-May-05 1191.50 19.40 2.95% 11.63%1-Jun-05 1191.33 19.08 -0.01% -1.66%1-Jul-05 1234.18 19.15 3.53% 0.37%1-Aug-05 1220.33 17.62 -1.13% -8.33%A B C D E F123456789101112131415161718192021222324252627282930313233343536373839404142434445464748491-Sep-05 1228.81 17.92 0.69% 1.69%3-Oct-05 1207.01 17.45 -1.79% -2.66%1-Nov-05 1249.48 17.54 3.46% 0.51%1-Dec-05 1248.29 17.12 -0.10% -2.42%3-Jan-06 1280.08 18.57 2.51% 8.13%1-Feb-06 1280.66 20.24 0.05% 8.61%1-Mar-06 1294.87 21.67 1.10% 6.83%3-Apr-06 1310.61 20.95 1.21% -3.38%1-May-06 1270.09 19.68 -3.14% -6.25%1-Jun-06 1270.20 19.53 0.01% -0.77%3-Jul-06 1276.66 17.88 0.51% -8.83%1-Aug-06 1303.82 21.99 2.11% 20.69%1-Sep-06 1335.85 22.98 2.43% 4.40%2-Oct-06 1377.94 24.13 3.10% 4.88%1-Nov-06 1400.63 26.91 1.63% 10.90%1-Dec-06 1418.30 27.33 1.25% 1.55%3-Jan-07 1438.24 26.62 1.40% -2.63%1-Feb-07 1406.82 25.94 -2.21% -2.59%1-Mar-07 1420.86 25.53 0.99% -1.59%2-Apr-07 1482.37 26.74 4.24% 4.63%1-May-07