Apex Corporation manufactures pens. to bring these pens to market, a fixed cost of $75,000 was incurred. please read description

Question

Apex Corporation manufactures pens. to bring these pens to market, a fixed cost of $75,000 was incurred. Apex will sell the pens for $2.10 each. The cost to produce each pen is $0.85

how many pens must apex produce to breakeven?

what will the profit or loss be if apex sells 30,000 pens?

what will be profit or loss be if apex sells 100,000 pens?

 

 

Answer 1

Here are the answers, then I'll explain how I arrived at them:

 

1) Apex Corporation must produce 300,000 pens to breakeven

2) $67,500 loss if Apex sells 30,000 pens

3) $50,000 loss if Apex sells 100,000 pens

 

Explanation for (1):

The main insight here is understanding that profit is the difference between price of the pen minus cost of the pen. So, if you sell me 1 pen, then you know you've made 25 cents, since $2.10 (price you sold it to me for) minus $0.85 (how much it cost you to make) is 25 cents. If you want to make back your $75,000 cost of making pens (breakeven), then how many pens do you need to sell me if for each one you make .25 cents (as explained above)? In algebra terms, the equation you want to write is .25x = 75,000, where x is the number of pens sold and .25 represents a quarter of a dollar (.25 cents). Solve for x. x = 300,000 pens. (You may need a sales team for this!).

 

Another way to say it: how many quarters (x) do I need to have $75,000 (and thus breakeven)?

 

Explanation for (2):

So now that we know the golden nugget fact that for each pen you sell me you make 25 cents, this question is more straightforward. To know how much loss or profit you have, you need to (a) know how much you'd make from selling 30,000 pens, and (b) subtract that amount from 75,000 (cost to produce the pens). 

 

(a) .25*30,000 = $7,500

(b) $75,000 - $7,500 = $67,500 loss <-- your answer (note: this is a loss because you only made $7,500. You'd have to make another $67,500 in order to break even, and then even more to be profitable).

 

Explanation for (3):

Repeat the same process as the Explanation for (2). 

 

(a) .25*100,000 = $25,000

(b) $75,500 - $25,000 = $50,000 loss <-- your answer

 

I hope this is helpful! Let me know if you have any more questions. 

 

-Sean

 

 

Answer 2

You can tell that Apex makes $1.25 in profit for each pen sold because 

 

$2.10 - $.85 = $1.25

 

That means if they sold 30000 pens, then they made

30000(1.25) = 37500

The problem though is that they spent $75000 in startup costs so you must subtract that from the profit that they made selling the pens so

$37500 - $75000 = $-37500 so that they still have a loss.

 

You can do the same thing for the 100000 pens.

 

To find the breakeven point you need to know how many pens are sold, so call x = number of pens sold and you get

x(1.25) - 75000 = 0

x = 75000/1.25 = 60000 pens