Need equation to find break-even point for products with fixed costs [closed]

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This is probably highschool-level stuff, but I haven't been in highschool for a long time...

Anyway, I have a product with known costs for a single production run. It will be sold by someone making 25% commission. In addition to the commission, we will have to pay payroll taxes amounting to 9% of the commission paid.

I need to figure out how many dollars' worth of products need to be sold in order to break even on the combined total of the product run, the commission to that point, and the payroll tax to that point.

In plain English, here's the equation I'm working with:

$ProductionRun + ($TotalSales * 25%) + ($TotalCommission * 9%) = $TotalCosts

However, what I'm after is the dollar amount where TotalSales matches TotalCosts.

How would one go about this?

algebra-precalculus percentages

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asked Jul 30 at 17:38

Matthew

31

closed as unclear what you're asking by callculus, amWhy, Taroccoesbrocco, Shailesh, José Carlos Santos Jul 31 at 19:09

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Why do you think that they don´t match? Do you make any profit?
  – callculus
  Jul 30 at 17:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  We're in pre-production. I need to calculate the break-even point for projections.
  – Matthew
  Jul 30 at 21:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do the answers capture the meaning of the question?
  – callculus
  Jul 30 at 22:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
  – Matthew
  Aug 4 at 15:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
  – callculus
  Aug 4 at 15:43
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

This is probably highschool-level stuff, but I haven't been in highschool for a long time...

Anyway, I have a product with known costs for a single production run. It will be sold by someone making 25% commission. In addition to the commission, we will have to pay payroll taxes amounting to 9% of the commission paid.

I need to figure out how many dollars' worth of products need to be sold in order to break even on the combined total of the product run, the commission to that point, and the payroll tax to that point.

In plain English, here's the equation I'm working with:

$ProductionRun + ($TotalSales * 25%) + ($TotalCommission * 9%) = $TotalCosts

However, what I'm after is the dollar amount where TotalSales matches TotalCosts.

How would one go about this?

algebra-precalculus percentages

share|cite|improve this question

asked Jul 30 at 17:38

Matthew

31

closed as unclear what you're asking by callculus, amWhy, Taroccoesbrocco, Shailesh, José Carlos Santos Jul 31 at 19:09

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Why do you think that they don´t match? Do you make any profit?
  – callculus
  Jul 30 at 17:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  We're in pre-production. I need to calculate the break-even point for projections.
  – Matthew
  Jul 30 at 21:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do the answers capture the meaning of the question?
  – callculus
  Jul 30 at 22:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
  – Matthew
  Aug 4 at 15:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
  – callculus
  Aug 4 at 15:43
  

  
  
  
  

 | 
show 1 more comment

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

This is probably highschool-level stuff, but I haven't been in highschool for a long time...

Anyway, I have a product with known costs for a single production run. It will be sold by someone making 25% commission. In addition to the commission, we will have to pay payroll taxes amounting to 9% of the commission paid.

I need to figure out how many dollars' worth of products need to be sold in order to break even on the combined total of the product run, the commission to that point, and the payroll tax to that point.

In plain English, here's the equation I'm working with:

$ProductionRun + ($TotalSales * 25%) + ($TotalCommission * 9%) = $TotalCosts

However, what I'm after is the dollar amount where TotalSales matches TotalCosts.

How would one go about this?

algebra-precalculus percentages

share|cite|improve this question

asked Jul 30 at 17:38

Matthew

31

This is probably highschool-level stuff, but I haven't been in highschool for a long time...

Anyway, I have a product with known costs for a single production run. It will be sold by someone making 25% commission. In addition to the commission, we will have to pay payroll taxes amounting to 9% of the commission paid.

I need to figure out how many dollars' worth of products need to be sold in order to break even on the combined total of the product run, the commission to that point, and the payroll tax to that point.

In plain English, here's the equation I'm working with:

$ProductionRun + ($TotalSales * 25%) + ($TotalCommission * 9%) = $TotalCosts

However, what I'm after is the dollar amount where TotalSales matches TotalCosts.

How would one go about this?

algebra-precalculus percentages

share|cite|improve this question

asked Jul 30 at 17:38

Matthew

31

share|cite|improve this question

share|cite|improve this question

asked Jul 30 at 17:38

Matthew

31

asked Jul 30 at 17:38

Matthew

31

asked Jul 30 at 17:38

Matthew

31

31

closed as unclear what you're asking by callculus, amWhy, Taroccoesbrocco, Shailesh, José Carlos Santos Jul 31 at 19:09

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

closed as unclear what you're asking by callculus, amWhy, Taroccoesbrocco, Shailesh, José Carlos Santos Jul 31 at 19:09

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Why do you think that they don´t match? Do you make any profit?
  – callculus
  Jul 30 at 17:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  We're in pre-production. I need to calculate the break-even point for projections.
  – Matthew
  Jul 30 at 21:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do the answers capture the meaning of the question?
  – callculus
  Jul 30 at 22:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
  – Matthew
  Aug 4 at 15:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
  – callculus
  Aug 4 at 15:43
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Why do you think that they don´t match? Do you make any profit?
  – callculus
  Jul 30 at 17:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  We're in pre-production. I need to calculate the break-even point for projections.
  – Matthew
  Jul 30 at 21:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Do the answers capture the meaning of the question?
  – callculus
  Jul 30 at 22:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
  – Matthew
  Aug 4 at 15:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
  – callculus
  Aug 4 at 15:43
  

  
  
  
  

Why do you think that they don´t match? Do you make any profit?
– callculus
Jul 30 at 17:47

Why do you think that they don´t match? Do you make any profit?
– callculus
Jul 30 at 17:47

We're in pre-production. I need to calculate the break-even point for projections.
– Matthew
Jul 30 at 21:57

We're in pre-production. I need to calculate the break-even point for projections.
– Matthew
Jul 30 at 21:57

Do the answers capture the meaning of the question?
– callculus
Jul 30 at 22:38

Do the answers capture the meaning of the question?
– callculus
Jul 30 at 22:38

Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
– Matthew
Aug 4 at 15:16

Yes, now I'm just trying to wrap my head around how to get it into my Excel spreadsheet. :)
– Matthew
Aug 4 at 15:16

In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
– callculus
Aug 4 at 15:43

In the first cell of column A (A1) you insert 0. Then at the next row (A2) you insert the formula $text=$A$1+1$. Then you hover the mouse cursor over a small square at the lower right-hand corner of the cell, which is called the Fill handle. As you do this, the cursor will change to a thick black cross. Hold and drag the fill handle down the column over the cells where you want to copy the formula. This can be done as well for the next column. First you input in cell B1 the formula $text=A1/(1-0.2725)$. Then you copy the formula in the same way as for the column A.
– callculus
Aug 4 at 15:43

 | 
show 1 more comment

2 Answers
2

active

oldest

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up vote
1
down vote



accepted

If $s$ is sales and $p$ is production cost, your commission is $0.25s$ and your payroll tax is $0.09 cdot 0.25s=0.0225s$. The total costs are then $p+0.2725s$ and you break even when this is $s$. You need
$$p+0.2725s=s\s=frac p1-0.2725approx 1.3746p$$

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edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

add a comment | 

up vote
0
down vote

If I understand what you want correctly, here's how I'd solve the problem

Since commission is 25% of sales, we multiply total sales by 0.25. Moreover, due to taxes, we multiply the commission by 1.09

So:

$$textrmProduction_Costs + textrmTotal_Salescdot0.25cdot1.09=textrmTotal_Sales$$
$$textrmProduction_Costs = 0.7275*textrmTotal_Sales$$

Hence, sales need to be $frac 1 0.7275 cdot100%-100%=37.457%$ higher than production costs.

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

If $s$ is sales and $p$ is production cost, your commission is $0.25s$ and your payroll tax is $0.09 cdot 0.25s=0.0225s$. The total costs are then $p+0.2725s$ and you break even when this is $s$. You need
$$p+0.2725s=s\s=frac p1-0.2725approx 1.3746p$$

share|cite|improve this answer

edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

add a comment | 

up vote
1
down vote



accepted

If $s$ is sales and $p$ is production cost, your commission is $0.25s$ and your payroll tax is $0.09 cdot 0.25s=0.0225s$. The total costs are then $p+0.2725s$ and you break even when this is $s$. You need
$$p+0.2725s=s\s=frac p1-0.2725approx 1.3746p$$

share|cite|improve this answer

edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

If $s$ is sales and $p$ is production cost, your commission is $0.25s$ and your payroll tax is $0.09 cdot 0.25s=0.0225s$. The total costs are then $p+0.2725s$ and you break even when this is $s$. You need
$$p+0.2725s=s\s=frac p1-0.2725approx 1.3746p$$

share|cite|improve this answer

edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

If $s$ is sales and $p$ is production cost, your commission is $0.25s$ and your payroll tax is $0.09 cdot 0.25s=0.0225s$. The total costs are then $p+0.2725s$ and you break even when this is $s$. You need
$$p+0.2725s=s\s=frac p1-0.2725approx 1.3746p$$

share|cite|improve this answer

edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

share|cite|improve this answer

share|cite|improve this answer

edited Jul 30 at 17:55

edited Jul 30 at 17:55

edited Jul 30 at 17:55

answered Jul 30 at 17:51

Ross Millikan

275k21184351

answered Jul 30 at 17:51

Ross Millikan

275k21184351

answered Jul 30 at 17:51

Ross Millikan

275k21184351

275k21184351

add a comment | 

add a comment | 

up vote
0
down vote

If I understand what you want correctly, here's how I'd solve the problem

Since commission is 25% of sales, we multiply total sales by 0.25. Moreover, due to taxes, we multiply the commission by 1.09

So:

$$textrmProduction_Costs + textrmTotal_Salescdot0.25cdot1.09=textrmTotal_Sales$$
$$textrmProduction_Costs = 0.7275*textrmTotal_Sales$$

Hence, sales need to be $frac 1 0.7275 cdot100%-100%=37.457%$ higher than production costs.

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

add a comment | 

up vote
0
down vote

If I understand what you want correctly, here's how I'd solve the problem

Since commission is 25% of sales, we multiply total sales by 0.25. Moreover, due to taxes, we multiply the commission by 1.09

So:

$$textrmProduction_Costs + textrmTotal_Salescdot0.25cdot1.09=textrmTotal_Sales$$
$$textrmProduction_Costs = 0.7275*textrmTotal_Sales$$

Hence, sales need to be $frac 1 0.7275 cdot100%-100%=37.457%$ higher than production costs.

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

add a comment | 

up vote
0
down vote

up vote
0
down vote

If I understand what you want correctly, here's how I'd solve the problem

Since commission is 25% of sales, we multiply total sales by 0.25. Moreover, due to taxes, we multiply the commission by 1.09

So:

$$textrmProduction_Costs + textrmTotal_Salescdot0.25cdot1.09=textrmTotal_Sales$$
$$textrmProduction_Costs = 0.7275*textrmTotal_Sales$$

Hence, sales need to be $frac 1 0.7275 cdot100%-100%=37.457%$ higher than production costs.

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

If I understand what you want correctly, here's how I'd solve the problem

Since commission is 25% of sales, we multiply total sales by 0.25. Moreover, due to taxes, we multiply the commission by 1.09

So:

$$textrmProduction_Costs + textrmTotal_Salescdot0.25cdot1.09=textrmTotal_Sales$$
$$textrmProduction_Costs = 0.7275*textrmTotal_Sales$$

Hence, sales need to be $frac 1 0.7275 cdot100%-100%=37.457%$ higher than production costs.

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

share|cite|improve this answer

share|cite|improve this answer

answered Jul 30 at 17:54

Rushabh Mehta

454110

answered Jul 30 at 17:54

Rushabh Mehta

454110

answered Jul 30 at 17:54

Rushabh Mehta

454110

454110

add a comment | 

add a comment |