Yes. There are many ways a business can save money in cloud computing.
Economies of scale: The cloud computing providers buy the infrastructure in bulk from the vendors and some of the savings therein are passed on to the consumers. The costs work out to be much lower than what an individual would have paid for if they have to buy the infrastructure.
Running expenses: The infrastructure maintenance, upgrades, repairs and replacement of components cost money. These are all avoided as the service providers maintain and manage the infrastructure.
Pay-as-you use:Cloud computing runs on the model of pay-for-what-you-use. This means that the consumers only pay for the services they have consumed and need not pay a fixed rate as in the case of traditional hosting.
Capital expenditure: Businesses acquire infrastructure and other expensive equipment and it keeps reducing in its value due to depreciation. By moving to the cloud the expenses are spread over many operations which they would avoid in case they had to do it in physical infrastructure i.e. they will put in several applications on the cloud and gain better benefits.
Support: Maintaining and monitoring servers round the clock will require technical staff to work for deploying, upgrading, configuring etc. It means an organization may need 2 or 3 staff in a 24-hour period. Salaries and other benefits are all eliminated as the cloud providers take responsibility for the servers and other issues.