Posted by **Teresa** on Thursday, March 13, 2008 at 7:12pm.

A common stock is just paid an annual dividend of $2 yesterday. The dividend is expeccted to grow at 8% annually for the next 3 years, after which is will grow at 4% in perpetuity. The appropriate discount rate is 12%. What is the priceof the stock?

What I know:

Differential growth

DIV=2

g1=.08

g2=.04

r=.12

yr.end 5=Div4(1+g2)=2.52(1.04)=2.6208

p4=DIV5/r-g2=2.6208/.12-.04=32.76 FV

p4/(1+r)^4=32.76/1.12^4=20.82

Present Value of all Div as of yr end 0 is 20.82 + 32.76 =

??? not sure about this step

- Finance -
**Damon**, Thursday, March 13, 2008 at 8:00pm
Perhaps my reply to your previous question would help. On the other hand perhaps I am way off base not being a financial type at all.

by the way, my g for geometric series is starting value.

my r is ratio of value at year (n+1) to value at year n.

in that case sum of infinite series is g/(1-r)

by the way, for just n terms

sum = g + g r + g r^2 +...+ g r^(n-1)

= g (1-r^n)/(1-r)

- Finance -
**Damon**, Thursday, March 13, 2008 at 8:22pm
let's see what the dividends are worth after 3 years (n = 4 because we start at the beginning of year one and the end of the other years)

V3 = 2 + 2(1.08/1.12) + 2(1.08/1.12)^2...

g = 2

r = 1.08/1.12 = .9463

so

sum after three years = 2(1-.9463^3)/(1-.9463) = 2(.1526/.0537) = 5.683

now we go on forever at 4%

g = 5.683

r = 1.04/1.12 = .9286

sum to infinity = 5.683/(1-.9286) = 79.56

- Finance -
**Damon**, Thursday, March 13, 2008 at 9:36pm
wait a minute, we have to subtract the first three years at 4% off the infinite 4% years because we did those years separately with 8%

sum at 4% after three = 2(1-.9286^3)/(1-.9286)

= 2*(.1993/.0714) = 5.583

so it is

79.56 - 5.58 = 73.98

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