# Break even point

• Jun 9th 2010, 11:04 AM
petedam
Break even point
So here's the question that i have and i hope someone can help me with this because i am kind of stumped. :( MY main struggle is determining which is VC and which is FC.

John and Jack have opened a shop in Kelowna to build customized patio furniture. The projected selling price of a patio set will be $3,000. They estimate that the table will use twenty (20) board feet of lumber at a cost of$12 per board foot, $10 per table for hardware, and another$15 for custom finishing materials such as stain, varnish, or painting. Each patio set comes with four (4) chairs. Each chair will use six (6) board feet of lumber, $6 for hardware, and$10 for finishing materials. They estimate the labour time per table to be twenty-five (25) hours, and per chair, ten (10) hours for construction and finishing work. John found warehouse space that they can rent for $2,300 per month including heat. Other utilities will be$275 per month. Other required costs are insurance at $3,500 per year. They will pay themselves$20 per hour (treat this as a variable cost). They will pay a sales commission (based on selling price) of 4% per complete set sold. Jack estimates that they can build 125 sets per year.

1. How many patio sets must they construct to break-even? Calculate the break-even point in:
a. units.
b. sales dollars.

• Jun 9th 2010, 11:31 AM
e^(i*pi)
Quote:

Originally Posted by petedam
So here's the question that i have and i hope someone can help me with this because i am kind of stumped. :( MY main struggle is determining which is VC and which is FC.

John and Jack have opened a shop in Kelowna to build customized patio furniture. The projected selling price of a patio set will be $3,000. They estimate that the table will use twenty (20) board feet of lumber at a cost of$12 per board foot, $10 per table for hardware, and another$15 for custom finishing materials such as stain, varnish, or painting. Each patio set comes with four (4) chairs. Each chair will use six (6) board feet of lumber, $6 for hardware, and$10 for finishing materials. They estimate the labour time per table to be twenty-five (25) hours, and per chair, ten (10) hours for construction and finishing work. John found warehouse space that they can rent for $2,300 per month including heat. Other utilities will be$275 per month. Other required costs are insurance at $3,500 per year. They will pay themselves$20 per hour (treat this as a variable cost). They will pay a sales commission (based on selling price) of 4% per complete set sold. Jack estimates that they can build 125 sets per year.

1. How many patio sets must they construct to break-even? Calculate the break-even point in:
a. units.
b. sales dollars.

Selling Price: 3000 (given)

Labour time (time per table + time per chair):
$\displaystyle 25 + 4\cdot 10 = 65 \text{ hours}$

Materials per item (selling price-total cost)

$\displaystyle 20 \cdot 12 + 10 + 15 + 4(12 \cdot 6 +6 + 10) +0.04 \cdot 3000 + 65 \times 20 = 2192$ (edit: 20 should be 12 since each lumber is 12 not 20)

Yearly Production = 125 (given)

Other costs (Insurance + Storage + Rent)

$\displaystyle 3500 + 275 \cdot 12 + 2300 \times 12 = 34400$

To break even Revenue = Loss

$\displaystyle 3000n - (2192n + 34400) = 0$

Solve for n which is the number of units sold
• Jun 9th 2010, 11:42 AM
petedam
http://www.mathhelpforum.com/math-he...74e4a84b-1.gif

can you tell me why you did this (4(20.6 + 6 +10)

as well you treated wages as fixed cost...i am suppose to add to this Materials per item (selling price-total cost) aren't I?
• Jun 9th 2010, 11:48 AM
e^(i*pi)
Quote:

Originally Posted by petedam
http://www.mathhelpforum.com/math-he...74e4a84b-1.gif

can you tell me why you did this (4(20.6 + 6 +10)

as well you treated wages as fixed cost...i am suppose to add to this Materials per item (selling price-total cost) aren't I?

Yes you're right, I changed this in hindsight. The 4(20*6+6+10) is the cost of the chairs. Each chair costs 20*6+6+10 and there are 4 of them
• Jun 9th 2010, 11:49 AM
GeoC
Given what you've been asked, essentially all costs are variable except rent, insurance and utilities, since they will be relatively fixed regardless of the units produced -- although in long term, all these costs mentioned are not really fixed (you can cancel insurance, and end your lease, quite easily as compared to owning a facility).

The other costs are variable because they scale with the production. So find the level of production needed to cover the above costs.
• Jun 9th 2010, 11:52 AM
petedam
according to your revenue equation....i got an n value 0f 0.02241...it doesnt make sense.
• Jun 9th 2010, 12:07 PM
e^(i*pi)
Quote:

Originally Posted by e^(i*pi)
To break even Revenue = Loss

$\displaystyle 3000n - (2192n + 34400) = 0$

Solve for n which is the number of units sold

Quote:

Originally Posted by petedam
according to your revenue equation....i got an n value 0f 0.02241...it doesnt make sense.

I get an answer of 42.57

$\displaystyle n = \frac{34400}{3000-2192} \approx 42.57$

I attach an excel file for you to look at if you wish (it has the same info on, nothing new). It's just be easier to chop around the numbers

nb: it should be safe but since I use linux I can't be sure that it's totally safe.
• Jun 9th 2010, 12:10 PM
petedam
Quote:

Originally Posted by e^(i*pi)
I get an answer of 42.57

$\displaystyle n = \frac{34400}{3000-2192} \approx 42.57$

I attach an excel file for you to look at if you wish (it has the same info on, nothing new). It's just be easier to chop around the numbers

nb: it should be safe but since I use linux I can't be sure that it's totally safe.

sorry....i am an idiot and can't solve for n.
• Jun 9th 2010, 12:17 PM
petedam
http://www.mathhelpforum.com/math-he...c2a32fda-1.gif (edit: 20 should be 12 since each lumber is 12 not 20)

shouldn't it be 2037?

Because there are two of them should it be (65 x 20) x 2? for labour

Again thanks a bunch!