Dividends

[asedersten]

What equation would I use to solve this problem?


Williams Inc. PAID a $3 dividend YESTERDAY and that dividend is expected to grow at 4% every year thereafter. If the discount rate is 10%, what would be the present value of the expected dividend stream (aka the expected price of the firm's stock)?

 

[tkhunny]

You must, must, must, must, must, must, must, must get used to the concept of BASIC PRINCIPLES. With jsut a tiny bit of practice, you can solve ALL such problems with remarkably little difficulty.

Define a few terms and you are off...

Yesterday's Dividend = $3 (Year 0)
Next Year's Dividend = $3*1.04 (Year 1)
Next Next Year's Dividend = $3*1.04^2 (Year 2)

Are we beginning to see the picture?

If we define r = the growth rate, we have these payments into perpetuity.

$3*(1+r), $3*(1+r)^2, $3*(1+r)^3, $3*(1+r)^4, $3*(1+r)^5, $3*(1+r)^6, ...

If we define i = discount rate, and v = 1/(1+i), we have this present value:

$3*(1+r)*v + $3*(1+r)^2*v^2 + $3*(1+r)^3*v^3 + $3*(1+r)^4*v^4 + $3*(1+r)^5*v^5 + $3*(1+r)^6*v^6 + ...

This expression can be massively simplified. (You had better know how to do this.)

$3*(1+r)*v(1 + (1+r)*v + (1+r)^2*v^2 + (1+r)^3*v^3 + (1+r)^4*v^4 + (1+r)^5*v^5 + ...)

$3*(1+r)*v*[1/(1-(1+r)*v)]

You're not going to make me do ALL the work, are you?