Most businesses and organizations are realizing it's time to update their old web sites if they haven't done so recently.
The primary motivation is to make sure their site looks and operates properly on smaller tablet and smartphone devices as well as the standard desktop display.
The scaling of a web site to function properly on various sized displays is called "responsive" design. With the move of eyeballs from office desktop to mobile technology, businesses realize the the dominate way customers access their sites will be on small displays.
On most mainstream Content Management Systems (CMS), responsive software has been incorporated to make sites scaleable automatically to various screen sizes. With Drupal, an Open Source CMS we use, "Bootstrap" software is included on newer themes/CMS versions that make the transition to responsive seamless. Other CMS, like Wordpress and Joomla, also have made the switch to incorporate responsive design in their newer CMS versions and themes available for free or purchase.
For customers/clients, the upgrade need not cost upwards of five figures as some web design shops charge. The hard work to develop "responsive" design modules such as Bootstrap is now off-the-shelf stuff.
Upgrading from an older CMS version and theme/design to the newest CMS/theme with responsive design can take significant time. But the transition isn't difficult or as time-consuming as some clients might think.
Before making the site redesign decision to ensure "responsive" compatibility with all variety of screen sizes, clients should be sure to obtain proposals from at least three reputable web design/development firms.
The customer should have a solid understanding from the proposal how much is being charged for "responsive" software upgrades, versus the basic design upgrades and enhancements. If an organization is in the dark about such things, it would be money well spent to hire a web design/development firm just to evaluate site upgrade quotes.
While there is a cost to incorporating responsive design in site upgrades, the heavy (costly) lifting has already been done for those utilizing mainstream CMS software packages.