Discounting dividends and terminal value in valuation

I am new to finance and valuation in particular. I have a query regarding discounting dividends and terminal value for valuation using dividend discount model.

I have created an illustration to help in understanding how many years do we have to discount to find the total equity (which is then divided by number of shares to find the value of share)

Suppose I wish to value the firm for 1)Today 2) FYE2015 3) FYE2016 4) FYE 2017 with reference to the image below.

Can you tell me if my understanding is correct?

1) TODAY:

x/(1+r) + y/(1+r)^2 + z/(1+r)^3 + TV/(1+r)^3


2) FYE2015

y/(1+r) + z/(1+r)^2 + TV/(1+r)^2


3) FYE 2016

z/(1+r) + TV/(1+r)


4)FYE 2017

TV


If this is incorrect, then what should it be?

Can you tell me if my understanding is correct?

Yes it's correct, with minor clarification: you're valuing "ex dividend", meaning for FY2017, e.g., you're valuing the company the next moment the dividend was paid out. Should you be interested in "cum dividend" value, you'd add the value of dividends for the year you are entitled for.

...then what should it be?

Assuming what you wrote is correct, Terminal Value (TV) in Dividend Discount Model is Present Value of all future dividend inflows. Generally speaking, TV will be: $$TV=\frac{d_t}{r_t}$$

where $d_t$ is constant dividend paid forever (follows from definition of "terminal"), usually assumed equal to $z*(1+r_t)$, and $r_t$ is constant discount rate applicable to terminal period.

Beware of three caveats:

1. All values are real (cleaned of inflation)
2. You can't "port" rates estimated for one currency, say dollar, to cash flows estimated in another currency, say peso. You should carry out the total valuation exercise, including estimation of dividends and discount rates, in a single currency.
3. There will be a certain leeway in estimating $r_t$, to which the model is very sensitive. The right thing here is not to find the "right" $r_t$ that does not exist, but to (i) apply it consistently to all your valuation universe of companies so that your relative valuation is right (ii) make your assumptions transparent so that they can be discussed (iii) make it comply to common sense.
• Thanks for the detailed explanation. Especially the last caveat regarding Rt. That 's something I have infact practically observed in my valuation. However, I would like some more info regarding ex-dividend and cum-dividend valuation you talked about. Since, my example is hypothetically based on assumption that the data is available immediately after the closing of last financial year. When we're valuing a firm in October, wouldn't last fiscal year dividends be already paid? (assuming year end in March 31) So the valuation has to ignore that dividend and only the future are to be considered. – Saurabh3321 Oct 25 '15 at 11:08
• With your last example (October valuation), your last statement about only taking into account future dividends is correct (why would anybody bother with past in DCF???). However, in this case you would need to adjust discount factor for the first year since your discount horizon is not a whole year anymore. – Sergey Bushmanov Oct 25 '15 at 11:28
• Got it. Without the adjustment, I'd end up getting the value of the firm at the end of last fiscal year, right after the dividend was paid. Thanks for the help :) – Saurabh3321 Oct 25 '15 at 11:45
• If you're interested in understanding DCF, the 'The dangers of DCF' by James Montier may be very helpful. – Sergey Bushmanov Oct 25 '15 at 11:50