When calculating terminal value in a DCF why do we raise the denominator to 5 if we are doing a 5 year DCF (I'm assuming if its a 10 yr DCF you would raise the denominator to 10). I just don't get why you would raise the value of all future cash flows beyond period 5 to the 5th power (esp since you use 5 to discount the 5th yr) but I understand there's no number to represent the number of years past the forecasted period.

Region

Deleted, thought the question was asking something else.

I'm not really sure what your question is, to be honest. Is it why the power in the terminal value is discounted like the power in the previous period? If so...

(1) P = C(1+g)/(1+r) + C(1+g)^2/(1+r)^2 + ...

(2) P(1+r)/(1+g) = C + P

(2) - (1) = P( (1+r)/(1+g) - (1+r)/(1+r) = C

(2) - (1) = P = C(1+g)/(r-g)

This formula is in time zero, which means when you calculate the terminal value representing all cash flows from time six onward it is expressed in the same period as time five cash flows and has to be discounted at the same rate (power 5) to get the present value.

Again, no idea if this is your question...

Yes this is exactly what I was asking sorry about that. I appreciate your response but I'm still just a little confused about what you're saying. I'm not trying to challenge financial theory here btw I'm just genuinely curious why its the way it is

We assume different growth rates will occur during different stages of the business's life cycle. The terminal year marks the end of our forecast period, beyond this point we have to make reasonable assumptions about how our target company will progress.

"We assume a high growth rate (usually over 10%) for business in its early stage of expansion. This rapid-growth stage is often followed by a decelerated growth stage, as the company will likely struggle to maintain its high growth rate due to the rising competition within the industry.

As this same company moves closer to maturity, it is expected to hold a steady market share and revenue. We often assume a relatively lower growth rate for this stage, usually 5% to 8%." -Corporate finance institute

Forecast period (terminal year) -> terminal period

does that help at all?

The short answer is that the terminal value is a perpetuity and they are discounted at n-1.