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阿熊 · 2025年06月22日

NO.PZ2018103102000105

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

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=18.63


PV=r×(1+r)3


RI3

​=0.109×1.1093


2.77

​=18.63


V0=28.25+3.421.109+4.221.1092+2.771.1093+18.63=55.43


为什么第三年到永续用的是折现三年而不是两年呢,谢谢老师

1 个答案

王园圆_品职助教 · 2025年06月22日

同学你好,因为这里计算PVRI用的其实时RI4啦

因为从第3年开始RI永续不变,所以其实这里是PVRI 3 = RI4/ r了

所以解析最后是RI1到RI3和位于第三年年末的PVRI3一起折现到0时刻就可以获得答案了

你要是直接用RI3也是可以计算的,就是PVRI2=RI3/r

然后把RI1,RI2和PVRI2一起折现到0时刻,也会得到和本题最后一样的答案的

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NO.PZ2018103102000105问题如下 Matt is evaluating Company M using the multistage resiincome mol. He hforecastethresiincome per share will constant from ye3 into perpetuity anthe short-term ROE is higher ththe long-term ROE. He halso estimatethe earnings anvin for the following three years in the following table. What`s the intrinsic value of Company M? A.$27.18B.$48.91C.$55.43C is correct.考点Multistage ResiIncome Valuation解析先计算出每一年的 BV1 = BV0 + EPS - vin 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*= 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}=18.63PV=r×(1+r)3RI3​​=0.109×1.10932.77​=18.63V0=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=55.43V0​=28.25+1.1093.42​+1.10924.22​+1.10932.77​+18.63=55.43虽然计算中并不涉及,但题目中的long-term ROE是否并不适用第一年到第三年?一至三年的EPS/BV并不等于这个14.5%。谢谢

2025-06-01 08:48 1 · 回答

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