甲公司目前的资本结构(账面价值)为:长期债券1200万元,权益资本800万元(1

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问题 甲公司目前的资本结构(账面价值)为:长期债券1200万元,权益资本800万元(100万股,目前股价为10元/股)。目前正在编制明年的财务计划,需要融资1000万元,有以下资料:(1)本年派发现金股利每股1.0元,股利支付率为20%,预计保持不变。(2)需要的融资额中,有一部分通过明年的利润留存解决;其余的资金通过增发5年期长期债券解决,每张债券面值100元,发行价格为115元,发行费为每张5元,票面利率为8%,每年付息一次,到期一次还本。(3)目前的资本结构中的长期债券是2年前发行的,发行价格为1100元,发行费率为2%,期限为5年,每年付息一次,到期一次还本,票面利率为10%,债券面值为1000元,目前的市价为1050元。(4)目前10年期的政府上市债券到期收益率为4%,票面利率为5%。市场组合平均报酬率为10%,甲公司股票报酬率与市场组合报酬率的协方差为8%,市场组合报酬率的标准差为20%。(5)预计每股股利可以长期稳定按照5%的增长率增长。(6)公司适用的所得税税率为25%。已知:(P/F,5%,5)=0.7835,(P/F,6%,5)=0.7473,(P/F,8%,3)=0.7938,(P/F,9%,3)=0.7722,(P/A,5%,5)=4.3295,(P/A,6%,5)=4.2124,(P/A,8%,3)=2.5771,(P/A,9%,3)=2.5313要求:(1)计算增发的长期债券的税后资本成本。(2)按照到期收益率法计算目前的资本结构中的长期债券的税后资本成本。(3)计算明年年末的资本总额。(4)计算长期债券筹资额。(5)计算明年年末的资本结构中各种资金的权重。(6)确定该公司股票的β系数并根据资本资产定价模型计算普通股资本成本。(7)根据股利增长模型估计普通股的资本成本。(8)根据(6)和(7)问的结果取平均值计算权益资本成本。(9)按照账面价值权数计算明年年末的加权平均资本成本。

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解析(1)假设增发的长期债券的税前资本成本为r,则:100×8%×(P/A,r,5)+100×(P/F,r,5)=115-58×(P/A,r,5)+100×(P/F,r,5)=110当r=5%时,8×(P/A,5%,5)+100×(P/F,5%,5)=8×4.3295+100×0.7835=112.99当r=6%时,8×(P/A,6%,5)+100×(P/F,6%,5)=8×4.2124+100×0.7473=108.43根据(6%-r)/(6%-5%)=(108.43-110)/(108.43-112.99)解得:r=5.66%(1分)即增发的长期债券的税前资本成本=5.66%增发的长期债券的税后资本成本=5.66%×(1-25%)=4.25%(0.5分)(2)假设目前的资本结构中的长期债券的税前资本成本为K,则:1000×10%×(P/A,K,3)+1000×(P/F,K,3)=1050100×(P/A,K,3)+1000×(P/F,K,3)=1050当K=9%时,100×(P/A,9%,3)+1000×(P/F,9%,3)=100×2.5313+1000×0.7722=1025.33当K=8%时,100×(P/A,8%,3)+1000×(P/F,8%,3)=100×2.5771+1000×0.7938=1051.51根据(K-8%)/(9%-8%)=(1050-1051.51)/(1025.33-1051.51)解得:K=8.06%(1分)目前的资本结构中的长期债券税后资本成本=8.06%×(1-25%)=6.05%(0.5分)(3)明年年末的资本总额=1200+800+1000=3000(万元)(0.5分)(4)明年的每股股利=1.0×(1+5%)=1.05(元)明年的每股收益=1.05/20%=5.25(元)明年的利润留存=100×(5.25-1.05)=420(万元)长期债券筹资额=1000-420=580(万元)(1分)(5)原来的长期债券的权重=1200/3000×100%=40%增发的长期债券的权重=580/3000×100%=19.33%权益资本的权重=1-40%-19.33%=40.67%或:权益资本的权重=(800+420)/3000×100%=40.67%(1分)(6)该股票的β系数=该股票报酬率与市场组合报酬率的协方差/市场组合报酬率的方差=8%/(20%×20%)=2普通股资本成本=4%+2×(10%-4%)=16%(0.5分)(7)普通股的资本成本=1.05/10+5%=15.5%(0.5分)(8)权益资本成本=(16%+15.5%)/2=15.75%(0.5分)(9)加权平均资本成本=6.05%×40%+4.25%×19.33%+15.75%×40.67%=9.65%(1分)Answer: (5points)(1) Assuming that the pre-tax cost of debt of additional issued long-term bond is r,100×8%×(P/A,r,5)+100×(P/F,r,5)=115-58×(P/A,r,5)+100×(P/F,r,5)=110When r=5%,8×(P/A,5%,5)+100×(P/F,5%,5)=8×4.3295+100×0.7835=112.99When r=6%,8×(P/A,6%,5)+100×(P/F,6%,5)=8×4.2124+100×0.7473=108.43(6%-r)/(6%-5%)=(108.43-110)/(108.43-112.99)r=5.66%Pre-tax cost of debt of additional issued long term bond=5.66%After-tax cost of debt of additional issued long term bond=5.66%×(1-25%)=4.25%(2) Assuming that the pre-tax cost of debt of long-term bonds in current capital structure is K1,000×10%×(P/A,K,3)+1,000×(P/F,K,3)=1,050100×(P/A,K,3)+1,000×(P/F,K,3)=1,050When K=9%100×(P/A,9%,3)+1,000×(P/F,9%,3)=100×2.5313+1,000×0.7722=1,025.33When K=8%100×(P/A,8%,3)+1,000×(P/F,8%,3)=100×2.5771+1,000×0.7938=1,051.51(K-8%)/(9%-8%)=(1,050-1,051.51)/(1,025.33-1,051.51)K=8.06%The pre-tax cost of debt of long-term bonds in current capital structure =8.06%×(1-25%)=6.05%(3) The total capital at the end of next year=12,000,000+8,000,000+10,000,000=30,000,000(RMB)(4) Dividend per share of next year =1.0×(1+5%)=1.05(RMB)Earnings per share of next year=1.05/20%=5.25(RMB)Returned earning of next year = 1,000,000×(5.25-1.05)=4,200,000(RMB)The amount of fund raised by Long-term bond=10,000,000-4,200,000=5,800,000(RMB)(5) The weight of the original long-term bond=12,000,000/30,000,000×100%=40%The weight of the additional issued long-term bond=5,800,000/30,000,000×100%=19.33%The weight of equity capital =1-40%-19.33%=40.67%or =(8,000,000+4,200,000)/30,000,000×100%=40.67%(6)βof the share = Covariance of Stock Return Rate and Market Portfolio Return Rate divided by the variance of Market Portfolio Return Rate=8%/(20%×20%)=2Cost of capital of common stock=4%+2×(10%-4%)=16%(7)Cost of capital of common stock=1.05/10+5%=15.5%(8)Cost of equity capital=(16%+15.5%)/2=15.75%(9)Weighted Average Cost of Capital =6.05%×40%+4.25%×19.33%+15.75%×40.67%=9.65%
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