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明明要加油 · 2023年08月12日

请问老师题目表格里面给了Long-term ROE，这个是用不上吗，是干扰项吗？

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

终值的现值:

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

$V_0=28.25+\frac{3.42}{1.109}+\frac{4.22}{1.109^2}+\frac{2.77}{1.109^3}+18.63=55.43$

我在算终值TV 的时候，是用RI3 2.77/14.5%=19之后，再加上2.77的和，处以1.09的三次方。最后和答案哪个也对不上。

后来改用，Re=10.9%, 基本算出了结果。

也就是说，求永续年金也是用cost of equity是吗？题目这个给的是干啥用的呢，或者什么时候能用到呢？

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王园圆_品职助教 · 2023年08月12日

同学你好，首先，表格中的Long-term ROE确实是多余条件，就是迷惑项目，没有任何作用

”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. “题干这里都说了，三年以后RI就保持不变了，运用PVRI = RI/Re即可计算出答案，计算和ROE本身就无关

另外，同学要注意，我们学过的所有equity相关的折现模型里，折现用的分母都是Re，和ROE始终是无关的，不要把两者混淆哦

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