I don't know if you have ever head of the dictum "buy cheap and buy twice" I don't think a free software like WHMCS exist but some larger web hosting companies give WHMCS free as part of reseller hosting plan.
I have tested WHMCS, even though here we build our own custom billing system. WHMCS is extremely powerful tool for for as low as 12.95 per month that is a extremely great investment. They have put so much afford in like fraud checks for free, Payment gateways and build in support system. All this makes it the only tool you will need to virtually run your company. Its a great buy and very cheap, and support on hand to help you if you have any complications.