Pricing: Variable Duration and Rates

The simplest equation for price is:

Price = Duration x $/hour

The problem is that price is what the market is willing to pay, not some rubbish about cost plus profit. If the price is too high and the duration cannot be changed then the average hourly rate is too high. The issue is that not every hour of work is worth the same value. Take this article for example: Why I charge $500 an hour. Is the hourly rate reasonable? Well that depends on which hours are charged.

When I was studying, my industrial engineering tutor indicated that he charged $1000/hour. We all considered that was extortionate. But then he explained that each hour visiting the clients factory taking observations and measurements, was followed by time spent writing a report and employing the services of a typist. So he didn’t really charge a $1000/hr, it was more like $1000/week. The issue is which hours are charged and which are not, some businesses charge the extortionate rates for every hour worked. If you work for the 5% of business which are big business, then may get away with such fees for a while. But if working with the 95% of businesses which are small business, then likely to encounter trouble.

As I demonstrated in a previous article can charge rates from $5/hour to say $220. The exploratory work is charged at $5/hour, whilst the final hour presenting the solution, is charged at $220/hr. For example a 5 hour job, would be 4 hours at $5/hr plus 1 hour at $220/hr = 20 + 220 = $240, equivalent to an average rate of $48/hour. But if I used this average hourly rate and the duration of the project increased the resulting fee would become increasingly unacceptable.

If I had employees then the hourly rates would vary dependent on the role of the person performing a given task. So hourly rates vary. By breaking a job down into various tasks and applying different hourly rates, it is possible to get a more reasonable fee. Though getting a fee can still be a problem, if the hours for a task are highly variable and uncertain.

The Problem of Estimating Time

I have illustrated various calculations before. Here I will present yet another example. For most structural projects it is necessary to calculate the reference wind speed (Vzu) for the site, and also a reference pressure (qzu).

Its a relatively simple sequence of calculations:

First calculate the site wind speed for 8 compass directions.

calculation of wind speed for a given direction

Then find the maximum wind speed from all 8 directions.

Calculation of Site Reference Wind Speed

Then calculate the pressure on a building surface.

Calculation of wind pressure on surface

It is however simpler if the surface pressure is defined in terms of a site reference pressure. Then we just need to identify Cfig and Cdyn for the given surface.

Surface Pressure in Terms of Site Reference Pressure

Where reference pressure (qz) is defined as follows:

Site Reference Pressure

Ignoring all the silly subscripts it is a relatively simple sequence of calculations. Assuming I know the following inputs off-the-top of my head.

Inputs for the calculations

Then I can just feed the values into a calculator and calculate the result. So using ATCalc I get qzu=0.83kPa, and it took 31 seconds to calculate. Of course I need to write the result down and present in a report of some description.

Example Calculations Using ATCalc

Assuming I have a spreadsheet which can do the calculations for me, then all I need do is type in the data, I don’t need to be concerned with arithmetic operators and sequence of operations. The time then drops to 13 seconds to input the data.

Calculating Reference Pressure Using a Spreadsheet

However I need to do this calculation for 8 compass directions if the conditions are not all the same in each direction. Thus assuming spreadsheet already setup, then just need to input 8 lots of the data, so estimate of time is 13×8=104 seconds, or 1.73 minutes.

Taking into consideration administration and marketing concerning selling the work to the client, registering the project and dispatching the finished report the minimum time for a project is likely 1 hour, but assume can collapse time down to minimum of 15 minutes.

Now assuming an hourly charge out rate of $55 to $220/hour, then the fee is between $13.75 and $55. Just one little problem though, it can take a lot longer than 1.73 minutes (say 2 minutes).

Issues Which Can Increase Calculation Time

Referring to the inputs above. The value of V[R] is basically looked up in AS1170.2, I rarely use a value other than 45 m/s, hence the reason from the top of my head. The main occasions I use some other value is when assessing existing construction, in which case I could spend a week or so messing with statistics and probability, attempting to justify a lower wind speed. So the 2 minutes becomes a week.

The directional multiplier Md, is generally read straight from the code, typically expect a value less than 1. However if only calculating a single reference wind speed, the direction where Md=1 controls the calculation, all other factors being equal. If other factors not equal, then there maybe a benefit to looking up the value of Md for each direction considered. It is also to be noted that only sub region A4 has Md<1 in all directions. Giving consideration to Md is only going to add a few minutes of extra time, as it is just looking up values in the code, for a limited number of sub regions. Unless have local weather data for a region not covered, and going to do the statistics to determine values of Md: in which case may take several days. {Something I’ve never done}

Terrain category multiplier, this can typically be averaged in 1000m averaging distance. So need a map of the site, this I get from either UBD street directory or from Location SA (formerly Atlas SA). Below are shown two examples. One for a building within the town centre of Maitland SA (sample 2), and another on the outskirts of the developed area (sample 1).

Terrain Category Averaging Distance Building in Maitland SA
Terrain Category Averaging Distance Building on outskirts of Maitland SA

For sample 1, can see that only the SE to NE sector contains built-up township, the rest contains open space, rural crop land. Whilst for sample 2, the W to N sector contains rural crop land, with the rest being the township.

For other projects and situations each sector is not so clear, and the terrain within a sector can vary between the rural crop land and the built-up township. Depending on the complexity of the terrain, each direction may take an hour of assessment, with all 8 directions requiring 8 hours in total.

The shielding factor (Ms) also requires looking at a map. It also requires height and spacing of buildings. Each direction can take an 1 hour to check.

Topographical factor (Mt), this requires a topographical map, and the generation of elevation profile in each direction. Once again assessing each direction can require up to an hour of calculation.

So to the basic two minute calculation, we can add 8 hours for terrain category, 8 hours for shielding and 8 hours for topography. Bringing total to 24 hours and 2 minutes (say 24 hours).

So using the basic hourly rates of $55/hr and $220/hr we get a fee ranging between $1320 and $5280. None of which would be considered reasonable for either a $500 garden locker, a $2000 shed, $30,000 verandah, or a $500,000 house.

Other Issues

An employer has to pay their personnel at their pay rates, so if the business is not going to get paid for such effort it is not going to do the work unless it needs to be done. It only needs to be done if the multiplier magnifies the wind speed, and the only factor which does that is the topographical factor (Mt). All other factors we are looking to reduce the value of the wind speed and the only time that matters is for extremely expensive commercial/industrial buildings, or if assessing existing construction which want to avoid knocking down due to non-compliance.

So likely that the task is 8 hours duration, so fee between $440, and $1760. We can dismiss the high figure because its a routine calculation and can be done by a junior level engineer and does not require a senior level engineer. But still as a member of the public lets assume our view is that $55 is more than enough fee.

So for a $500 garden locker that amounts to 11% of the cost of construction, for the $500,000 house, it is 0.011%. For the garden locker we can eliminate the assessment by making use of the simplified wind loading code (AS4055) and wind classification system and regional wind speed maps. However, if use Location SA, will discover that there is no wind speed given for most rural townships. Still as long as there is no topographical factor we can keep the calculation simple. Likewise for the house, we can use the simplified classification system. (N1:qzu=0.69kPa, N2:qzu=0.96kPa). But the calculation above indicates a value of qzu=0.84 which lies between wind class N1 and N2. To get the wind class N1 value, shielding (Ms) needs to be considered. Whilst to get wind class N2, the terrain has to be similar to an airfield, not rural crop land, so working from surface roughness lengths (z0), and terrain category averaging is beneficial.

As determining site wind speed is a routine exercise, effort is required to drop the 24 hour detailed assessment down to less than 1 hour. Also much of the exercise is a drafting exercise: M[z,cat], Mt,Ms are basically mapping exercises, and generating detail sections. So gathering the data and documenting it, in a useful and informative manner is some 80% of the effort. So we could charge a lower rate for that task, say $33/h. So 0.8*8=6.4 hours, 6.4*$33=$211.20 plus 1.6*$55=$88, to give total of $299.20. We can now identify that it is the mapping and profiling which takes most of the time. If we can automate such task, a task which otherwise delays moving on with more important tasks, then we can potentially drop the whole task down to 2 minutes.

But what is this 2 minutes worth with respect to the $500,000 house? Clearing not going to spend $1000 on calculations to save $1000 worth of materials. The materials adding resistance and making the structure more robust are more beneficial, than calculations (scrap paper) which suggest the extra material is not necessary.

The calculations have to add value, and there is a point in time at which the calculations cease to add value because the results are common place and familiar to all. So that which had value yesterday may not have value tomorrow.

So my time does have value, according to the federal minimum wage $19.49, to the professional employees award $33.60. To these rates however need to add operating expenses. The common rule of thumb is to multiply the employee rate by 2 or 3 to get charge out rates. Thus: min: $39.98 to max:$100.80. (assuming the rule adequately covers the operating costs)

But according to internet search unskilled plan drafters (and building designers) are charging $150 to $190 /hour. I say unskilled because the typical person providing services as a plan drafter is not even adequately qualified in drafting (technical drawing) and have poor knowledge of trigonometry and geometry. No skills in design, and limited knowledge of construction processes/techniques, and limited knowledge of forms of construction. The only major expense they have is computer software for drafting: (AutoCAD, Revit, ArchiCAD, Tekla), some of which is extremely expensive.

Any case, when making a judgement of value, consider own hourly rate multiplied by 2 or 3, then estimate hours believe the task is likely to take.

But even then as demonstrated above a task can either be simple and take 2 minutes or be involved and complex and take several days. In value-analysis it isn’t the cost hoping to minimise it is the value which hope to maximise.

When considering value it is the total package of goods which needs to be considered. The calculation of wind speed is seldom done as a stand alone exercise, it is generally done at the beginning of more comprehensive structural calculations. As a consequence the cost of an involved wind speed assessment can be absorbed elsewhere in the costing if some other aspect becomes simpler than estimated.

Similarly if have adequate tolerance on all other duration’s, then the total fee should have adequate juggle room, to allow for redistributing the costs at the end of the project when actual duration’s may be known. Though in many circumstances the detailed breakdown of task cost is not known, as it is far too expensive to monitor the work to that level of detail. For example most consultants only track whole hours, some break time down into 15 minute blocks, with respect to employee time and the projects they have been working on. Whilst they may determine fees based on on whole days and or weeks depending on typical length of projects. So a project of only 2 hours duration would be charged for a whole day, they would likely expect the project to go away as being too small for their business.

However if don’t have hourly paid employees then time can be more directly considered a poor measure of work and its value, and we can move away from selling time. Time is an indirect measure because the duration for the task is unknown and uncertain, and the hourly rate is itself is just an arbitrary number. So neither duration or hourly rate are constants. Whilst the market value is also not a constant, as it varies with the individual: but for a given market sector it maybe considered near enough constant.

If the market price or value is constant, then there is more than one way that the two numbers duration and hourly rate can used to produce that constant. That is there are multiple solutions to the equation: Price=Time*rate. Given the price and any of the other two factors, we can calculate the other.

So we can make a judgement of the price, then work backwards and decide an hourly rate or a duration. If we don’t like the results then we repeat, until all three variables are found to have acceptable values. Also it is not the hourly rate for an individual project which matters but the average hourly rate for the year across all projects: or more to the point the total income generated for the year. Can we cover our expenses? Can we reduce the time we take to generate the income required? What do we do with the spare time?

As I have mentioned before most builders are not interested in reducing construction time. They sell time, if the time reduces then their income reduces. If they finish the project sooner, then they have to find another project. Projects are not abundant and tend to be seasonal, with the seasons spanning years. So could have 5 years with many projects, then 10 years with few projects. Is it possible to remove time from their costings? How well do they estimate time? Time will have to be indirectly involved as long as employees are on hourly rates rather than some incentive payment scheme.

Some builders do avoid time, by basing estimates on area rates, such as $/sq.m, with the area rates changing with the nature of the project. They may also have fixed rates for various tasks, or use percentage rates based on associated costs, such as the cost of materials. For example the rule of 3 may apply again, where by the cost of materials is multiplied by 3 to get the total cost of the project, which hopefully covers the labour costs involved.

What happens to value pricing, when the market determines the costs, and starts valuing things at no more than their cost? Sheds and carports for example people can determine the cost of materials at retail prices. When they do such costing, they usually find the prices from suppliers to be far too high if not extortionate. They then decide to fabricate and build themselves. If they don’t have the resources and capability to fabricate and construct themselves, then such option is not available to them, and they have to buy from the suppliers.

However no supplier has to aim for maximum profit. They could place supplying and satisfying a need, as the purpose of business rather than maximising profit. Such supplier may then reduce their per unit profits and supply at lower price. Their objective to increase sales volume, rather than maximise profit from volume sold. They achieve the funds they need to finance their current and future activities, with reasonable reserve and no more than determined to be needed.

So we can partially get away from time, by considering various small tasks and the duration of those tasks and the cost from hourly rates. However once we have set a rate for the task, we don’t adjust its future value based on adjusted hourly rates, we simply judge a new rate for the task. In same manner to the judgement of the new hourly rates. Put simply the federal minimum wage and the industrial award rates of pay are all based on subjective judgement. Even if calculated, the values going into the calculations are a matter of subjective judgement.

Hourly wage rates are a matter of negotiation, bargaining and haggling: reconciling the conflict between two opposing subjective judgements. There are some things however we don’t expect to haggle over price, such as medical services, and many other services. If the wages are a matter of subjective judgement, then anything derived from the rates is also a matter of subjective judgement.

Today many of the things we need are judged to have too high a price. The problem is the hourly rates are too high for the hours which are needed for the work. The problem is the average hourly rate needs to be reduced, the work therefore needs subdividing between people of different pay rates or the individual gets paid different rates for different tasks.

The whole is different than the sum of its parts: it could be more or it could be less than the sum, all that is certain is that it is different.

So as I said the process is iterative. Deciding on the parts, judging the parts, then calculating the total, judging the total and returning to the parts and adjusting, until all parts and whole are acceptable. Of course the result may not be acceptable to the market. But that just represents another input to the iterations. Generally my judgment is on the low side, the only time I get a high fee is when someone else makes the offer. So I won’t be haggling any time soon.


Revisions:

  1. [29/12/2019]: Original