Supernormal Growth: shares w/ $2 div growing 20%/yr for 3 yr

Q. Current company dividends are $2 per share (Do). The dividend is expected to grow at 20% per year for next three years (Gs) and then 6% per year for the foreseeable future. You demand a required rate of return of 10%. What would you pay for a share of this stock?

So, I figured out the D1, D2, D3 using the supernormal growth rate and then figured out the present value of D4 to infinity and came up with $85.05...but got 3 points deducted by my instructor without explanation.

I had D1 = Do(1 + Gs) = $2.40 and PV of this is $2.18
D2 = D1(1+Gs) = $2.88 and PV of this is $2.38
D3 = $3.456 plus the present value of D4 to infinity = $107.136 whose PV = $80.49

$2.18 + $2.38 + $80.49 = $85.05.

Not sure where I messed this up...ideas?

Re: Supernormal Growth

You simply MUST learn to write out expressions using basic principles.

I used

s = 1+Gs = 1.2

and

g = 1+0.06 = 1.06

and defined

v = 1/(1.10)

Now write the expression:

2(1 + sv + (sv)^2 + (sv)^3 + ((sv)^3)gv + ((sv)^3)((gv)^2) + ((sv)^3)((gv)^3) + ...)

A little algebra

2(1 + sv + (sv)^2 + (sv)^3 + ((sv)^3)[gv + (gv)^2 + (gv)^3 + ...])

You must then recognize the pieces

2(1 + sv + (sv)^2 + (sv)^3 + (s^3)(v^3)[gv/(1-gv)])

2((1-(sv)^4)/(1-sv) + (s^3)(v^3)[gv/(1-gv)])

Nowhere near your $85. Almost half!

It appears that you are short one 20% increase. After that, I'm not sure what you did. I'm a little surprised it was only three points off. Count your blessings!