Break Even Analysis problem

Okay, see if this makes sense and point out any flaws.

ftcut = # of feet cut

Your efficiency adder formula is: effadd = .01*ftcut/1000

The trick in determining the effadd across multiple feet is to use the average effadd for all of the metal used. This ends up being effadd/2 since the first 'foot' has an effadd of 0 and the last foot would be whatever the formula above generates. Dividing by 2 should be the average across all ftcut.

The amount of wasted metal is: wm = ftcut*effadd/2. I believe this is accurate, since, if the effadd were 0 (i.e. no loss of efficiency), then the formula above would be 0, which would imply you should never replace the equipment.

The cost of the waste is: wc = wm*metal cost = $2*wm.

Setting wc = to $8K and solving for ftcut should yield the number of ftcut where the metal lost equals $8K.

expanding the formulas to be ftcut:
$8000 = $2 * ftcut * (0.01 * ftcut/10000)/2

Solving for ftcut
ftcut = (8000*100000)^0.5 = 28,284 ft

Now, I could argue that this is not the true break even, and I think that is the bigger issue of this problem. The calculations above just provide the number of feet cut when the total ftcut inefficiencies could have paid for a new machine. Typically, a break even analysis in performed upon two different offerings. In this case it would compare a new machine with one that has already cut some amount of metal and has some inefficiencies. Putting it another way, comparing a new machine against one that has just cut 1 foot of metal (and thus has a slight inefficiency) will show that after a certain amount of feet (probably in the billions) it would have been better to scrap the 'old' machine and buy the new one.

As you say, there are many other variables, wear & tear, depreciation, opportunity cost, etc. Generally, you should have a corporate rate of return on investments and also use that in determining when equipment should be replaced.

Pauley