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company is expected to pay future dividend as follows
Y_{1}=\$1
Y_{2}=\$1.5
Y_{3}=\$2
From Y_{4} the dividend will consistently grow by 4% each year. The Ke is 10%.
Required:
Estimate the market Price of each share.
Is that ans 28.69 or 29.69 .??? Can you tell do we include growth or not
I think it’s
PV(Y1) = Y1 / (1 + Ke) = $1 / (1 + 0.10) = $0.909 PV(Y2) = Y2 / (1 + Ke)^2 = $1.5 / (1 + 0.10)^2 = $1.239 PV(Y3) = Y3 / (1 + Ke)^3 = $2 / (1 + 0.10)^3 = $1.5
From Year 4 onwards, the dividend grows by 4% each year. To calculate the PV of these growing dividends, we can use the dividend growth model:
PV(Y4 onwards) = Y4 / (Ke – g) = $2 / (0.10 – 0.04) = $40
Finally, we sum up all the PVs to get the market price of each share:
Market Price = PV(Y1) + PV(Y2) + PV(Y3) + PV(Y4 onwards) = $0.909 + $1.239 + $1.5 + $40 = $43.648
But without seeing the answer I can’t be sure
Why didnt we Convert the Year 4 perpetuity to Y0. Like the way did in a sum , Cant Co… where they asked about current share price … and mentioned year 3 dividend 0.5 with growth from subsequent year….?
Like if we do the similar way we get ans 29.69 and this is a academic question of my friend she asked for answer i stated 29.69 after similar calculation as Cant Co their answer key was mentioned this answer but there is no explanation.. Thats why asked
The reason for not converting the Year 4 perpetuity to Year 0 is because the perpetuity is an inflating perpetuity that starts from Year 4 and continues indefinitely.
To calculate the present value of an inflating perpetuity, the dividend growth formula is used.
MV(XD) = PV(Y4 onwards) = Y4 / (Ke – g) = $2 / (0.10 – 0.04) = $40
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