SOLIDWORKS Costing information is saved with the model files after it has been calculated. When you open this model on another computer you will get a prompt that the referenced Costing Template (.SLDCTM, .SLDCTC, .SLDCTS) is missing on the computer, but you can save out a temporary template file from the Costing information saved within the file.
If changes are to be made and all the template information is required, there is a Costing Pack and Go functionality. This will automatically include the Costing Template and model files in a ZIP folder. You can also include the Costing Report.
The ZIP file contains all items in the same folder. You can then copy to the Costing Template to the templates folder on the new computer to be used for future costing calculations (Options > File Locations > Costing Templates).