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Augee · 2024年04月09日

PVRI3的计算有点不懂

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

老师按照李老师公式,PVRI3不应该是2.77)*W/(1+10.9%-W),其中W=1-g=94.5%,然后再用10.9%来折现吗,算出来的终值等于15.96,PVRI3则等于11.7。

1 个答案

王园圆_品职助教 · 2024年04月09日

同学你好,要看题目条件做题啊

题目这里都说了“He has forecasted that residual income per share will be constant from year 3 into perpetuity”第三年以后的RI都是保持不变的了

李老师一共给了四种PVRI计算的方式,此时就不适用于有w的那个公式了,而是应该用第一种情况来计算

另外,题目的g是分红的增长率g,而老师上课推导1+g=w公式里的g是指RI的增长率,因为RI始终是在下滑的,这个g应该本身就是一个负数,且必须是RI的增长率而非分红增长率

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