How much does power amplifier really matter comparing to other hi-fi components?

What is the best ratio (out of a total of 100%) in terms of money to put in a high-end hi-fi set containing:
1. CD player/DAC, 2. Pre-amp, 3. Power-amp, 4. speakers.
(25% will be assigned to each if the 4 parts are equal).
Can we take this as a reference to distribute the budget when buying power-amp?

Looking forward to learning experiences and technical information from audiophiles including hi-fi dealers.
25% each is about right. Except you left out wire. Your 25% amp budget is for preamp and amp. I'd go integrated if I were you. Your 25% wire budget has to cover all power cords, interconnects, and speaker cables. Unless you want a really good system and then it should be 20% each, and you add 20% for vibration control and room treatment. Now you're talking!

Depends on the loudspeaker. If you have something really efficient, a nice pair of Quicksilver monos will do the job. But if you have Magnepan 20s, the sky is the limit. 
Matching amps to speakers is a critical consideration. Depending on the 1. CD player / DAC and the 3. Power-amp compatibility;  the 2. Pre-amp might be superfluous.
It’s hard to say. It really depends on the chain

In a recent video series Jay compared a rogue audio class D amp to a high end amp. I dont remember if it was duel mono or not because he didnt specify the elite amp, but for sure it was over $30k vs an amp less than $2k.
While differences were there, they wernt profound and many couldnt even tell the difference

My point is, Jay’s chain is unreal. Hes using power cords that are more expensive than most peoples entire hifi setups. In addition he has 2x Everest power conditioners as well as Synergistics top of the line conditioner. Then add to it the pre amp, the super high end interconnects, his very substantial electric setup behind the wall, ext..
All of this helped to make up for many of the cheap amps inadequacies as well as color the sound and change the sound signature.

If you were to take the same amps in a more modest setup I’m sure you would hear a much bigger difference between the amps

So to sum up a lot of it depends on the rest of the chain. In a mega high end setup the amps impact is much more minimal as long as the power and current capability is there.

In a more modest setup the amp choice will matter much more.

i think the 20-25% figure is fair
As for the pre-amp, this is also difficult to put a value on. some ppl with higher end DCS or even something like the lumin x1 choose to skip the pre-amp all together and go straight to amp.

Others will find that the pre-amp is the 'heart" of their system and actually put #1 cost priority to their pre.

I think you should make a decision on the speakers which will be the most important/influential and from there it will be much easier to assign values.
If you were, for instance, to enjoy horn speakers and were to go after something like klipsch higher end stuff then you would find that you can save a lot on the amp because so much less power is needed to run something so efficient. 
On the flipside if your flavor was something more like high end magico you would find that the amp choice is very important and you would need to allocate significantly higher percentage of $ to the amp 

So really it starts with the speakers, from there you can start assigning values to the remainder of the chain

Thank you so much for the knowledge.
To pair with an efficient pair of speakers like Raidho XT2, what would be the best proportion of budget for pre-am vs power-am? 50-50, 80-20 split or what?
@questforhifi, Jay compared a Rouge IceEdge 1200 module-based amp, not a Rogue amp which is a hybrid using tube driver and Hypex modules as outputs, just a clarification.
“How much does power amplifier really matter comparing to other hi-fi components?”

Lots and lots. 
I put 1/3 rd into speakers since they are what determines the Sonic outcome and it’s quality in build,drivers,and Xover are 
what determines its tonal accuracy and naturalness .$10-20k
The Source  such as the dac $5-7 k is equally important in quality 
since the music starts there , makes or break the sonics upstream 
accuracy in the original recording , I feel you just need-to spend more with these 2 areas,  while not sacrifice the quality of a good 
integrated amp, or amp,preamp,$7-10k and very respectable cables around $ 5k in cables for all cables is pretty respectable maybe a bit more ,this is good quality mid 
Audiophile cost quality , by today’s pricing, if you can afford more 
that's great. 
Source and speakers first. Whatever remains should go into powering them. 
“How much does power amplifier really matter comparing to other hi-fi components?”

Lots and lots.
Lots of variables to consider, particularly speaker sensitivity and listening levels. 

Generally speaking, you never want to get even close to maximum power, even with short peaks because manufactures usually specify amplifier power when it reaches 1% THD. THD often rises quickly once you get close to maximum power, so keeping 10% below rated power is generally fine and is often close to minimum THD+N.

Provided you are willing to always keep the volume control well below maximum, consider a higher rating than speakers as they are can accept term short peaks without damage.

A good starting point, but always check specifications.
Post removed 
the secret is that speakers are the most important element ... BUT YOU SHOULD SPEND MOST MONEY ON THE SOURCE ...
This is a massively complex question. It sounds like you want to build a high end system from scratch which can be a big job, particularly with the reduced number of dealers. I'd find an audio dealer whose taste runs to your own and begin the work. What kind of music do you prefer, what's your budget, size of the listening room, do you have any pieces already to carry you for a while.... are all things the dealer can use to guide you.

To  your specific question, in terms of amp vs. pre-amp I'd put more into the amp. As others above have noted, the amp is tremendously important. Say 2/3rds to amp and 1/3rd to pre. Similarly, I'd spend more on the DAC than the transport/streamer.
I agree also with pani that the speakers and amp should be purchased and matched together. 
Good luck!!
Just to be sure, I asked around. Blackhawk said it is the most important, Moab said it is, F1 of course, Sovereign, Koetsu, right on down the line. Can you believe, every single component insists it is the most important! "Listen," I said, "you can't all be most important!" OH YES WE CAN they shouted back.  

I'd believe them if I were you. The Blackhawk in particular was getting pretty heated over it, and the power cords, one went Nova the other went freaking Supernova. I am not kidding.   
i read back many years ago in a stereo review magazine that you should buy the most watts that you can afford!
Speaker amp match is critical
dont skimp on power 
call manufacturer of amplifier to discuss speakers
that is what I did and it worked

been  been using separates fir 50 years
just went integrated 
so happy!
Don’t be fooled by high price
some superb gear out now for little compared to the past
consider Classic D amp- on my second and thrilled and the room does not cook!
I had B&W 801 model 80 speakers from 1980. I used GAS Ampzilla, Ampzilla II, Hafler, Marsh 200c, Aragon 4004 II, and lastly a Denafrips Thallo 120w amp. The last amp made me regret all the years I wasted with the other amps. Spend as much money as you can because it will be amortized over many years.
My recs
Peachtree Nova 150 ( 150 for 8 and 250 watts for 4 ohms) clean power 
Great  sound stage!
I am using a pair of Elac 2,0/6.2 bookshelf speakers designed by Andrew Jones and are unreal for the price- Jones designed for TAD Pioneer etc
These speakers can go forever with great bass clean ,upper end  zero zero fatigue!

pure enjoyment - not fatigue!!!!!

You want to make sure that you don't get a bright or harsh amp, unless you like that sort of thing.  A  bright, let's just call it headache inducing, amp can ruin the sound of your system.
Don’t feel higher cost is needed to have a great listening environment. My last and current set up cost a mere fraction of the previous setups 
this one superseded the others by far 

No opinion can be ventured without an overall budget. Can you spend $10K?  Credible products are available in each area for $2K to $3K. If that’s a stretch are you handy?  DIY options are out there. Don’t neglect your room furnishings and speaker placement.
In my experience this is impossible to determine. I currently use an Audiolab 6000CDT with Denifrips Ares ii total recommended retail cost AUD$2300, with Audio Physic speakers and 2 subwoofers RRP cost AUD$9500 and Vincent pre / power amp at RRP AUD$4800. So that's roughly speakers 60%, amps 30% and CD / Dac 10%. The fact is I got the speaker / subs for $4800, the amps for AUD$2600 and the CD / Dac for AUD$2000 so actual was nearer 50%, 25% and 25%.  So $ spend is what I aimed for looking at the market and how they each performed and matched. So the ratio depends on the equipment and deals you can get. I have always found bargains in speakers and never paid more than 60% of RRP. In this case my electronics were a rare bargain both open box but clearly never used (both sealed inside boxes) whereas the CD I bought because its great value anyway as was the dac getting about 15% off each. My second system is Audio Physic speakers list AUD$3000, paid AUD$1000 boxed and new (4 years old left at back of warehouse by mistake when they moved store), Naim Unitilite  (pre / power / CD/ Streamer / DAC / tuner) ex demo list AUD$4500 paid AUD $2500. So that's originally a 60/40 split at $7000 becoming roughly a 75/25 split on paid price. So making up a fixed percentage is just not possible if you are searching the market as you may buy separates or combined components as applicable/ available.
Hello cclee2022.  If the power amp limits you, you will not hear the total advantage changing components might give you. So, some might say that if the power amp is not great, your system will not "sing."  Conversley, there is less difference among good power amps than there is between preamps and CD players. Power amps are more important than cabling. Pruifi's new amp modules, used by NAD and many others are superb.  I use two stereo pair daily. At least as good, and I think smoother on the top end, is the Starke Sound A4-320, I have three of them. They are simply stunning. Home trials are allowed. Check their website. Last year, they put them on a "Black Friday" special. If they do it again, I will order two more. At the regular price (under $1500 last time I checked), they are the best bargain since the Magnepan LRS. On sale they are a no-brainer. I used to build my own power amps, not any more! I use electronic crossovers from miniDSP and DBX. Get the passive crossovers out of the amp/speaker path. You will be suprised! Most power amps have the ability to control the motion of the actual driver diaphragms ("dampong factor"). Coils and capcitors interfere with that. Also, the speaker cables are much less fussy when connecting the amp directly to the voice coils in the drivers. Are you "handy" with tools and small parts? Try the kits from Akitika. Happy listening!
What influences the sound characer the most, in order of magnitude:

1. Speakers
2. ROOM ACOUSTICS (often forgotten)
3. Amplifier
4. Source (CD player, streamer, DAC)
5. Cables

I'd spend my money in that order.
SQ is not proportionatel to expenditure.  Allocating expenditure by percentage is not likely to give you the best bang for the buck.  Pick components whose sound you really like.  Be prepared to dive in deeper if required and spend less on other areas where you don't discover a stand-out for you.

That said, I mainly agree with Pani.  Transducers are the area that influences SQ the most, that is record players, digital players and speakers.  Money spent there will have the most effect.  Then look at amplifiers.  For some, room treatment is a must, but it is best not to listen in compromised rooms, some of which remain compromised however much is spent.  Wiring comes last.  Whatever Miller says, it cannot influence SQ to the extent active components do.

Foolishly, Miller advocates equal expenditure on room treatment and wires.  That means you only spend 16.67% on players and on speakers, when if you were more sensible it would be 25%,  That's a stonking 50% uplift.

If I had to decide in the restrictive manner proposed by OP (and did not have a compromised room) I would go:
30% speakers, 25% player, 35% all amplification (less if you go integrated), 5% room, 5% wires.  And that's generous on the room and wires.

If you are digital believer and only run digital, I would drop expenditure sharply on the player (incl DAC).  True converts know that if you have sorted jitter, clock error and have a good DAC, bits is bits, so any decent player will do.  Read errors are almost non-existent on every player.

The strongest part of any system is it’s weakest link. …or something along those lines
50% gear/cables, 50% room treatment and speaker/listening position placement.

That is not COST, it is the importance and true perspective of a TOTAL system.

The cost of gear and cables can be 100% of the cost, but it's still only 50% of the sound. By putting 5-10% ($$) in room treatment you can reduce your gear cost buy 50-75%. The sound can cost a lot of money or VERY well spent money. The well spent money part, usually comes with a lot of poorly spent (learning) money through the years. :-)

I look at it like this TOO.. 300hz and down gets a certain kind of control system (bass control system) fed from an active preamp (integrated or separate), power amp (class Ds), cables and speakers.

300 hz and up gets a very well made versatile valve power amp for 8 months out of the year and class ds for the HOT summers where I live.

When I was finished with one system I was still under 10k and everything was new or freshly gone through and or moded up.. Room included. The front room my wife's system.

I could add in 15K speakers that I have, but the 1500.00 speakers with the brand new cabinets I purchased for 200.00, work as good because of the room size and type of speaker. I could add a 8K preamp I have but the C20 that cost me 1700.00 total with a complete rebuild, and on and on and on....

The NUGGET from all this is:
I can build a 60K system or a 8K system. I have both... 50% is still the room.. at 5-15% of 8K. LOL :-)

ROOM first, speakers second. I'm sorry I work backward than most people. Then the power amp matches the speaker and the room temp issues.. It's a BIG issue where I live..

Source is source pick what ever you like for your Karaoke Christmas hootenanny. :-)

It all matters...if you did a mashup of all the above posts you would find that "it all matters".  

Assigning percentages to components is a fool's errand, you may like to think about it in those terms, but you'll never match it as you move forward.

My simple rule of thumb is that any component that is a transducer requires more dollars.  That would be speakers (signal to sound), cartridge (squiggles to signal), cd/dac (digital to analog). 

After that you pick the order of spending, but it all matters!

This guy trying look for good advices and you send him out like drunk girl looking for quite place to sleep a frat house. but it not your fault because op give very little information.
take money you pay for speaker- Raidho and how much you have leftover. That the question is what do you have after purchase the Raidho? That good speaker I have that in workshop system I just cover that tweeter when use machine because ribbon no like dust.
It is a system and the system will only be as good as the weakest link. You can have the best amp but a bad pre-amp and the pre-amp will not let the amp shine. I my self would consider the pre-amp a little more important than the amp. If you have a budget and have to compromise some where in the system chain the pre-amp would be my last to compromise.
I forgot to mention with amplification ,never skimp on quality- power for on transients dynamic range on peaks can be 10 x 
the power in milliseconds and your speakers will dictate the efficiency and what’s required ,balance,quality,and quantity of necessary power . I always look at thepower supplies 
and capacitor reserves on any products , for tubes most important 
theQuality of chokes and powersupplies , and ample size,
in Solid state ,my Coda for example has a potted 3 kva transformer which is Huge ,and over 80k in capacitance , and over 120 amps short term on demand current ,  that’s why it’s important to see the quality and exactly what’s under the hood , just keep this in mind ,and digital at least 2 linear power supplies ,which my M3 Bricasti dac streamer has, 3 even better ,like on their M1,m21 
two good size linear power supplies is ample and my streamer board is included ,with ample filtering and low noise.
Assuming a budget of $10K-$15K, I might put nearly everything into a pair of JansZen Valentina A8 active speakers. Plus as little as $550 for a Bluesound Node (the source) and < $100 for cables.  Then trade up from the Node later (to Bryston/Cambridge Edge/Exasound).  That's assuming I lived within reasonable driving distance of the JansZen shop in Ohio (otherwise, I'd be reluctant to put all my component eggs into their basket).

But suppose a $5K budget instead, as a more reasonable entry point for a "high end" clean slate system. Assume we're going for digital not vinyl. Then very roughly:
1. 60% for speakers (because they make a bigger difference than anything else and are a little harder to trade up due to size/weight);
2. ~10% for a streamer/DAC (such as the Bluesound Node);
3. 30% for an integrated amp (maybe Peachtree or Cambridge Audio);
4. very little on cables (Bluejeans Cable for speaker wire; for everything else, just use what comes in the boxes with your components for now.)

For half that budget, you could build around a pair of KEF LS50 active speakers ~$1250) plus < $1K for everything else, with change back.

As between pre- and power-amp, it's really a question of what kind of sound you like (warm, analytical, bassy, slightly rounded edges, etc.) and then carefully matching components, within your budget, to get that sound. You can combine a relatively expensive power amp that has a sound you like with a passive or very clean active power amp that is not very expensive. Or, you can spend more on a pre-amp that gives you the sound you like and less on a power amp that adds nothing but power to the sound. Personally, I'd rather have a pre-amp determining the sound and a very neutral power amp. These days I run a Parasound JC2 preamp ($4500 when not on sale) with a pair of VTV Purifi 1ET400A mono blocks (about $2000). Some folks prefer combining tube or hybrid preamps with solid state power amps. But instead of adding the distortion of tubes, I've just ordered a Schiit Lokius tone controller ($300), which allows me to tailor the sound to the peculiarities of specific recordings.
     Every component shares a slice of responsibility, when it comes to accurate sound reproduction (not to mention: room treatment).

     ie: Picture all of your components (sources, cables, pre/power amps and speakers) as panes of glass, through which you want to observe something living.

      The accuracy/enjoyment of your observations will be determined by how many and how dirty the panes.

       How critical you are as listener, will determine your level of involvement and investment.
I believe it’s a good percentage of your system and should be chosen per your speakers and their capacity. Don’t forget your power conditioner and monitor. I spent 500$ on one that insures it’s protection. 
Everything matters. Amp matters a lot. Recently I’ve owned 3 amps I can swap among in my system. Each has a very distinct sound. All 3 are way more than enough power (120 - 275 Watts / ch) for my 96dB Tannoys, so overhead & drive capabilities are not really a variable. I’m even writing down particular combinations of cartridge & amp that work best together lol.
You didn’t specify your budget!  I can’t believe all these people made recommendations without that info.  It matters because up to a certain level, you’d be better off with an integrated vs. separate power and pre.  An integrated will compromise on the preamp section, but save $ on an interconnect.
I would think speakers would have the biggest impact.  I also think a pair of REL's make a huge difference, especially a lower listening volumes.
Clearly, speakers are central. However, you can get and use a perfectly great speaker that is not that pricey. An “honest” transducer need not have the big scale of a large, expensive speaker. And matching your speaker with your amp is also central.
Percentages are not important or relevant. Having the appropriate speaker to amp match is.

I love the question.  What you didn't ask about was the way more expensive room treatments, cables, power conditioners, isolation pads, racks, and subwoofers.  Those actually cost more than the components in question in both my listening rooms.  

To answer your question, I have a dedicated listening room and nearfield setup in my office.  I'll start with the big system with BIG speakers that unsurprisingly ate up 40% of the total cost despite answer 1 equipment, the DAC/clock/upsampler stack being absolutely ridiculously expensive, possibly the most expensive, and only accounting for 9.8% of the total budget:
1) 9.8%
2) 19.1%
3) 31%
4) 40.1%

The little nearfield office setup does have small-ish speakers.  But they are possibly the best nearfield speakers and are shockingly expensive for their size, yet answer 4 this time is only 8.5% of the total cost:
1) 17.6%
2) 28%
3) 45.7%
4) 8.5%

Responses received are eye-opening. Learning the motto of “it all matters” and the various distribution of components / contributions for a true hi-fi experience can be a great option s reference for beginners like me.
It all matters from the perspective you need these components in order to create a system. Most of the answers you got are nothing but audiophile nonsense. The amp, preamp, DAC if you go digital are way less important than the speakers and room. If you want a true high fidelity experience just spring for a pair of  Dutch and Dutch 8c and a decent streamer, apply EQ accordingly and room treatments. If you want a passive speaker most of your budget should be speakers and room treatments. As long as you get speakers that are not crazy to drive there are literally dozens of amps and preamps, DACs that will work and don't cost an arm and leg. 
TAS Robert Harley’s book “The Complete Guide To High-End Audio v6” book has an budget example of 36% speakers, 50% amplification+DAC, 9% power conditioner, and 5% interconnects+ cables.  But these percentages are not set in stone- you may get a great deal or discount or may want to pay premium for desired component.  But maybe having a place to start vs no clue is a good thing.