Perspective on percentages

[rockstar.esq]

Estimating involves a lot of details and mathematics which must often be communicated with great speed and precision.  Unfortunately, there are terms that are so frequently misused that the information being shared is of little value.  A percentage is a simple concept with great utility and flexibility depending on your perspective.

Sometimes 10% to one party isn't 10% to the other

Subcontractors regularly call to request bid results of the General Contractor (GC) estimator to define how closely their bids are following market prices.  Estimating often requires discretion during the bid (before the deadline) in order to maintain a fair competition for the subs, and to protect the firms interests.  All too often, the focus on discretion leads GC estimators to be incredibly reluctant to provide their bidding subs transparency in bid results.  The best bid results many GC estimators will offer is a percentage presented in vague terms.  "You were 10% higher than the low bid" is a typical example.

For simplicity's sake, let's assume that the inquiring subcontractors bid was $100,000.  Ten percent of $100,000 is $10,000.  So we might think the low bid amount was $90,000 so far, so good. But it's wrong!

"Yep, that's the look of someone who's made a rookie mistake."

If the low bid actually was $90,000, adding 10% would make the 2nd low bidder $99,000 not $100,000 because 10% of $90,000 is $9,000.

In order to figure out the low bid amount, using only the information provided we can lay out what we know in an equation.

The percentage given represents the difference between the low bid, and the calling subs number in proportion to the low bid amount.

Putting this into an equation gives us:

($100,000-$Low bid)/($Low bid) = 10%

Solving for low bid we have:

($100,000)/( 10%+1) = $Low Bid

$100,000/1.1 = $90,909.09

Deducting the calling subs bid from the low bid give us the dollar amount they lost by.

$100,000 - $90,909.09 = $9,090.91

This means the calling subs was $9,090.91 higher than the low bid.

Rounding to an even $9,000, it's plain to see that the calling sub would have needed to cut 9% from their $100,000 proposal to match the low bid amount.  Since the entire point of bid results is to define what you'd need to improve, it's imperative to correctly interpret what you're being told.  The GC's is telling the sub they are 10% higher than the low bidder, when the Sub actually needed to cut 9% to match the low bid amount.

That simplified example might lead you to think 1% is no big deal, and on smaller projects, that might be true.  Have a look at what happens when we run through that example again with a 30% difference.

($100,000)/(30%+1) = $Low bid

($100,000)/(1.3) = $76,923.08

$100,000 - $76,923.08 = $23,076

Round that to $23,000 and the sub only needs to cut 23% from their bid to make up a 30% difference at the GC's desk.  A 7% difference in perspective can lead to completely wrong conclusions.

Just to sum up, the GC is calculating the bid-result difference as follows:

($Sub bid - $Low bid) / ($Low bid)= % Higher than low bid

The sub is calculating the percent they must cut their amount to meet the low bid as follows:

($Sub bid) / (1+ % Higher than low bid) = % to match low bid

Many GC estimators prefer to give bid results in percentages because this minor obfuscation  spares them from actually speaking dollar amounts aloud where they might be overheard and misconstrued as bid shopping.  Bid shopping is when a GC informs a colluding subcontractor of their competitors price for the purpose of soliciting a lower bid.  In some cases bid shopping is illegal, and in all cases it's unethical.

Subs calling for bid results should be prepared to think on their feet to rapidly calculate the hard numbers behind the percentages.  Responding to the percentage provided with "So the low bidder was $XYZ amount?" gives subs a chance to confirm what they're being told, without obliging the GC estimator to speak the number aloud.

                      

Photo by Andrew Dobrow

Contractor cloaking technology isn't very sophisticated

Subs should be especially conscientious about clarifying the bid results they receive from  Project Managers (PMs).  PM's traditionally "buy out" the estimate which means they're checking their estimators work, and addressing the problems they find.  They might have discovered that the  bid-day low sub was missing some costly scope inclusion, which made a different bidder the legitimate low-bid.  This vital error-checking process naturally requires  discretion to avoid the appearance of impropriety.  PM's providing bid results after all that review may be looking at a considerably different situation than their estimator presented.  Honest PM's will do their best to work out the errors in the order of bid-day performance.  If the corrective addition to the low bid makes the new total higher than the 2nd low bidder, the PM will hire the 2nd low bidder (provided their scope is complete).

I should mention that it's a curious coincidence that many of the most dishonest PM's I've encountered have a habit of saying every bid was "close" or "within 2%".  Estimators should be particularly wary of clients showing any signs of dishonesty.  The false pretense of a  hotly contested bid is a potential warning sign of bid-shopping, especially when similar projects deliver a larger spread between bidders.

Where percentages work, and where they really don't!

There are several components of an estimate that operate on percentages.  Profits, taxes, fees, and bonds are frequently calculated as percentages of the total costs.  There are some estimators who believe that overhead should be calculated as a percentage of project cost despite the many ways this goes wrong.  Unfortunately, this archaic thinking is sometimes bound into contractual terms where change orders are limited to predefined percentages for overhead and profit.

Overhead is the cost of doing business over time, which is not directly driven by the project cost.  Imagine a one month duration project that has a slightly cheaper level of finishes, resulting in a lower total project cost.  Did that decline in finish alter the rent at your office? No, your rent is the same regardless of what your client's project costs, so why jeopardize the means to cover your overhead by pricing it as a percentage?   This practice virtually guarantees that projects above a certain value will be overpriced, while projects under that value will be under-priced.  In extreme cases, you'll never win big jobs, and you'll go broke doing little ones.

The difference between markup and margin

All business is a balance of risk versus reward; estimators calculate that potential reward in terms of profit.  It's here that we encounter some terms that are often misunderstood, and misapplied.  Let's say we've got a project worth $100,000 after all the costs are included.  Now for that $100,000 worth of work (risk), we'd like to see 25% profit (reward).  This percentage is known as markup.

$Subtotal X Markup % = $Profit

$100,000 X 25% =  $25,000

We add that profit to our subtotal and our bid amount is $125,000.

Now let's say we won ten such jobs in one year.

10 x $125,000 = $1,250,000

That means the company had a total revenue of $1.25 Million.  So the boss is reviewing the books at the end of the year which will show all the costs, and all the earnings.  The difference between all the costs and all the earnings is your total profit.

We know that every estimate had $25,000 for profit, there were ten jobs, and to keep things simple, we say everything went perfectly according to plan on all of them.  This means the total profit should be $25,000 X 10 = $250,000.

Let's take that $250,000 total profit and divide it by the $1,250,000 total revenue to determine the percentage of profit we're actually earning.

($250,000) / ($1,250,000) = 20%

The percentage of profit we're actually earning on our revenue is known as the Margin. As we can see, a 25% markup yielded a 20% margin.  This is where estimators need to consider what's going on from an owner's perspective.  The overall risk versus reward to the firm is the total revenue versus the total profit.  They're not working off the subtotals of every estimate, they're working off the contracted total amounts.  Margin makes sense when you're working off of revenue amounts, because it directly speaks to the profitability of your entire operation.

Imagine how serious it would be for someone who misunderstood markup to be margin.  The 5% difference between 25% and 20% may not seem like much until you consider that profit to be their annual income.  That would be like working five days a week and only getting paid for four!  Many entrepreneurs  have failed because they didn't understand this concept until it was too late.

Photo by strange_r

Jim knew things weren't adding up, but he couldn't figure out why.

Just like the bid-results example above, the differences grow with the percentages in question.  A 25% Markup results in a 20% margin, whereas a 33% markup results in a 25% margin.  The percentage of markup is always higher than the margin percentage.

Putting this into formulas we get:

% Margin = (% Markup)/(1 + %Markup)

% Markup = (%Margin) / (1- %Margin)

We can calculate the total with a specific margin by using this formula:

$Total = ($Subtotal) / (1- %Margin)

So why do people get this wrong all the time?

The construction industry is very competitive which means that contractors must bid with lower profit percentages in order to win work.  It's quite common for hard-bidding GC's in tight markets to bid with less than 5% markup.  The difference between markup and margin is quite small when the percentages in question are in the single digits.  If the project isn't worth very much to begin with, these differences become even less significant.  Sadly, many firms have leadership that developed bad habits when they were small and just starting out, that are ruinous to the larger operation they oversee in the present.

Fiddling with your fee

Sometimes markup is known as a fee which can get confusing when we are dealing with cost-plus contracts.  Cost plus contracts are invoiced on a "time and material" basis with either a fixed fee (set dollar amount), or a fixed percentage.

In the case of a percentage based fee, it's absolutely critical to understand whether the fee is actually a markup, or a margin.  Contracts stipulating that the contractors fee may be no more than XYZ% of the total invoiced amount, are allowing the fee to be calculated as a margin.

Conversely, contracts stipulating that the contractors fee may be no more than XYZ% of the total time and material costs, are requiring the fee to be calculated as a markup.

This same logic applies to contractually stipulated overhead and profit percentages on change orders.  It's been my experience that if the client took the trouble to stipulate overhead and profit percentages, they'll likely limit those percentages to markup only.

I hope this article has helped to shed a little light on how percentages change with perspective.

 

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© Anton Takken 2016 all rights reserved

 

 

[Steve Sells]

in a culture that actually uses terms like 110% in a regular basis, we should not be surprised

[gote]

How true all this is. In the production of small numbers of a machine, one of the big mistakes is in the pricing of bits and pieces. A single bolt takes the same overheads in sourcing, buying, storing, documentating and and and as a hundred or a thousand. In fact, for a single bolt the overheads are several times the cost of the bolt. A good design uses as few different pieces as possible and as few pieces as possible totally. It does not matter if a few bolts are oversized if they are the same as the other ones.

For the buyer, the price of erecting the machine is an important factor that is often overlooked. If it takes weeks rather than hours o get the cheaper machine up and running it is no longer so cheap. I have ereected a production unit in nine months that took four years for the competition. My customer paid a bonus. The competiror nearly filed for bancruptcy. 

Another thing is that the important figure is the first one not the last one. The difference between 200 and 100 is greater than between 201 and 202. Put this way it looks as a silly statement but I have seen people haggle over the supply of foundation bolts and forgetting the price of the machine. The haggler was very happy that he had been able to get the bolts for free but they were useless and my foreman bought new ones.