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The process of calculating a conventional bid for a project can be an anxiety inducing task. For the inexperienced, it can be downright daunting. Estimating sufficient time, material, and profit margins, while staying competitive, can also require a significant amount of time. Many contractors slowly fine tune this process to meet their needs. Unfortunately, however, many times these procedures are not easily adjusted for different sizes or types of projects. This is where some of the more complex mathematics you thought you would never use becomes useful. A basic parabolic formula, y = a(x-h)2 + k, can be used as an easily adjusted method for calculating bids or estimates. Using this formula, the additional allowances that are necessary as the project size increases are automatically included, exponentially. While it may seem a more complicated method, using this formula is a simple three step process; figuring project size, setting the parabolic curve, and inserting numbers.

As with all bid calculating processes, the first step is to determine the scope. Considering the majority of my work consists of residential framing, I use the square footage of framing under roof. The method of scope measurement you choose is not as important as the fact that it be accurate, consistent from one project to the next, and relative to the amount of work you will be doing. For instance, if you are a landscaper and have a project where 5000 square feet of sod will be laid, you shouldn't deduct house footage from one bid and not the next. Furthermore, you would not use the square footage of the house as the scope measurement because it does not have any bearing on the work you will be doing.

Setting the parabolic curve is the only area where a little pre-bid experimentation is necessary. If you have some previous job experience, this step can be quite fast. Simply take a successful bid from a small, medium, and large job and use those numbers as numbers as targets for your curve. You should be able to use the scope measurement numbers in the formula to achieve the target number from past experience. If you do not have any previous jobs to use as targets, you will have to estimate a low and high target number. I recommend that you start with the curve a little steep, that is a higher “a” value.

Inserting the numbers is the final step in using the parabolic formula for bid calculations. “y” is the adjusted unit price you are calculating. This result will be multiplied by the total scope measurement, or the “x” value. “a” is the curve factor. The higher this number is, the faster the curve rises. “x” is the scope measurement, in my case, the square footage under roof. “h” is, in most cases, considered to be zero. It can, however, be used to quickly adjust for different types of work that have the same scope. For instance, if house A was 3245 square feet, and I was responsible for the turn key completion and house B was the same size but I was only responsible for exterior cornish, variable “h” would be a higher number for house B because the cost is obviously going to be lower. My typical work load does not vary this drastically, so I tend to forgo this option. Variable “h” also introduces another “trial and error” variable, which reduces the benefits of using this type of equation, unless you already have enough successful bidding experience and are just using this equation as a time saver. The final variable, “k”, is simply the cheapest per unit price that you would complete the smallest project for. In my residential framing work, this would be $1.75 per square foot. One caution about this variable, the smaller the “x” variable average is, the more accurate this number must be. For instance, in my framing work, the smallest project I would be likely to do would be no smaller than 1000 square feet. However, a cabinet maker whose smallest job would be a three foot vanity, will have to make every penny count or loose money.

At first glance, using the parabolic equation as a bidding tool may not appear to be any less complicated than a “from scratch” calculation for a project, however, in the long run it is. While it may take a certain amount of time to fine tune the equation to meet your business needs, in the long run, time will be saved because of the steps saved in the bidding process. Furthermore, it allows you to use past experience as a bidding tool without having to pour over project histories to glean the numbers and information pertinent to the current project. The three steps it takes to set up this equation, figuring project size, setting the parabolic curve, and inserting the numbers, are small investments that will pay significant dividends of time.

y = a (x - h)2 + k
adjusted price per foot = .06(sqft under roof/1000)2 + 1.75

My process of calculating a framing bid begins with the scope measurement, total square feet under roof. In my case, I divide this number by 1000 to the the “x” variable down to a manageable number. This step is not necessary, but it allows me to easily remember all the variable values. Of course, every project is going to be a little different. So, after calculating “y”, the adjusted price per foot, I have other values that I add if applicable, $.20 for special ceilings, $.50 for pitches of 7 to 9/12, $.60 for variable wall heights, etc.

House A = 1500 square feet, 6/12 pitch, no extras

.06(1.5)2 + 1.75 = 1.885 + no extras 1.885 * 1500 = $2827.50 framing labor bid

House B = 5264 square feet, 9/12 pitch, 2 tray ceilings.

.06(5.264)2 + 1.75 = 3.4126 + .50(9/12 pitch) + .40(special ceilings) = 4.3126 per square foot 4.3126 * 5264 = $22,702 framing labor bid

Why not charge the same base for all houses and just add for the extras? Simple, the larger the house the larger the details. By applying the curve to the base, you are, in effect, applying it to the details. Furthermore, something like a special ceiling in a 1500 square feet home is most likely to be simpler and faster to build than one in a 5000 square foot home. A 9/12 pitch may not require scaffolding on a 1500 square feet home, but it most definitely will on the larger.