Shall have done？

I would think it acceptable only if you were indirectly quoting a command. For example, if an agreement said:

"Company A shall contribute 50 million dollars to the Venture before March 1."

Then you could say:

"The agreement says that by the end of next month, company A shall have contributed 50 million dollars to the joint venture."

Isn't "shall" more definitive than "will"? and it is used more often by the British English speakers as opposed to the American English speakers?
So, whether it's Future Tense or Future Perfect Tense, the issue is the usage of Shall Vs. Will.

Jim Van is correct that the issue is Shall vs. Will.

I agree with Ruricolist that shall is used with first person only. But even in paraphrasing, I would make the correction:

The agreement says that by the end of next month, company A will have contributed 50 million dollars to the joint venture.

Or, without correction, use quotation marks in writing:

The agreement says, "By the end of next month, company A shall have contributed 50 million dollars to the joint venture."

My teacher told me that should/could/would also denote the future tense and with the addition of have, the future perfect. Should is used for first person and would for second and third persons and could for both. So a revision would be: "He would/could have done [this]".

@Teacher Habib - In Third person singular, 'has' is used when the verb 'have' is the main verb - 'He has a large house', or is the auxiliary in Present perfect - 'He has already spoken to the boss' or Present perfect continuous - 'He has been cleaning the car.'

But in your example - 'He will have taken his food', we have Future perfect where 'have' is used together with the modal verb 'will', and modal verbs are always used with the base form of the verb, which is 'have' - 'He might have time later on', 'She could have been wrong', 'He must have forgotten to do it'.

The same thing happens in Future continuous, where we use the base form 'be', not 'is'- He will be having his lunch then, so better phone later'.

We can also have a Future perfect continuous (the most exotic tense), combining 'will', 'have' and 'be' - 'By the end of next month, he'll have been working here for ten years'.

By the way, your example isn't very natural in Standard English, although it almost works in Scottish English - 'You'll have had your tea.' (which really means 'I don't want to make you any tea'). Better might be something like 'He'll have finished eating by then'.

The original questioner's assumption is correct: in normal conversation 'shall' is only used in First person singular and plural, mainly in offers and suggestions and their related question tags - 'I'll open a window, shall I?', 'Lets go out tonight, shall we?'

In British English, it is also used interchangeably with 'will' in First person singular and plural, with no change of meaning (although there used to be a distinction in the past). 'We will / shall just have to wait and see'. I do this, but this use of 'shall' is declining.

In legal English, however, 'shall' is also used in the Third person, to denote obligation (it seems shall is used for people, must for things) - 'The tenant shall keep the apartment in good order, and the rent must be paid by the allotted day each month', 'The parties to this contract shall abide by the conditions herein and all aforesaid conditions must be adhered to'.

In the example - 'Company A shall have contributed 50 million dollars to the joint venture.' the only way I can read this is as a Future perfect, with this element of obligation. But something is missing - the date by which this obligation must be fulfilled
- 'By the date set out in Clause 3 of said contract, Company A shall have contributed 50 million dollars to the joint venture.' In other words, Company A must contribute that sum before the date specified.

This is confirmed in a discussion document on legal English, where the writers quote an authority talking about "the use of the perfect infinitive after shall as denoting  ‘...events expected to be completed by a certain time in the future’ and give the example sentences: 

‘The Fund shall have performed all obligations required  to be performed by  it' 
'Buyer shall have received a certificate on behalf of the Fund to such effect.’ "

As to the old distinction, the two forms were apparently used in (S.E.) England in opposite ways, depending on the grammatical person:

First person - will = wishes, desires, shall = simple futurity
Second and Third persons - will = simple futurity, shall = obligation (hence the legal sense)

This explains this rather obscure linguistic joke: 'There was a non-English speaker of English (variously portrayed as French, Scottish, or Irish) who was drowning and cried out “I will drown; no one shall save me!”. The idea being that nobody would save him, because they thought he meant - 'I want to drown; no one should save me'.

What he should have said, of course, was 'I shall drown; nobody will save me', where both 'will' and 'shall' refer to simple futurity. Obvious, isn't it?

Fowler wrote quite a bit about this, but noted sadly 'It is unfortunate that the idiomatic use [of shall], while it comes by nature to southern Englishmen (who will find most of this section superfluous), is so complicated that those who are not to the manner born can hardly acquire it'. Nowadays, I doubt even a southern Englishman would make or even recognise the distinction.

I've written more about this here:

http://random-idea-english.blogspot.com/2010/12/do-you-think-people-will-still-say.html

Often it is hard to tell whether it is shall or will as it is only 'll. I do catch myself saying things like "Sh'we go?" "Washaweedoo?" - I guess I picked this up in childhood.
The legal use of shall with the second and third person is very similar to the same-rooted German word "soll": so maybe this is the original meaning.

@jayles - I think there are two separate things here:

1. standard contractions, which are used both in speaking and writing - where I would suggest 'll is never a contraction for shall - "We'll just have to see." (will) - or "We shall just have to see."

2. Natural spoken shortenings, as in your two examples - "We sh'll just have to see" (like gonna etc) - but when we want to say shall, there's always at least a sh', not just a 'll.

@WW I tend to agree.My understanding of Ngram is that the incidence of 'shall' is declining on both sides of the Atlantic, and American usage is no more or less than Brit, in writing at least.

@jayles - OALD marks shall as (especially British English). I still occasionally use it as an alternative to will in the first person, which I don't think is done much in North America. But I agree its use id declining.