The house has an "as is" value.
H&BU as-vacant hasn't changed.
H&BU as-improved: What should be done with the property as-it-is? There are four choices:
1. Demolish
2. Remodel (change the use or improve the functionality)
3. Renovate/Repair
4. Leave as-is
Option #1 is if the improvement has no more remaining economic life; effectively the land is more valuable as a site ready for something else than it is with the existing improvement on it. Economic life is the question here (does the improvement continue to contribute value?). A brand new house that has a lot of remaining useful life may not contribute any value to a site. Likewise a tear down is usually at the end of its economic life (and useful life).
I doubt if your situation falls under #1.
Option #4 is what most of us run into in the residential world. That would be H&BU as-improved is "as is". One doesn't have to change anything; just maintain the house with normal maintenance and maybe some minor refurbishing. It is safe to say that isn't the option in your scenario.
Your subject is probably a combination of #3 and #4. If it is a major work in progress, they might be renovating/replacing/repairing some components (replacing the roof, for example) and they might be remodeling to improve the functionality (they may be changing the kitchen layout to bring it up to current market expectations).
If the answer is #3/#4, the the existing improvement (in its current as-is condition) contributes value to the site. It is that contributory value (added to the site value) which constitutes the market value of the subject.
As Randolph points out, H&BU also is used to determine who is likely buyer for the property given what its H&BU as-improved is.
If nothing had to be done to the house, your likely buyer will be an owner-user or potentially an investor who will rent to a tenant.
If the house is half-way through a major renovation, then the likely buyer (at least in my market) is someone with the wherewithal to finish the job. Those buyers are typically contractors or investors and they will purchase the house to complete the work and then sell it at a profit.
You need to figure out (a) what should be done with the house as-improved (and I'm assuming the thing to do to it is to finish the work in progress) and based on that determination, you need to figure out who the likely buyer will be. You need to figure out who the likely buyer will be because that will tell you what kind of comps to use, and what kind of motivations and expectations drive such buyers.
In my experience, a contractor or investor would be the likely buyer. An owner-user doesn't usually have the wherewithal to complete such a project and why should they? They want to use the house, so they'll buy one ready-for-use (or with minor work that they can do while living there).
An investor or contractor will price the subject based these three factors:
(a) how much they think they could sell it for (and they usually plan on selling it relatively fast and at the low-end of the range) once it is renovated/remodeled/fixed,
(b) how much will it cost them to complete the project (which includes selling costs), and
(c) how much reward (profit) do they require to go forward with the project (this is known as Entrepreneurial Incentive, or EI)?
Do not make the mistake of assuming that if the house is worth $300k when all the work is done, and it would cost $50k to complete the work, then the value is $300k - $50k = $250k. That isn't how the likely buyer (contractor/investor) would act.... and neither would you (would you buy a house for $250k if you knew it was going to cost you $50k plus the time and effort to finish the work... with the risk that something might go wrong... just so after all that is done, it is worth $300k? I sure wouldn't).
While I do not believe this type of assignment is necessarily difficult, I do believe it requires the appraiser to understand H&BU analysis and to be able to identify what should be done with a property in its as-is condition and who is the likely buyer that would purchase the property to do what should be done.
If you are unsure of how to apply this analysis, you should stop the assignment because you risk making a mistake in the analysis that could have significant impact on the results. Also, per the GSE certification (if this is being done on a GSE-mandated form) the appraiser certifies she/he is knowledgeable in the property type (read Certification #11 in the 1004); I would characterize an assignment that involves a renovation project in-the-works as a unique property-type that requires experience and competence.
While the USPAP allows an appraiser to gain experience and knowledge while doing an assignment (if the appraiser discloses the lack of knowledge to the client and documents in the report what steps he/she took to gain competence) the GSE certification does not allow that.
If you lack the experience and want to complete the assignment, you could work with another appraiser if that other appraiser has the competence and co-signs the appraisal, and if that is acceptable to the client; that would be my recommendation. That way, the next one is all yours.
Good luck!