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The ART of CROSS-OVER ANALYSIS
Cross-Over Analysis
As an owner, or manager, you will at times face the options of buying one of two comparable pieces of equipment.
Usually each will have its own set of fixed and variable costs. The questions is: Which machine should you buy?
Suppose you are still the copy shop owner from our example in Chapter 8 and you can bury one of two copiers.
Which machine you will buy depends mostly on the volume of copies you expect to do. So the first thing to do is
figure out the cross-over point, that is, the unit (V) volume at which the cost of the two machines is equal…Cross-
over analysis will identify that point.
Here’s the formula:
Cross-over units = (Machine 2’s fixed costs – Machine 1’s fixed costs) divided by (Machine 1’s variable cost –
Machine 2’s variable costs)
At 250,000 copies (per year), the total cost of each of the two machines is equal.
Above and below that volume, one machine is preferable to the other. Which one?
To fine out, calculate the cost of each machine at a unit volume just below the cross-over point and just above that
point.
For instance, at 240,000 copies the cost of each machine is as follows:
These two calculations tell us that Machine 2 is the cheaper one, at 240,000 copies.
At 260,000 units the cost of each machine is as follows:
These two calculations tell us that Machine 1 is the cheaper one, at 260,000 copies.
So we see that Machine 2 – the one with the lower fixed costs – will be preferable below the cross-over point, and
Machine 1 will be preferable above that volume.
Again, which machine should the copy shop owner buy? It depends on the volume he expects. If the volume will be
above 250,000 units, he should purchase Machine 1. If the volume will be lower, he should purchase Machine 2.
This, of course, assumes that he can forecast the volume with some accuracy. Also, as with break-even analysis,
these calculations ignore any differences in copy quality, speed, reliability, and so forth.
As an owner, or manager, you will at times face the options of buying one of two comparable pieces of equipment.
Usually each will have its own set of fixed and variable costs. The questions is: Which machine should you buy?
Suppose you are still the copy shop owner from our example in Chapter 8 and you can bury one of two copiers.
- Machine (1) has fixed costs of $10,000 and variable costs of two cents a copy.
- Machine (2) has fixed costs of $5,000 and variable costs of four cents a copy.
Which machine you will buy depends mostly on the volume of copies you expect to do. So the first thing to do is
figure out the cross-over point, that is, the unit (V) volume at which the cost of the two machines is equal…Cross-
over analysis will identify that point.
Here’s the formula:
Cross-over units = (Machine 2’s fixed costs – Machine 1’s fixed costs) divided by (Machine 1’s variable cost –
Machine 2’s variable costs)
- Cross-over units = (5,000 – 10,000) / (.02 - .04)
- Cross-over units (-$5,000) / (.02)
- Cross over units = 250,000 copies
At 250,000 copies (per year), the total cost of each of the two machines is equal.
Above and below that volume, one machine is preferable to the other. Which one?
To fine out, calculate the cost of each machine at a unit volume just below the cross-over point and just above that
point.
For instance, at 240,000 copies the cost of each machine is as follows:
- Machine 1 (240,000 x $0.02) + $10,000 = $14,800
- Machine 2 (240,000 x $0.04) + $5,000 = $14,600
These two calculations tell us that Machine 2 is the cheaper one, at 240,000 copies.
At 260,000 units the cost of each machine is as follows:
- Machine 1 (260,000 x $0.02) + $10,000 = $15,200
- Machine 2 (260,000 x $0.04) + $5,000 = $15,400
These two calculations tell us that Machine 1 is the cheaper one, at 260,000 copies.
So we see that Machine 2 – the one with the lower fixed costs – will be preferable below the cross-over point, and
Machine 1 will be preferable above that volume.
Again, which machine should the copy shop owner buy? It depends on the volume he expects. If the volume will be
above 250,000 units, he should purchase Machine 1. If the volume will be lower, he should purchase Machine 2.
This, of course, assumes that he can forecast the volume with some accuracy. Also, as with break-even analysis,
these calculations ignore any differences in copy quality, speed, reliability, and so forth.
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