题目
A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to:
选项
A.$31.
B.$126.
C.$133.
答案
B
解析
B is correct. The value of the perpetuity one year from now is calculated as: PV = A/r, where PV is present value, A is annuity, and r is expressed as a quarterly required rate of return because the payments are quarterly.「huixue_img/importSubject/1564548693095485440.png」 B正确。 一年后的永续年金价值计算如下：PV = A/r，其中PV为现值，A为年金，r表示为季度要求收益率，因为支付是按季度来的： PV4 = $2.00/(0.06/4)= $133.33。 今天时间点上的现值是： PV0= FV4*(1＋r)^(–N)=$133.33*(1＋0.015)^(–4) = $125.62≈$126. 注意：第一笔现金流（股利）发生在t=5时刻，第二年第一个季度末，PV算下来是在t=4时刻的现值PV4，所以还要折现一次到t=0时刻。