# Confusion on adding percentage of cost to that cost.

12 views

### stromm...@gmail.com

Jul 10, 2005, 10:05:29â€¯PM7/10/05
to

Here's my view. Say I have a product with my cost of \$100.00

I want to add 28% to that. I think I should end up at \$128.00.

My math is simply \$10.00*1.28 = \$12.80

However, I have had someone else tell me that I'm wrong and need to do
the following.

First. 100-x=y
Second. 100/y=z
Third. A*z=\$\$\$.\$\$

So,
First. 100-28 = 72
Second. 100/72 = 1.38888889
Third. 10*1.3889 = \$13.89

Now to me this person is crazy. I mean I sold stuff for years and
sales tax wasn't that complicated. If something was \$10.00 + %5.75tax,
the total is \$10.58.

Not 100-5.75 = 94.25, 100/94.25 = 1.061007, \$10.00*1.061007 = \$10.61

Why would he think that he's correct? Is it some accounting practice,
but not real world practice? Or maybe something a person not originally
from the US would have learned?

Thanks for clearing this up.

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### Joseph Sroka-10.2.8

Jul 11, 2005, 2:50:31â€¯AM7/11/05
to

stromm...@gmail.com wrote:

> Here's my view. Say I have a product with my cost of \$100.00
>
> I want to add 28% to that. I think I should end up at \$128.00.
>
> My math is simply \$10.00*1.28 = \$12.80
>
> However, I have had someone else tell me that I'm wrong and need to do
> the following.
>
> First. 100-x=y
> Second. 100/y=z
> Third. A*z=\$\$\$.\$\$
>
> So,
> First. 100-28 = 72
> Second. 100/72 = 1.38888889
> Third. 10*1.3889 = \$13.89
>
>
> Now to me this person is crazy. I mean I sold stuff for years and
> sales tax wasn't that complicated. If something was \$10.00 + %5.75tax,
> the total is \$10.58.
>
> Not 100-5.75 = 94.25, 100/94.25 = 1.061007, \$10.00*1.061007 = \$10.61
>
> Why would he think that he's correct? Is it some accounting practice,
> but not real world practice? Or maybe something a person not originally
> from the US would have learned?
>
> Thanks for clearing this up.

First the short answer: I think that you are right and "someone else" is wrong.

However, quoting markups and markdowns is not something that I do in a
*business setting*. *Maybe* there are some people that calculate a 28
percent markup as done by "someone else".

Here's a mathematics compare-and-contrast of yours and *someone else"'s*
methods.

In your example, let's call the \$100 cost to you, WP (wholesale price).
Your method adds 28 percent to WP and comes up with RP (retail price).

So, what you have done is RP = 1.28*WP. So, you can honestly state that
your markup is 28 percent of the WP, the cost to you.

*Someone else" does RP = WP/(1-.28) = WP/.72, a higher retail price than yours.

So, "someone else" can honestly state that his markup is 28 percent of the
RP, the retail price.

I have no idea why anyone would calculate or state their markup as done
by "someone else". Oh, here's a thought... some businesses apparently
like to think of markup (gross profit) as a percent of sales, so in THAT
case, selling the object for \$100/.72 = \$138.89 results in a 28 percent
profit on *sales*.

Your method result in a 28 percent profit on *cost*.

--- Joe Sent via 10.2.8 at 10:06pm PDT, July 10, 2005.

--
------------------------------------
Delete the second "o" to email me.

### Bob

Jul 11, 2005, 2:50:30â€¯AM7/11/05
to

On Mon, 11 Jul 2005 02:05:29 GMT, stromm...@gmail.com wrote:

>
>Here's my view. Say I have a product with my cost of \$100.00
>
>I want to add 28% to that. I think I should end up at \$128.00.
>
>My math is simply \$10.00*1.28 = \$12.80

Given your statement of the question, what you did is correct.

(Though please note that you changed the numbers by 10-fold from your
line 2 to line 3.)

>
>However, I have had someone else tell me that I'm wrong and need to do
>the following.
>
>First. 100-x=y
>Second. 100/y=z
>Third. A*z=\$\$\$.\$\$
>
>So,
>First. 100-28 = 72
>Second. 100/72 = 1.38888889
>Third. 10*1.3889 = \$13.89
>
>
>Now to me this person is crazy. I mean I sold stuff for years and
>sales tax wasn't that complicated. If something was \$10.00 + %5.75tax,
>the total is \$10.58.
>
>Not 100-5.75 = 94.25, 100/94.25 = 1.061007, \$10.00*1.061007 = \$10.61
>
>Why would he think that he's correct? Is it some accounting practice,
>but not real world practice? Or maybe something a person not originally
>from the US would have learned?
>

Not sure what the person was trying to do. It is a common problem to
"do the reverse". Eg... sells for 12.80. Markup was 28%. What was your
cost. But what you show above does not fit that.

SellPrice = cost + (cost * rate) = cost(1+rate)
where rate is the tax or markup, as a decimal.

According to your statement, you have Cost, want SellPrice. It is a
proper question to have SellPrice, and want Cost. Your friend may have
been thinking of that -- though did not do it right. You might explain
that case to him.

Key... be clear what the question is.

bob

### ticbol

Jul 11, 2005, 1:20:04â€¯PM7/11/05
to

I say, something even a person originally from US should have learned.
Otherwise, this person originally from US might be laughed-at by
persons not originally from US.

Let us analyze your \$10-stuff example.

You said if 5.75%, you just add 5.75 % of \$10, which is \$0.58, to the
\$10. So you sell the stuff at \$10.58.
Ok, so sale price is \$10.58.
Then taxman gets his 5.75% of \$10.58.
0.0575 times \$10.58 = \$ 0.61
\$10.58 minus \$0.61 = \$9.97
Hey, that is not \$10, after tax!

Suppose we follow this former foreigner.
Sale = \$10.61
Tax = 0.0575 times \$10.61 = \$0.61
After tax, \$10.61 minus \$0.61 = \$10
Hey,....
Zeez, is there magic in what the guy learned from outside the US?

Hardly. The guy just learned Math as Math is learned in and out of the
US.

It is Accounting, maybe.
But it is just Algebra. Algebra anywhere.

----------
You want a crazier formula?

Say, you have a product that worth "x".
You know the sale tax is "t" percent.
You want add "y" to "x" so that the selling price is (x+y).
How much should this additinal "y" be so that, after tax, you'd end up
exactly with "x" from this product.

Sale price = x+y
Tax = (x+y)*t
Net = Sale minus tax = (x+y) -(x+y)t = (x+y)(1-t)

Net = x, so,
(x+y)(1-t) = x
(x+y) = x/(1-t)
y = x/(1-t) -x
y = x[1/(1-t) -1]
y = x[(1 -1(1-t))/(1-t)]
y = x[t/(1-t)] ---the formula.

Note: t is in decimals.
So if the sale tax is 5.75%, then t = 0.0575

Apply this crazier formula to your \$10 example.
x = \$10
t = 0.575
y = 10[(0.0575)/(1 -0.0575)]
y = 10[(0.0575)/(0.9425)]
y = 10[0.061]
y = \$0.61 -----***

Meaning, you really need to sell the product at \$10.61 (not at \$10.58)
if you want a net of \$10 after tax.

--------
By the way, if you want to add 28% to \$100, you will really end up with
\$128.

Nobody anywhere will say "No way".

### Strommsarnac

Jul 11, 2005, 7:15:53â€¯PM7/11/05
to

So I guess it comes down to what is proper? I now understand how the
two formulas could be correct depending on who is doing the looking. I
can definitely see how the IRS would say "no way" to the quick formula
:)

So, if I have a product I make and want to put in a percentage of
markup (to cover my labor) and then also add a percentage for a rep who
sells the product, but still be competitive in the market....

Quick formula or long formula?

### Bob

Jul 12, 2005, 12:10:03â€¯AM7/12/05
to

On Mon, 11 Jul 2005 17:20:04 GMT, "ticbol" <tic...@yahoo.com> wrote:

>
>Let us analyze your \$10-stuff example.
>
>You said if 5.75%, you just add 5.75 % of \$10, which is \$0.58, to the
>\$10. So you sell the stuff at \$10.58.
>Ok, so sale price is \$10.58.
>Then taxman gets his 5.75% of \$10.58.

No, no, no.

The taxman gets 5.75% of the sell price, \$10.00. 0.58. Sales tax is
not charged on sales tax.

bob

### ticbol

Jul 12, 2005, 3:27:44â€¯PM7/12/05
to

Strommsarnac,

What is the quick formula? Is that the one by the guy who was not
originally from the US? Is that the one were he got \$10.61?

And \$13.89?, which should have been \$138.89 because it was based from a
\$100.

----------------------------
Or, the quick formula is 100 *1.28 = \$128 ?
And the long formula is 100*1.38889 = \$138.89 ?

-------------------------------------

>So, if I have a product I make and want to put in a percentage of
markup (to cover my labor) and then also add a percentage for a rep who

sells the product, but still be competitive in the market....

Quick formula or long formula? <

Is that applicable here?
Or, are the "quick" or "long" formulas mentioned above applicable to

The "long" formula is to get back the price you want, even after tax.

....but still be competitive...
Looks like you have a different wish here. I'd say, to be less
complicated, just use the "quick" formula.
Regarding the analyzed \$10-stuff, the \$9.97 is surely more competitive
than the \$10----both after tax.

### ticbol

Jul 12, 2005, 3:27:43â€¯PM7/12/05
to

Bob,
What is sales tax then?

--------------
Taxman sees sale is \$10.58
Taxman gets his 5.75% of that, which is \$0.61

Taxman doesn't know---and he never cares---that 5.75% of \$10 was added
to the \$10.

Taxman never cares too if the original \$10 were sold at \$20. In this
case, if sales is \$20, tax is 5.75% of \$20.

--------------------------

Sales tax, Bob, sales tax.

### Kevin Karplus

Jul 12, 2005, 8:10:37â€¯PM7/12/05
to

On 2005-07-12, ticbol <tic...@yahoo.com> wrote:
> Taxman sees sale is \$10.58
> Taxman gets his 5.75% of that, which is \$0.61
>
> Taxman doesn't know---and he never cares---that 5.75% of \$10 was added
> to the \$10.
>
> Taxman never cares too if the original \$10 were sold at \$20. In this
> case, if sales is \$20, tax is 5.75% of \$20.

Taxes are computed differently in different countries (and even
different states in the US).

In California, the sales tax is expressed as a percentage of the price
charged *before* sales tax is added on and retailers are allowed to
advertise the price without including the taxes. Thus a \$1 item
actually costs the customer \$1.08 (if you are in a county with an 8%
sales tax rate---the rate varies from place to place in the state).
The retailer gets to keep \$1 and has to send the \$0.08 to the state.

Other places may well use a different basis for the computation, but
this is not a math question but a tax-law question.
I believe that most states in the US use the pre-tax price as the
basis, but I have not researched it other than in the states I have
lived in (Illinois, Michigan, New York, California).

------------------------------------------------------------
Kevin Karplus kar...@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus
Professor of Biomolecular Engineering, University of California, Santa Cruz
(Senior member, IEEE) (Board of Directors, ISCB)
life member (LAB, Adventure Cycling, American Youth Hostels)
Effective Cycling Instructor #218-ck (lapsed)
Affiliations for identification only.

### Bob

Jul 13, 2005, 12:47:15â€¯AM7/13/05
to

On Tue, 12 Jul 2005 19:27:43 GMT, "ticbol" <tic...@yahoo.com> wrote:

>
>Bob,
>What is sales tax then?

Tax on the merchant's selling price. This is standard US procedure and
may be different from European VAT. (If you know of a US place that
does it differently, let us know.)

Item sells for \$10.00. Sales tax is 8.25% (here), or 0.83. Merchant
collects 10.83, sends 0.83 to the state government.

If you honestly thought it was calculated otherwise, this serves to
reinforce the point that a number of us made in response to the OP...
be sure you understand the question before answering it. People will
quibble over getting different answers, when the discrepancy was in
how they understood the question.

By the way, we do have an example here (California) of something like
what you tried. There is also a state gasoline tax -- which is
included in the regular selling price. The sales tax is calculated on
top of that. So sales tax is paid on the gas tax. But that is
something of a special case.

regards,

bob'

### Kevin Killion

Jul 13, 2005, 11:06:14â€¯AM7/13/05
to

You're both right -- it's a matter of definitions.

My wife used to be a buyer at Carson Pirie Scott, a major retailer in
Chicago. She used to talk about "markups" in this way and it drove me
(a math major) nuts.

Suffice to say that it was COMMON in her business for "markup" to refer
to the amount added to the price, as a percentage of the FINAL price.
If a price were doubled, math majors and other normal people (!) would
call that a 100% increase; she and everyone down at CPS would call that
a 50% markup.

(By the way, for other responders who mentioned taxes: there is no
reference to tax anywhere in the original post.)

-- Kevin Killion

stromm...@gmail.com wrote:

> Here's my view. Say I have a product with my cost of \$100.00
>
> I want to add 28% to that. I think I should end up at \$128.00.
>

> My math is simply \$100.00*1.28 = \$128.00 [DECIMAL FIXED]

>
> However, I have had someone else tell me that I'm wrong and need to do
> the following.
>
> First. 100-x=y
> Second. 100/y=z
> Third. A*z=\$\$\$.\$\$
>
> So,
> First. 100-28 = 72
> Second. 100/72 = 1.38888889
> Third. 10*1.3889 = \$13.89

--

### Robert Morewood

Jul 13, 2005, 6:45:10â€¯PM7/13/05
to

stromm...@gmail.com wrote about someone telling him that to
"add 28% to \$10" he should do the following:

: First. 100-28 = 72

: Second. 100/72 = 1.38888889
: Third. 10*1.3889 = \$13.89

This assures that the added amount (\$0.89) is 28% OF THE FINAL TOTAL.

Of course most (all? - anyone have a counter example?) sales taxes
are computed (by law) as a percentage OF THE SALE PRICE, not as a
percentage of the grand total. (Most Canadian provinces have TWO
sales taxes, federal and provincial, and it is unconstitutional for
one level of government to tax the taxes of another level of government.
So sales tax as a percentage of the grand total would be unconstitutional
here.)

However, I do have an example where the calculation should be done as
above. Condominiums in BC must put a percentage of their TOTAL BUDGET
into a continguency fund. Normally, managers find the budget by
adding up all the expected operating expenses for the year (say \$10).
Then they have to add an amount (say 28%) for the contingency fund.
If they just add 28% of \$10 (makes \$2.80) then the total budget is
\$12.80 and the contingency fund gets only \$2.80/\$12.80*100%=22%
of the budget, violating the law! On the other hand, the managers
in the condominium I used to be part of always did it this way.
(Actually the legal requirement is only 10% so our condo always
put aside 9%. But the law has no teeth. Managers do not even have

Robert, who is
|)|\/| || Burnaby South Secondary School
|\| |ore...@olc.ubc.ca || Beautiful British Columbia
Mathematics & Computer Science || (Canada)

### Guess who

Jul 13, 2005, 3:34:13â€¯PM7/13/05
to

On Wed, 13 Jul 2005 15:06:14 GMT, Kevin Killion
<kevin...@shsmedia.com> wrote:

>You're both right -- it's a matter of definitions.

There is "Markup" and "Margin". The concepts used to be part of a