解析:
(1)假设半年的税前债务资本成本为rd
1000×4%×(P/A,rd,10)+1000×(P/F,rd,10)=1075
假设折现率是4%
1000×4%×(P/A,4%,10)+1000×(P/F,4%,10)=1000
假设折现率是3%
1000×4%×(P/A,3%,10)+1000×(P/F,3%,10)=1085
(rd-3%)/(4%-3%)=(1075-1085)/(1000-1085)
rd=3.12%
年有效的税前债务资本成本=(1+3.12%)^2-1=6.34%
债券的税后资本成本=6.34%×(1-25%)=4.76%
(2)每季度股利=100×8%/4=2(元)
优先股每季度资本成本=2/(125-1.5)=1.62%
优先股的有效年资本成本=(1+1.62%)^4-1=6.64%
(3)按照资本资产定价模型计算:
普通股资本成本=6%+1.2×5%=12%
按照股利增长模型计算:
普通股资本成本=[5.23×(1+5%)/75]+5%=12.32%
平均的普通股资本成本=(12%+12.32%)/2=12.16%
(4)加权平均资本成本
=4.76%×40%+6.64%×10%+12.16%×50%
=8.65%