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daiwin18 · 2021年09月28日

关于RI3的计算

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

关于RI3的计算为何不能用(ROE-r)*B的公式去计算呢?

3 个答案

王园圆_品职助教 · 2021年10月01日

嗨,努力学习的PZer你好:


同学你是说你用长期的ROE-re得出了正确答案C????

我按照你的理解,那第三年就不需要继续用表格中的数字求RI,而是直接用(ROE长期-re)*B2来计算第三年的RI3,然后RI3直接作为永续年金折到第二年年末和RI2一起往前折现,加上RI1的折现和期初B0,是得不到任一选项答案的。

请问同学是怎么用长期ROE-re 算出来正确答案的呢??

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努力的时光都是限量版,加油!

Chandler · 2021年10月04日

我觉得同学提问的意思是,1、2、3年的RI分别计算出来,再把第三年后面的当作二阶段算PVRI,再折现,类似于FCFF的多阶段。 提问的同学可以参考下别的助教回答的答案,能解答你的疑问。

王园圆_品职助教 · 2021年09月29日

嗨,爱思考的PZer你好:


题干的意思是说,从第三年开始,以后每一年的RI就都不变,都等于第三年算出来的值

因为题干给了前三年分别计算RI所需要的表格--就是让考生分别计算三年的值;

又因为题干给了长期ROE不等于短期ROE--也就是告诉考生题目中的ROE可能只是干扰项。

另外,按照同学你的理解方式,应该三个选项中都没有正确答案吧?那这样的话,这道题就没法继续做了不是吗?

确实有的时候涉及到时间点的表述,题目可能会给考生造成误解。我们在做题的时候都不可能100%保证理解题目的意思。但这里建议同学,要是计算出来的答案没有任何一个符合,就说明理解题目的思路可能是有问题的,需要调整思路或者重新理解一下题干哦~~


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

daiwin18 · 2021年09月30日

请老师再读一下题干“will be constant from year 3 ”,翻译是从第3年开始是常数。按老李上课的画图方法,就是第3段开始ROE为常数项,而且也有答案是C:55.43

王园圆_品职助教 · 2021年09月28日

嗨,爱思考的PZer你好:


同学你好,因为在第三年当年,公司依然处在短期阶段的高速增长里面,题干中说了“the short-term ROE is higher than the long-term ROE."

如果同学用永续增长阶段的ROE带入短期的计算,肯定不会得到准确的值的。

这里给出的ROE是迷惑选项,永续阶段是指第三年之后的每一年都跟第三年的RI的值一样,但是第三年之后公司才进入永续的ROE阶段。

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加油吧,让我们一起遇见更好的自己!

daiwin18 · 2021年09月29日

但题干说“ residual income per share will be constant from year 3 into perpetuity”,那应该从第3年开始就是long time ROE吧?这样ROE-re得出的RI才是常数啊

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