To calculate the expected value of the dividend is we use Future value formula and to calculate discount value we use present value of the expected dividend.
current dividend = $1.75
Growth rate for first 5 year is 15% and then 5% forever
Required rate of return is 12%
(A) Expected Dividend = D0((1+r)n-1)/r
= 1.75((1.15)5-1))/0.15 = $15.75
It means to get $15.75 after five we have to invest $1.75 every year for five year.
(B) Present Value = here we use growing annuity.
D0/(r-g)*(1-((1+g)/(1+r))n
Where r = Required rate
g = Growth rate
n = no. of year
= 1.75/(.12-.15)*(1-((1.15)/(1.12))5
= $13.69
So the present value is $13.69 if $1.75 will growth @ 15% for 5 year.
Note: we can do this problems into excel also by using formula PV and FV.
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