"We have offered them a discount of 2 months, which I know is not substantial..."A discount of two months (17%) is very substantial for a one-year prepayment (your customer can maybe get 1% a year from keeping that money in a savings account). You'll need to evaluate whether it's worth it to your business to give them even that discount.
For example:
- If you're financing your company off credit card debt at 20%, than giving someone 17% off to get money up front would actually save you money.
- If you're suffering desperate cash-flow problems and need money tomorrow to pay your operating expenses, then it might be worth giving someone a steep discount to get money today.
- If it costs you $500 a month in expenses to provide the service, then a 50% discount on $1000 would wipe out all your profit.
If you're getting adequate revenue from your current paying customers to keep the company going, you may not want to give that kind of discount. The problem with giving them a discount is that they'll expect another discount when the contract comes up for renewal in a year. And they'll tell their friends that your company gave them a discount, so future customers might also ask for one.
If you do end up giving them a discount, you might want to negotiate additional terms that are advantageous to you, such as being able to say on your web site that this company is your customer, and being able to use them as a reference for other customers. That might be worth something if they're a billion dollar company with some name recognition.