Making a sale that's over the customers budget

I have been working on an offer for a software project, requested by a customer.
I'm pretty sure that the price of the offer will be over their budget.

The price itself is nothing special, it is a very reasonable estimate to their requirements and at a very reasonable rate.

The project itself, I find very interesting, because of its size, the revenue it will provide as a whole, and the project is just an interesting thing to do.

Now, I'm wondering if there are any techniques, practices, or reasoning for situations like this. For example, seeing part of it as an investment (reusable parts of the software), or a base for negotiating with the customer, or ... ?

EDIT: More details on the product have been requested. The project is not extremely big, but as I'm saying, in my situation a nice project to be working on.

The customer is a psychologists practice of multiple psychologists.
The request consists of a few parts:

• website + CMS,
• users can schedule their own appointments (mini-zocdoc), accounts and files (frontend)
• the therapists can manage their schedule, appointments, clients and files (backend)

On the selected answer: I've received many good answers here, and know where to go from here. Thanks everyone. I've selected Zuly Gonzalez's answer, because of its clarity and completeness, but the other answers are a good help forward as well.

The key is to show your client the value that you are providing them, and translate that into dollars saved. Will you increase employee productivity? Will you increase conversion rates on their website? Will you help them land a big client?

Use the total cost of ownership to translate the output of this project into money saved by the client. Compare the cost of this project to what it would cost your client if they did nothing, or if they used a different solution to solve the same problem. You can incorporate the reusable parts of the software you mentioned in your calculation of the total cost of ownership.

Most technical folks hate marketing, but it really is a necessary evil. Marketing yourself is one of the most important skills you can learn. If you can always tie a project back to value (i.e. how much money a customer will save) you will be able to charge more for your services. As an example, $200,000 sounds like a lot until you consider that it will actually save you $1,000,000.

Edit based on your edit:

Here's a very quick analysis taking the requirements you listed.

website + CMS

users can schedule their own appointments

Missed appointments cost them money. Show how better appointment scheduling/management will reduce the number of cancelled appointments or no-shows.

the therapists can manage their schedule, appointments, clients and files

When customers say "the price is over our budget" - in a lot of cases it means "we want a discount". If the product that you offer is going to save them more money than they spend on it - what they say about their budget is just a negotiation technique.

What you need to do is clearly show why the ROI will be positive. Without knowing any details about your product, it's hard to provide any advice here really.

In your case, I'd price your project per hour and say something like this.

"Well as you know software projects always come in late and over-budget, largely because people underestimate the tasks. In reality, it's hard to estimate how much time it'll take to do something that hasn't been done before. So I like to be as realistic as possible. To complete your project starting from scratch, I think it will take X programmers working Y hours and so that means a cost of XYZ. But you'll find others who'll quote you less, and sometimes far less. Sadly, it's quite common in the industry for service providers to underestimate costs upfront to lure in customers, and then take longer and ask for more in the end: I suggest you be wary of seemingly low bids. With you, I want to be upfront and I would advise you to consider the quality of the experience rather than the projected cost of a quote that may be purposely underestimated." Or some variation thereof.

Getting the customer to pay what you are requesting is the best alternative. However, you also mentioned:

a base for negotiating with the customer

You can negotiate to keep the IP, and then white label it to them. That way you can sell the same solution to many practices. And in addition, charge them a fee for the branding.

The downsides to this approach:

• You would have to incur some of the upfront costs associated with the development of the solution.
• You'd end up having to work on selling this product to other practices. You're a service company, not a product company, so this will change the way your business is run.