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LHY · 2023年05月01日

PV计算这个分母是什么意思?

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

PV=r×(1+r)3


RI3

​=0.109×1.1093


2.77

​=18.63

2 个答案

王园圆_品职助教 · 2023年05月02日

是的,同学,就是这个意思

王园圆_品职助教 · 2023年05月01日

同学你是问这个公式的分母是什么意思吗?

首先,从第三年以后进入RI保持不变的阶段,所以根据多阶段模型中的PVRI = RI/r的公式,以RI4 = RI3为分子的话可以计算第三年年末的PVRI=RI3/r,然后直接将这个PVRI折现到0时刻的话,就是再除以(1+r)^3了

LHY · 2023年05月02日

就是RI4及以后都是2.77,所以RI4及以后的永续折现价值等于2.77除以要求回报率0.109对吧。然后再把这个数值折现到PV0.

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