The first aspect to consider when you try to cut costs on a new fence is scheduling the installation during winter, because contractors are not so busy and may be even willing to offer you discounts. Fencing in the cold season is possible during clear days with reasonable temperatures that do not interfere with materials used in the process.
The cost of a fence install also depends on the materials you choose. Fencing materials are priced by the lineal foot, but a forged iron fence will be more expensive than a PVC or chain link fence. There are also different installation requirements that influence the price. A quality residential fencing company in Denver will be able to give you an estimate based on your specifications.
Another aspect that must be taken into account is related to labor costs. Average fees vary between $30 and $50 per hour, but certain conditions can increase the cost (steep slopes on your land, areas that are hard to access, too many trees, pre-existent structures that must be removed etc.).
You can also cut on some costs if you deal yourself with the marking underground utilities and get the city permits, otherwise the contractor will entail additional costs for all these.
Another consideration that you must know about is that your geographical location may also affect the cost of having a new fence installed on your property.