In a previous article, we posted a problem and asked for your input. The problem that was posed is this:
Your firm is considering replacing and upgrading a machine that presently manufactures an average of 100 parts per hour, producing (on average) 150,000 parts a year.
Direct labor related to the machine’s operations is set at $15 per hour. The overhead factor is 2.80, so the overhead allocation is $15 times 2.80, or $42 per hour.
The machine being considered for replacement will manufacture at a rate of 300 units per hour (average).
The primary question posed was: Would you advise the purchase of the new machine as a good investment for the firm? Why, or why not?
If You Are Like Most Folks
If you are like most folks, you would calculate your answer along these lines:
You would have concluded that, since the new machine can produce parts three times faster than the existing machine, your firm can save 1,000 hours a year in direct labor. That is, 150,000 units at 100 units per hour equals 1,500 hours; whereas, the same 150,000 units produced at 300 units per hour would take only 500 hours.
As a result, direct labor “savings” would be $15,000 (as shown above), and the related overhead allocations would save another $42,000 annually (also shown above). Since the machine will cost only $45,000 installed, the calculated “payback period” is under a year—about nine-and-a-half months.
Is this really a valid calculation?
Your First Clue
The very first clue—the very first thing that should have made you doubt whether the purchase of the new machine would be a good investment should have been a look at the hours the existing machine was running.
If the existing machine were fully utilized, we would expect the productive hours on the machine to be in the range of 2,000 hours (i.e., 50 weeks at 40 hours a week—leaves two full weeks for downtime, setups, etc.).
Stated another way, the productive capacity of the existing machine would be 2,000 hours times 100 units per hour, or 200,000 units. Since only about 75 percent of the existing machines capacity is presently being consumed by production, we can readily assume this machine (at least) is not the “bottleneck” to producing more Throughput for the firm.
Furthermore, we can also readily conclude that, if it were the bottleneck—if the existing machine really were a capacity-constrained resource—this machine had not yet been fully exploited.
The numbers in our example clearly show that the existing machine still has 25 percent reserve capacity that has not yet been tapped (even if we limit ourselves to one eight hour shift a day, and operate only five days a week).
If the firm actually could uncover market demand for the remaining 50,000 units of available production capacity, they certainly had not done so yet.
So, let’s look at the real numbers that might result.
True Accounting (Not Cost-world Thinking)
In the real world—not the Alice In Wonderland world of cost-accounting—here is what the numbers might end up looking like:
Think about the answers to these questions:
- Where will the $15,000 in calculated “Direct Labor Costs” savings come from? Will the firm’s payroll actually be reduced by $15,000 when the new machine is placed in service?
- Where will the $42,000 in calculated “OH Costs” savings originate? When the new machine is placed in service, what overhead in the organization will actually be cut so that operating expenses are reduced by $42,000?
- If the $15,000 in direct labor savings are not real, and the $42,000 in overhead cost savings are also a cost-world-thinking fiction, how will the company reap payback on the acquisition of the new machine?
The Proper Calculation
Is there a calculation that saves a firm like yours from making bad “investment” decisions like the one above?
The answer is a resounding “Yes!”
Here is the correct formula:
Where ROI = return on investment, delta-T = change in Throughput, delta-OE = change in Operating Expenses, and delta-I = change in Investment.
When using this formula, we further define “Throughput” as the change in Revenue less the change in TVC (Truly-variable costs). TVCs are generally restricted to raw materials, commissions, labor (if paid on a piece-rate, but not hourly), unless there are other costs that truly and directly vary with changes in per-unit revenues.
Applying This Calculation to Our Example
This formula is very easy to apply to our example.
Since we know that the existing machine is not a CCR (“bottleneck”), changing the speed at which it produces will not change Throughput at all. Therefore, delta-T, in our example, calculates to zero.
Nothing in our calculation suggests that there will be a change in Operating Expenses either—up or down. Therefore, we will put down delta-OE as zero, also.
The change in investment was given to us in the original example. We know that we must invest $45,000 to purchase the new machine and have it installed. So, delta-I becomes $45,000.
Putting this all together we find that ROI = ($0 - $0)/$45000 = ZERO.
The ROI on this suggested “improvement” project is ZERO and the payback period is infinite. This investment will NEVER pay for itself under the present scenario.
We would be delighted to hear from you if you have a comment or opinion on this matter. We know it it somewhat controversial and may be surprising to some. Leave your comments here, or feel free to contact us directly, if you’d prefer.
We’re looking forward to hearing from you.
