Calling accounting majors

[LinktheDeme]

Hey I just got out of an exam and this one problem stressed me out to the point where I can remember it almost exactly and I don't think I did it right and since its a final exam I won't ever see this again and I wanna know if I did it right.

Question was something along the following if you decrease direct material cost by 2.75 in exchange for a 2,500 fixed cost yearly machinery is this viable? At what amount of units will this venture be justified?

Latter made me think I did something wrong in the first one I asked the teacher and he said don't infer based on the second question which makes me think I did it right and he wants to know min units that its not or I did it wrong and it wasn't viable

This is the information before the venture

Units 1000
Sales 50,000
Variable Cost
COGS (26000)
SG&A (4000)
Contribution margin 20000
Traceable Fixed Cost
SG&A(10000)
COGS (5000)
-----------------------
Segment Margin 5000

On a per unit basis thats
Sales 50
VC COGS (26)
SG&A (4)
CM 20
TFC
SG&A (10)
COGs (5)
---------------------
Segment Margin 5

So what I did was plug in the numbers that was given on a per unit basis first changing it to

Sales 50
VC COGs (23.25)
SG&A (4)
CM 22.75
TFC
SG&A (10)
COGs (5)
new machine (2.5)
----------------
Segment margin 5.25

Then I plugged it in to 1000 units

Sales 50,000
VC COGs (23250)
SGA (4000)
CM 22750
TFC
SG&A (10000)
COGs (5000)
new machine ( 2500)
--------------
segment margin 5250

Meaning I got $250 from doing the deal if I did it right so the next part I was really confused on what to do. So I knew based on what I had found that in order for it to be justified that it must be at least increase by $1 after $5000.

so I did 5250 -5000 to get 250

and what I did was 250/22.75 and got 10.989011 so I figured it was 10.989011 units difference than 1000 which would be 989.010989 units would be break even so anything above that would be good and I plugged it in to make sure I got at least close to 5000 at the segment margin and got

units 989.010989
sales 49450.5495
total VC (26950.5495)
CM 22500
Total TFC (17500)
---------------------
segment margin 5000

So i deduced based on what I got that anything above 989.01989 units would be when the venture was justified. But break even units is FC/ CM per unit so that would be

2500/2.75 which would be 909.09 I assume plugging that in will be CM = 20,000 or so anyway just wondering if i did it wrong and where I did it wrong cause this is the make or break A or B on the exam D:

[Azkarin2]

Here is how I would have done it.

Group all the variable costs and fixed costs together. In this type of problem it's easier to work with less variables. Basically you are going to set two equations to equal each other so that you can find at what quantity produced will you get the same profit.

The first equation will be the original scenario (before the price increase) is below. 20x is the contribution margin and 20 is the fixed cost.

20x - 15,000

The second equation takes into effect the change in DM and FC.

22.75x - 17,500.

Set these two equal to each other to get the following equation

20x - 15,000 = 22.75x - 17,500.

This gives you an answer of x = 909 units. So anything above 909 units, the switch to decreasing the DM in lieu of increased FC will be beneficial.

I don't think that your first strategy of dividing the difference by the DM will give you the correct result (sometime is does by dumb luck).