Assignment X2.8

In part (i) of the solutions to Assignment X2.8
an approximation is used that the next dividend is the last dividend which was paid 3 months ago multiplied by 9 months worth of the annual growth rate and this is then used in the normal simplified discounted dividend model formula.

Please can someone explain this approximation?

Shouldn't the next dividend in 9 months time still have the full year's worth of growth , i.e. given an assumption over the growth rate, the expected next dividend is still D0 ( 1+g) regardless of where you are in the year relative to that next payment?

Secondly in the solution nothing has been amended in the formula with regards to the fact that each future dividend is discounted by 3 months less.

To me the solution should have been this:

[2 * (1+5%) * (1+ 10%) ^ 0.25] / (10% - 5%)

 

Hello @Polz87,

I have picked up your point as per above.
First of all, the simplified model to value an equity is given by: D/(I-g). This formula assumes the following:

1. dividends are paid annually, with the next payment being made the next year.
2. dividends grow at a constant rate, g, per annum.
3. required rate, I, is independent of time at which the payment is to be made.

The question provides us with the following information: The scheme actuary has researched the company and found the following information:

•  the most recent dividend payment was $2, which was paid three months ago
•  dividends have been increasing on average by 5% pa for the last eight years
•  the required rate of return is 10%
•  the stock is currently trading at $35 per share.

So, to value the equity using the equation above, the following data should be picked up:

1. Next dividend payment (which is 9 months from now) will be equal to the dividend paid 3 months back, allowing for its annual growth which is equal to: 2 (1 + 5%)^(9/12)
2. The denominator stays the same, i.e. 10% - 5% = 5%

Now, coming to your suggestion. This is wrong because if you have a look at the derivation of the formula found on Page 13 of Chapter 12, you will see using the approximation of the sum to infinity of a Geometric Progression, we arrive at the formula I mentioned above. So, there is no need to discount the dividend payments.

Hope this helps.