Question

A company produces a consumer level scanner at a price of $72/unit and sells it for $84/unit. The monthly fixed costs incurred by this company are $23196. What should be the level in sales in order for the company to realize a 9% profit over the cost of producing the scanners?

Answer 1

Profit % = (total revenue - total cost)/total cost

Answer 2

Total revenue = 84 x number of units sold

Total costs = variable costs + fixed cost
Total variable costs = 72 x number of units sold
Total fixed costs = 23196

So set that whole thing up, and set it equal to 9% as the target for profit percentage, and then solve for the number of units sold.

Answer 3

this may be a dumb question but just wondering if you can explain the equation: Profit % = (total revenue - total cost)/total cost

How did you get that??? :P

Answer 4

well... is "I just know it" acceptable? didn't think so.

Think of easy numbers, maybe you'll "just know it" too...

If I buy a toy for $2 and sell it for $3, how much profit did I make?

Answer 5

$1?

Answer 6

right, perfect.

Answer 7

So, your profit % on that deal is (sales revenue - costs) / costs = (3-2)/2 = 1/2 = 50%

Answer 8

Which makes sense if you think about it... you made a profit of 50% of the cost of each toy, 50% of $2 = $ 1 profit per toy

Answer 9

OHH ok!! that makes sense now...but when i applied the equation and plugged in the numbers, the answer was wrong! :(

Answer 10

Here's what i did,

9% = (84x - (72x+23196))/ (72x-23196)

Answer 11

plus sorry*

Answer 12

The difference in the actual problem is that there are also "fixed" costs which don't vary with the number of units... this is typically like paying rent on a building... doesn't matter how many units you sell, still gotta pay the rent

Answer 13

isnt the fixed costs 23196?

Answer 14

yes it is... did you mean, in your correction, that it was "+" in the denominator?

Answer 15

yes!

Answer 16

i ended up with 7984.13

Answer 17

So, it simplifies to something like:
0.09 ( 72x + 23196) = 12x - 23196 ?

Answer 18

yup!

Answer 19

divide both by 0.09

Answer 20

oh? i just multiplied the 0.09 into the brackets

Answer 21

oh, that should work, sorry...

Answer 22

6.48x + 2087.64 = 12x - 23196 ?

Answer 23

AHAHHAHAHHAHAHAHAHHAHAHAHHAHA i put 20876.4 instead of 2087.64

Answer 24

yup!! now the answer is right! its 4580.37

Answer 25

hehe... lovely laugh, glad you caught it :)

that "x" is the sales figure to achieve 9% profit

Answer 26

teamwork... :) well done :)

Answer 27

sorry, but can you explain the definition of "sales figure"? :P BUT YES DEFINITELY!!

Answer 28

"how many units do I need to sell to make 9% profit?"

Answer 29

(flaky laptop) It's a typical business question... I know my fixed and variable costs, and I have a desired profit that I want to achieve, so how many units do I have to sell at some price to achieve that profit level?

Answer 30

But you can rephrase it in a bunch of ways.... what profit % will result from a set of costs and sales prices? What is the required sales price to generate a particular profit figure? If the market price for a product is x dollars, what must I keep my costs below to ensure a particular profit % ? Etc etc etc

Answer 31

so does variable cost = revenue while fixed cost = how much you spend?

Answer 32

no, variable cost is like "what costs does it take to make this particular unit"

Answer 33

like variable cost of making a single hamburger = cost of bun + cost of meat + cost of worker for a few minutes

Answer 34

ok!

Answer 35

this variable cost does NOT include the monthly restaurant rent, any sort of fixed fees that the restaurant owner might have to pay, or anything that doesn't change per burger

Answer 36

revenue is "per unit sold"

Answer 37

so if hamburger supplies cost me $1, and hamburger-maker's work costs me $0.50, then my variable costs PER BURGER are $1.50.

If I can sell burgers for $3, then I make $1.50 per burger.... EXCEPT that is not all profit unless I don't have any fixed costs like rent. Usually you do have fixed costs, so some of the money you make PER BURGER has to go to paying those fixed costs.

If you have $1500 rent, and you sell no burgers at all, you still have to pay the rent for $1500.

If you sell 10 burgers and make $1.50 per burger over your variable costs, that makes $15 extra above your burger and worker costs, but you still have $1500 rent... not enough.

Answer 38

OHHHHHHHHHHHHHHHHHH!! that makes a lot more sense now!!

Answer 39

If you sell 1000 burgers for $3 and you only spend $1.50 each to make each burger, you make 1000 x $1.50 = $1500 above and beyond what it costs you in meat, bread, and workers to make burgers... at this point, you have EXACTLY enough to pay your fixed cost rent. This is called BREAK EVEN POINT. At this point, total revenue = (fixed + variable cost). At this point, profit is exactly zero... but at least you aren't losing money.

Answer 40

Sales ABOVE the break even point mean you are able to make enough more money per unit sold to pay all your fixed costs like rent and still have $ left over... this is total profit. So if you sold 2000 burgers, you would have 2000x1.50 = 3000 variable costs. You would sell them for $3 each, making 3x2000=$6000. After paying the $3000 in variable costs, you would still have $3000 left. Now you pay $1500 rent, and you have $1500 left. That final $1500 is PROFIT (yay!!). And the percentage profit is the profit amount divided by the total costs.

Answer 41

You sound really smart... what grade level?

Answer 42

LOLOLOL! im not smart at all!! im in first year university, studying business and im getting really confuse because im not good at math! :P

Answer 43

well, you aren't doing so bad, and this is business :) If you get this idea, you are well on your way... work more examples, and use easy numbers to avoid hard math and focus on what's going on with variable vs. fixed costs, break even, profit and profit %, etc.

Answer 44

just wondering if you would mind me bombarding you with more questions? XP

Answer 45

If you get the ideas, you can use computers or calculators for the math... but all the business ideas in this problem are analogous to a simple fruit stand that must (a) buy fruit from wholesalers to sell as retail, and (b) pay fixed rent to property owner.

Answer 46

Oh... well, I do like this stuff... is this something you have to have tonight? I'll be on again tomorrow... would be glad to help... need to go soon though.

By the way, add me as a "fan" if you haven't already... you can see when I log on.

Answer 47

what other types of questions do you have ?

Answer 48

the one we just finished is the break-even analysis, there are other ones like market equilibrium and manufacturing functions!!

Answer 49

market equilibrium is the price where the demand for a product (in terms of # of units) is equal to the supply of the product.

Ex) demand for iPhones at a possible price of $50 is 1 gazillion, because everyone would want one at that cheap price. Apple would love to sell iPhones for $1 billion each if they could sell a gazillion of them, but of course that won't happen because nobody would pay that price. The equilibrium price is the price where the supply of phones Apple offers at that price is exactly equal to the demand for iPhones at that same price

Answer 50

so kind of like the x=y concept?

Answer 51

If Apple drops their asking price, more demand for iPhones will result. if they raise the price, less demand will result.

Answer 52

Not exactly...