This is the value you calculate the client could confidently receive upon delivery of a successful project. During the initial call, it's worth trying to gather a few key pieces of information that will help you calculate this. It will vary from business to business, but some examples of useful info that can go into the Expected Client ROI include:

Average Customer Value (for the client's business);
Number of new or renewed customers as a result of your project;
Amount of time saved as a result of your project;
Amount of money saved as a result of your project;
Number of new opportunities brought in as a result of your project.

You are looking to make some key business outcomes more tangible in order to assist with the value-based pricing effort. For example:

The client may charge $30/month per new customer, with average lifetime value of 10 x $30 = $300 per customer;
You are building a new website for the client, and he tells you that this could increase new signups by 10%—which you calculate to be roughly 100 extra customer signups over the next 12 months, based solely on the website improvement;
From this, you can simply calculate the rough expected project ROI as 'Avg. Customer Value x Number of customers' = $30,000

For our value-based bids, grounding this number in some tangible, expected business outcomes will be key.

Additional Factors

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Urgency

This factor relates to how urgently the client needs this project to be achieved. Are they rushing it through? Is there a major deadline coming up quickly? Or is it a lower-priority task—something that could be pushed off for later?

In terms of negotiating a bid, the higher the urgency of the project need, typically, the higher the price point you can expect for delivering well.

Stress

This refers to the stress level you will be onboarding with this project. It will be a subjective rating, combining multiple factors, but simply ask yourself—how stressed will I be by taking on this particular project? Perhaps it is a high-stakes client, and that will contribute as a high stressor. Perhaps you have other things going on and this will contribute significantly to tipping your natural calm.

Portfolio

This is an added benefit factor for you, as a solo or freelance business. The question relates to—how well would this project go into my portfolio? Beware of big name clients that dangle this as a 'major' factor for accepting a low bid—but it is a factor. Something that would look good in your portfolio will change from business to business, but it could include;

A recognisable company name;
A company that fits the vertical you are trying to break into;
A client with a strong network; or
A project that you feel confident you could deliver on exceptionally well.

Good Fit

This is another subjective 'benefit' which summarizes your general sense of the client and the project, as a whole. Is it something you're likely to enjoy working on? Do you feel comfortable with the client based on first interactions? Is there any odd tension or sources for concern? The good fit factor is the human factor of any project—and it should count for something.

Other

Project Costs

Any additional costs that you expect to arise directly from this projects—e.g. software, research spend, travel—can be added here. This value will only affect your 'Minimum Viable Bid' and 'Ideal Rate Bid'—it will not influence value-based bids, since these are derived based on value brought to the client and it's your responsibility to absorb any related costs in delivering that value.

Charts

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Value Bid Statistics

This gives the output of your 3 Value-Based Bid tiers.

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Minimum Viable Bid

This is derived from the [(minimum hourly rate x expected hours) x 1.05] + Project costs. The added 5% gives you some wiggle room for unexpected costs and added workloads.

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Value-Based Bids

This is a bar chart version of the statistics above.

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Minimum Versus Ideal Rate Bid

The Ideal Rate Bid is derived with the same formula as the Minimum Viable Bid, only using the 'Ideal Hourly Rate' as the variable input instead of Minimum Hourly Rate.

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Bonuses & Discounts

This chart shows the values that have been attributed to the various 'Additional Factors' listed above.

Based on your rating from 1-5, a weight is calculated which shifts the value to be added or discounted, accordingly;
Urgency & Stress are added to the Value-Based Bids as bonuses;
Portfolio & Good Fit are discounted from the Value-Based Bids, since they are benefits for you while working on the project.