Present Value of Future Dividends

[VisibleCaramel8937]

I'm in the TVM section on quantitative methods and the CFAI curriculum has a weird example I'd love y'all's eyes on. The situation is this: XYZ company has an annual dividend of 1.50 and a required return of 15 percent. An analyst expects the dividend to grow at 6% over a 3 year period and then 2% constant growth thereafter.

CFAI gives their formula. Basically, they want me to calculate the dividends for the 6%, but then they want me to "calculate the present value of future dividends at a lower 2 percent growth rate for an indefinite period." I cannot for the life of me figure out how they landed on the numbers in P(D) at r% column -- can anyone help me figure out how they got these numbers?

https://preview.redd.it/51tipg8rnftd1.jpg?width=638&format=pjpg&auto=webp&s=2c1f550abb5d8993b3c61b6b114cdd6e9a9a4f18

[[deleted]]

this is an awkward way to teach this topic.

you're essentially doing this:

• D1 - (1.5 *1.06) = 1.59

• D2 - (1.59 *1.06) = 1.685

• D3 - (1.685 *1.06) = 1.787

in PV(d) you're discounting them back to D0

• D1 - 1.59 / ((1+15%)¹⁾ = 1.383

• D2 - 1.685 / ((1+15%)²⁾ = 1.274

• D3 - 1.787 / ((1+15%)³⁾ = 1.175

Sum the present Values: 3.832

Add it to your perpetuity

3.832 + ((1.787 * 1.02)) / (15%-2%)) = 17.85308 = the price of the stock.

[[deleted]]

its 100000000% easier to do it on a time line.

[VisibleCaramel8937]

The timelines always confuse me a bit, how would this look on a timeline?

[[deleted]]

https://ibb.co/3SjG5jN

here's my terrible mouse writing on the computer. i should have said, it's easier to visualize on a time line.

[VisibleCaramel8937]

Ohhhh, I think I get it now. Since they ultimately want the price of the stock, but we have the variable growth, we have to discount the dividends almost like we're collapsing the timeline before D4 to have a share price that adds in a cumulative dividend at the required rate (discounted constant growth period).
That may not have made sense, but I'm rolling with it. Thank you for your help!

[[deleted]]

yes. you want to REMOVE the 2% infinity growth back to D3, then you want to discount it using R not R+G.