Precious Metals Forum

Go Back   Precious Metals Forum > Bunker Talk > STS

Like Tree3Likes
  • 1 Post By benjamen
  • 1 Post By benjamen
  • 1 Post By Golsil

Reply
 
LinkBack Thread Tools
Old 05-10-2013, 12:40 PM   #1
Super Moderator
 
benjamen's Avatar
 
Join Date: Mar 2012
Location: Migratory
Posts: 1,620
Liked: 685 times
Check my math

With the idea based on this thread:
http://www.pmbug.com/forum/f4/blowin...musement-2369/

I am trying to solve for the interest rate needed to just maintain purchasing power after accounting for a given time, tax rate, and inflation rate.

Amount invested: x
Years: n
Required return: i
Inflation rate: j
Tax rate: t

Equation I came up with to solve for i:
x = {[x*(1+i)^n-x]*(1-t)+x}*(1-j)^n

1: Base equation
x = {[x*(1+i)^n-x]*(1-t)+x}*(1-j)^n
2: move over the inflation term
x*(1-j)^-n = [x*(1+i)^n-x]*(1-t) + x
3: distribute the tax term
x*(1-j)^-n = x*(1-t)*(1+i)^n - x*(1-t) + x
4: factor out the x
(1-j)^-n = (1-t)*(1+i)^n - (1-t) + 1
5: move over the 1
(1-j)^(-n) -1 = (1-t)*(1+i)^n - (1-t)
6: factor out the tax term and move it over
[(1-j)^(-n)-1]/(1-t) = (1+i)^n - 1
7: move over the 1
[(1-j)^(-n)-1]/(1-t) + 1 = (1+i)^n
8: distribute the 1 that just got moved over by turning it into a (1-t)/(1-t) term
[(1-j)^(-n)-t]/(1-t) = (1+i)^n
9: move over the n exponent
{[(1-j)^(-n)-t]/(1-t)}^(1/n) = 1 + i
10: final
i = {[(1-j)^(-n)-t]/(1-t)}^(1/n) - 1

Plugging in an example of
Years: 10
Inflation rate: 3%
Tax rate: 30%
I got a required return to just break even at 4.198%

I believe this is correct. If anyone who is math inclined wants to check this out. Are there any errors? Can the result be reduced further?
bushi likes this.
__________________
I drive men mad
For love of me,
Easily beaten,
Never free.

PMBug 101 *** Forum Rules
benjamen is offline   Reply With Quote
Old 05-10-2013, 01:42 PM   #2
Super Moderator
 
benjamen's Avatar
 
Join Date: Mar 2012
Location: Migratory
Posts: 1,620
Liked: 685 times
Going further with this idea, what about pre tax 401k type plans where your employer matches you dollar for dollar? What return do you need to at least maintain the purchasing power of the pre tax dollars you put in the account? Where would you have been better off just paying tax on that income and taking it as income?

Equation I came up with to solve for i:
x*(1-t) = {[2x*(1+i)^n]*(1-t)}*(1-j)^n

1: base equation
x(1-t) = {[2x*(1+i)^n]*(1-t)}*(1-j)^n
2: move over the inflation term
x*(1-t)/(1-j)^n=[2x*(1+i)^n]*(1-t)
3: move over the tax term
x*(1-t)/[(1-t)*(1-j)^n] = 2x*(1+i)^n
4: Factor out x and bring over the 2
(1-t)/[2*(1-t)*(1-j)^n] = (1+i)^n
5: factor out the taxes
1/[2*(1-j)^n] = (1+i)^n
6: final
i = 1/[(1-j)*2^(1/n)] - 1

With the same example from above you get a negative 3.811% return needed, which is mostly because the match outweighs the other factors. Assuming 30% tax, as long as inflation stay under ~6.7% you need a zero rate of return to break even.
bushi likes this.
__________________
I drive men mad
For love of me,
Easily beaten,
Never free.

PMBug 101 *** Forum Rules
benjamen is offline   Reply With Quote
Old 05-06-2015, 09:13 PM   #3
Fly on the wall
 
Join Date: Apr 2015
Posts: 51
Liked: 9 times
Both seem correct to me. Having said that, I wonder if asking Warren Buffett, the genius of stock and other matters what his opinion would be? He sure has a way of knowing those pertinent facts and has a keen observational mind. That gentleman sure has an exceptional record that would be difficult for any normal person to match. He sure is in a league all by himself. His mastery of the stock market is absolutely remarkable.
Golsil is offline   Reply With Quote
Old 05-06-2015, 11:38 PM   #4
PM Bug Supporter
 
DoChenRollingBearing's Avatar
 
Join Date: Oct 2011
Location: SE USA
Posts: 1,275
Liked: 691 times
...

Warren Buffett also likes sending oil on his trains...!
DoChenRollingBearing is offline   Reply With Quote
Reply

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Math Question... No. 1? DoChenRollingBearing STS 10 05-01-2013 11:14 PM
Doing the math: what the FED's 2pct inflation goal and CPI massaging means for your purchasing power swissaustrian Fiat Ponzi 3 04-03-2013 12:10 PM
Is my math bad? (Junk silver) oppie2005 Silver Bug 6 10-14-2012 07:59 PM
Price Check DSAbug Gold Bug 6 03-31-2012 04:02 AM
cash or check? Shelby-villian PM Bug 14 11-21-2011 11:14 PM


All times are GMT -5. The time now is 10:17 PM.


Powered by vBulletin® from Jelsoft Enterprises Ltd.
Content Relevant URLs by vBSEO 3.6.0 PL2 ©2011, Crawlability, Inc.
Content of PMBug.com copyright © 2011 - 2019 Measuring Up. All Rights Reserved.