Understanding Business Agreements and Market Value
For me USD 20 per hour is a low price. I think they can pay that price. I can renegotiate but this situation does not give me much security in the future...How can I say in a professional way that I do not accept the proposal?
Many of the other answers focus on the dollar value, which somewhat misses the key point of your question: how to refuse or renegotiate the terms of the agreement. Therefore, let's first discuss what an "agreement" or contract negotiation is in pragmatic terms.
While you can look up the dictionary definition or research basic economics, in practical terms the value of a good or service is simply the intersection of how much a buyer is willing to pay and how much a seller is willing to accept. In this case, the client is the buyer and you are the seller. If they aren't willing to pay what you're willing to accept, then you haven't reached an agreement. On the other hand, if you're willing to work for the money they're willing to pay then it doesn't really matter what others in the industry are making because they aren't a party to your agreement.
If you are unwilling to work for what the client wants to pay, then you can renegotiate the deal or walk away. Those are really the only two options, although there are a few caveats that I'll cover later.
Renegotiate Based on Value
If you want the work more than you want to walk away, you can try for a better deal. You can point out the value of your work to the company, the difficulty they would presumably have in finding a replacement, or the additional costs they would bear in bringing a new person up to speed on the code you've written or educating that person about the company's unique needs. These all resolve to a dollar value.
Keep in mind that their budget problems are not yours, except insofar as they represent a risk to you getting paid at all. Business-to-business contracts (and as a freelancer you are in business) are all about allocation of risk. Perhaps you and the company might agree to a lower hourly rate in exchange for a lump sum signing bonus, or a flat-fee monthly retainer in addition to the hourly. As an offhand example, if you're willing to work for $15/hour plus a $1,000 signing fee, that may be a win-win for everyone.
However, keep in mind that the company may not value your work as much as you do. They may be deliberately low-balling you, or they may genuinely be unable to afford your services at this time. Regardless of their situation, your sole responsibility it to determine what price for your labor you can accept.
You must also keep in mind that (at least in the United States) companies have no responsibility other than contractual obligations to provide you with "security" of any kind. If it's not in the contract that they must pay you at least a certain amount then, regardless of the agreed-upon rate, they could give you zero work in a given period. You must either negotiate a minimum payment or a certain amount of work, or accept the risk as a cost of doing business.
Walk Away from Unacceptable Terms
If you can't reach a mutually-beneficial agreement about your rate, then you will have to turn down the proposal. This, too, is a normal part of doing business.
If you can't renegotiate because either party says that their proposal is firm (which would be polite) or "take it or leave it" (which is not), then if you can't accept the final offer you simply turn it down politely. A widely-accepted way to do this would be to say something along the lines of:
I'm sorry we were unable to come to a mutually-beneficial agreement. I respect your budget constraints, but I can't accept the offer as it stands. Please let me know if your needs or your circumstances change, and I'd be happy to work with you again in the future.
Then walk away. Your best offer (whatever it is) should be your final offer. It is not a negotiating tactic. It's simply a polite way of saying no, but leaving the door open to do business again in the future under different terms.
Caveats
If you rely on income from this one client for basic needs, then you may not be in a position to effectively negotiate or to walk away. In such cases, make the best deal you can, and then work under the available terms while you continue to look for other work.
If you're working under a fixed-fee agreement or have a burdensome notice period defined in the contract, this can be a problem. However, if your agreement is simply payment for time spent working then you can replace your current client engagement with a more lucrative one at your convenience, just as they can replace you with another vendor at their discretion. Both parties, you and the client, have business risk in this regard; neither party has "security" unless it's written into the contract.