How satisfy angry employees, without costing the company any extra expenses?

There are many ways to absobe the unger of employees. Some times its better to appreciate the employees like (Employee of the Month), give small gifts or appreciation certificates,  send circulation on the best performers, create a kind of competition inside the company, and satisfy the employees psychologically 

First and foremost give them a patient hearing till the anger subsides. Once that is done your chance of negotiating with them increases and can bring about a win-win situation

Try to understand the main cause of anger, suggest alternatives as per the company policy, assist and yes do remember to smile often as anger does not loves it.

When employees are generally angry its not always the pay/incentives they have an issue with. It is primarily the attention their query/complaint is given by the HR team and management.

1. The first thing that needs to be done is listen to what the employee wants/is not happy about.
2. If the mistake is on your part it is wise to apologise and accept your mistake, and provide that tiny facility that might be stopping the employee from delivering better. A good employee is always an asset and should feel like one.
3. If however the employee still isn't happy and wants an additional incentive/increase in remuneration for instance his/her performance should be reviewed and the decision taken accordingly.

I totally agree with Hind's comments but management first have to play very important role which is listening to their employees, identifying their needs and requirements. Then I believe everything will be open in front of management that how to deal with each individuals in different situation.

Really it depends

Mostly acording to the employee character 

some need to encourage them and some need to be punished 

Anger is the result of attention deficit of desirous action.When ever any employee is in anger it is not the course of one action..but the cumulative accumulation many more other unmet expectation set by the employer.

Priority shoulld be given with emphatic listening,

Apology if required in a convincing way

rectification that can be brought to to avoid leading further reaction of anger.

A credit of noticing and bringing out the flaws with tactical convincing lip service to gain teh confidence.