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千锤百炼 · 2022年07月26日

终值计算问题

NO.PZ2018103102000105

问题如下:

Matt is evaluating Company M by using the multistage residual income model. He has forecasted that residual income per share will be constant from year 3 into perpetuity and the short-term ROE is higher than the long-term ROE. He has also estimated the earnings and dividends for the following three years in the following table. What`s the intrinsic value of Company M?

选项:

A.

$27.18

B.

$48.91

C.

$55.43

解释:

C is correct.

考点:Multistage Residual Income Valuation

解析:先计算出每一年的BV

BV1 = BV0 + EPS - Dividends per share = 28.25 + 6.5 - 1.75 = $33,同理可得BV2 = $38.19,BV3 = $43.15

再计算出每一年的RI

RI1 = EPS1 – re*B0 = 6.50-10.9%*28.25 = $3.42,同理可得RI2 = $4.22,RI3 = $2.77

终值的现值:

PV=RI3r×(1+r)3=2.770.109×1.1093=18.63PV=\frac{RI_3}{r\times\left(1+r\right)^3}=\frac{2.77}{0.109\times1.109^3}=18.63

V0=28.25+3.421.109+4.221.1092+2.771.1093+18.63=55.43V_0=28.25+\frac{3.42}{1.109}+\frac{4.22}{1.109^2}+\frac{2.77}{1.109^3}+18.63=55.43

您好,

题中有提到长期的ROE为14.5%低于短期(3年)的ROE。解答中计算PVRI3是用RI3/Re。我的问题是,PVRI3=RI3/RE不是假设衰减因子w=1的时候才可以使用吗?题中长期ROE下行不会影响到w,是不是应该用RI3/(1+re-w)?

谢谢

1 个答案

王园圆_品职助教 · 2022年07月26日

嗨,爱思考的PZer你好:


首先,我们判断使用RI3/re来计算的依据是“ forecasted that residual income per share will be constant from year 3 into perpetuity”这句话,意思是第三年以后公司的RI不再变化

其次,题目中给出“short-term ROE is higher than the long-term ROE”的意思是告诉考生,短期的ROE 更高,所以短期的——也就是表格中的前3年RI需要单独计算,并且这三年计算出来的ROE值不可以用来计算未来的RI的值

题目只是说长期ROE会比较低,但是同时也给出了一个具体的数值——意思是长期来说,会一直保持这个ROE不变,有可能这种ROE的变小是第三年突然变小,然后持续保持不变的

而我们认为w=1的前提是RI始终保持不变:即长期ROE始终大于Re并且两者之差稳定,并使RI = (ROE-Re)*BV0这个计算的值保持不变即可,并没有要求长期ROE一定要和短期的一致

所以不存在你说的需要使用RI3/(1+re-w)来计算

最后,题目也没有给出衰减因子w不是吗?更加说明这种解题思路是不对的哦


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