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August 28th, 2017, 12:16 PM   #1
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Simple break even analysis

Hello. I have this task saying:

“Two different manufacturing processes are being considered for making a new product. The first process is less capital-intensive, with fixed costs of only 46400$ per year and variable costs of 720$ per unit. The second process has fixed costs of 400100$ but has variable costs of only 210$ per unit.

a) What is the break-even quantity, beyond which the second process becomes more attractive than the first?
b) If the expected annual sale for the product is 840 units, which process would you choose? "

I think I know the formula for a break even analysis. I think it is Q = F / p-c, where F = fixed cost, p = price and c = variable costs. My book says so since "we set total revenue equal to total cost, we get the break-even quantity point as

pQ = F + cQ
(p - c)Q = F
Q = F / p - c

Now, to question a). I need to find the Q. But, I do not have the p. What should I do?

In advance,
Thank you very much

Kind regards,
Pumaftw
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August 28th, 2017, 12:49 PM   #2
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$c_1(n) = 46400+720n$

$c_2(n) = 400100 + 210n$

the break even quantity occurs when the cost of producing $N$ items becomes cheaper for the 2nd process.

$c_1(N)>c_2(N)$

$46400 + 720N >400100+210N$

$510N >353700$

$N > 693.529$

so we would say $N=693$, as we can only produce integer quantities.

at $N>693$ process 2 becomes cheaper

b) Since you expect to sell 840>693 units you would want to use process 2.
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August 28th, 2017, 12:50 PM   #3
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Let x be number of units.
46400+720x is first process cost.
400100+210x is second process cost.

Break even is x where they are equal.
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August 29th, 2017, 12:57 AM   #4
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Thank you both for fast response. I wasn't all that wrong in my notes, I was somewhat in the right direction. Again, thank you!
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