- The required rate of return is used for discounting at k
- The dividends, Div, grow at rate, g
- You use the upcoming payment, not the current payment (Div1 = Div0 * (1+g)).

- The first term (a) is Div1 / (1 + k) (the first dividend discounted to today's dollars)
- The rate of growth of each term, (r) is [(1 + g) / (1 +k)] - each year the dividend grows by g, but is discounted by k
- The value of the series, S, is the price of the asset, P

P = [Div1 / (1+ k)] / [1 - ((1 + g)/ (1 + k)]

Expanding and simplifiying the denominator

= [Div1 / (1 + k)] / [(1 + k - 1 - g) / (1 +k)]

= Div1 / [k - g]

Expanding and simplifiying the denominator

= [Div1 / (1 + k)] / [(1 + k - 1 - g) / (1 +k)]

= Div1 / [k - g]

And this is how the formula for the DDM is derived from first principles.

Now based on this, how can we determine the price of an asset which experiences supernormal dividend growth during a period of it's life?

[Example] A start up business experiences a g of 25% per year dividend growth for three years before returning to a regular 9% per year growth pattern (g in both cases). The dividend is currently $3 and the discount rate is 12%. What is the price of the asset using DDM?

Immediately, it is obvious that a DCF is needed, but with the dividend model changing mid way, what strategy should be used? First calculate the last dividend payment of the super normal growth period: Div3 = $3 x (1.25) ^ 3 = $5.86. At year 3, the terminal value of the asset using the DDM is:

P = Div1 / [k-g]

= ($5.86 x 1.09) / (12% - 9%)

= $212.89

= ($5.86 x 1.09) / (12% - 9%)

= $212.89

However, recall that this terminal value is in Year 3 dollars. Now as of today, your future cash flows are [$3.75, $4.68, $5.85 + $212.89].

Using a DCF with discount rate of 12%, the NPV of this asset is $162.77. For an asset currently only paying out $3, this might seem high, but the effect of the supernormal growth so early in the assets life dramatically affects the value of subsequent cash flows.

## 4 comments:

You are a supernerd.

j/k

Sofia

Wow Josh!

So this is what you do in New York? Crazy!

Press on!!!

Sofia: I'll take being called a super nerd by an M.Fin candidate a compliment! ;)

Jose: I love it... It's a little trick I like to call 'math' ;)

Like I said...

SUPER.

NERD.

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