Is there a magic formula for spending on components in a system

I had such a clever response nearly completed when I left the page and lost it all. Now I must to condense the wisdom. Prepare yourself.

If you had $10k to spend,
( I'd suggest seeking financing for an $10k. haha-joke).

I will preface my remarks with full disclosure that you are reading a recommendation by someone who is enjoying his 2nd double of  Jethro T. Boots Kentucky Whiskey. CVS $8.99. Really tastes about the same as the $80 Japanese whiskey I had last week.

As the acknowledged weakest link in audio is the speakers,
you start there. Spend 6-12 months investigating what you want.
Find what you like. Not what somebody else likes. $4k is the max
you spend here. Leaves $6k. I am pretty good at math.

Then you will know what type and how much power you need. 
Your two brands to choose from are: Pass Labs and Line Magnetic.
If your speakers require massive power then I will offer a 3rd choice
for amplification. Magtech by Sanders. 

You buy everything used. From the original owner. Under 1 year old.

For a source-Stream with your own computer. Hardwire ethernet to your DAC to your router. Buy a Preamp/Dac combo for $1k. $5k left.

Pay $700 for a lifetime subscription to Roon. $4,300 left.

Hire an electrician to install 2 dedicated runs to your HiFi.
The cost of this will vary. Include the ethernet line. I did 
it for $350 at my house. Likely you will spend $1k.
$3,300 left.

Cables.com.  Buy used interconnects. Buy Kimber cables. 
Budget $1k. $2,300 left.

Buy 6 each  2' x 4' absorbing panels. Cost $60 each if you buy
new or $30 each if you make them. If you have a hard surface floor
get an area rug. Deal with windows with drapes. Cost $500.
$1,800 remaining. 

If you have LPs, buy a used Rega TT and a Schiit audio Phono stage.
End of original $10k.

That's all folks!!

Yes.
Spend $nil on CD player.

Don't be a cable chump.  Don't allocate much to cables until system spend gets to $10k.  Cables can never add as much as active components at this level.  Don't buy used cables, they deteriorate over time.

Yes.  If you don't have $30k for power amplifiers, choose high-efficiency speakers.

1970s Linn formula:   Budget $n.  Spend $0.8n on Linn front end.  Leaves $0.2n for the rest of the system.

Ideally....the GDP....

On a practical level....what you can rationally spend...;)

No...not in relation to components. There are some who would say if you spent say 20K on components, you should get at least $5000 worth of speakers. As if to say no speaker is worthy under that. Nothing could be further from actual as opposed to perceived truth.
The only formula (and there is no magic about it) is your satisfaction.
The trouble with all this audiophile stuff... people seem to be afraid to be satisfied thinking there is always something better.

Now that can be thought of as "magic" if one believes that beneath your component table lies the sirens of dastardly temptation beckoning and beckoning with the song in the winds of "you need to spend more money"