# Back-calculating productivity

by Admin Updated: July 27, 2018 |

## Back-calculating productivity is a technique for matching actual sales and production to targets

It is surprisingly common to find business plans with seemingly arbitrary estimates of production and sales expectations. The amount of productivity required to produce $1.2M from $1 units is likely wildly different from producing the same amount from $120 units.

This technique is useful for matching/scaling quantifiable long-term goals such as annual sales or production targets to more humanly understandable short-term goals such as weekly, daily or even hourly targets.

It’s called *back*-calculating because it starts with the result and figures our the smaller steps needed to achieve it.

### The calculation

- Decide on the time span and the target for that time span,

e.g. 1 year, 400 units. - Decide on a sensible period for the analysis (should not be shorter than the time required to produce or sell a unit),

e.g. monthly or weekly. - Determine the relationship of the time span to the period,

Assume 51 working weeks a year which means that a month is on average 51÷12 = 4¼ weeks. - Divide the target figure down to arrive at the activity rate,

400 is approx. 33 per month and approx. 8 per week. - Calculate forward to verify:

8 per week for 51 weeks is 408, but 33 per month is only 396...

### Rounding errors

It usually makes sense to round the figures in the calculation to whole numbers and in the above example the exact rate per week is approximately 7.8 which rounds to 8. This works in our favor (8×51=408 units per year, 8 more than our goal) but it is critical to be aware of how rounding errors can work against us: The rate per month is 400÷12 = 33⅓ but this rounds to 33 which is not enough.

**Basic rounding error:**In the above example the weekly rate rounds OK but the monthly rate is off. If we increase the target to 415 units per year, the rate per month is 415÷12≅34.6 which rounds up to 35 and gives us 420 per year, but the rate per week is 415÷51≅8.1 which rounds to 8, the number we already know produces only 408!**Compounded rounding error:**If we increase the target to 435 units per year, we now see a basic rounding error on the monthly rate (435÷12≅36.3 which rounds to 36 and gives us only 432 per year) but the rate per week is OK (435÷51≅8.5 which rounds to 9 and gives us 459 per year),...*unless*we used the rounded monthly rate of 36 in which case the weekly rate is still only 8 (from 36÷4.25≅8.47).

As a rule, only the very last number produced by subsequent calculations should be rounded.

### Unsafe assumptions

**Time:** There are not always 365 days in a year and not all days can be counted. A 30 day month that starts on a Monday-Thursday has 22 weekdays. A 30 day month that starts on a Saturday has only 20. Some months have public holidays.

**Fractional units:** Fractional units, while most accurate for the calculation, are generally not possible and must be rounded to whole numbers.

**Equal value of units:** Calculation necessarily assumes all units are equal in terms of the time required to generate them.

### Safety margin

Rounding can build in a safety margin but it is unreliable. It is essential to always perform the last step of the calculation to ensure a sufficient buffer.

### The question to the answer

Assuming a high level of confidence that the targets are achievable in principle, the key question is not so much *can* they be achieved as *will* they be achieved in practice?

For example, it might be possible to run machinery at 80% capacity every day for a year in principle, but is this realistic in terms of actual day-to-day operation?

### More info

“No-Nonsense Guide to Measuring Productivity” at hbr.org.

“Accounts don’t add up - rounding errors” at accountantforums.com.