Kiel ajn granda estas la takso, li klarigos ĝin.

Here kiel ajn means however or no matter how.

So Kiel ajn granda estas la takso... means However large the assessment/estimate is... The idea is concessive: the main statement stays true regardless of the size.

Ajn adds a sense like ever, any, or no matter which/how.

Compare:

• kiel granda estas la takso? = how large is the assessment?
• kiel ajn granda estas la takso = however large the assessment is / no matter how large the assessment is

So ajn is essential here. Without it, the sentence would no longer have the meaning no matter how.

Because kiel ajn granda works as a unit meaning however large.

Esperanto often keeps those words together:

• kiel ajn granda = however large
• kiel ajn malfacila = however difficult
• kiel ajn rapide = however quickly

Putting granda there makes the pattern very clear and natural.

Esperanto word order is fairly flexible. Here the sentence starts with the idea being emphasized: however large.

So the structure is naturally:

• Kiel ajn granda estas la takso...

This keeps the focus on granda. A more neutral order like la takso estas granda is possible in ordinary statements, but here the chosen order fits the kiel ajn + adjective pattern better.

Because granda is a predicate adjective after estas, not a direct object.

In Esperanto, predicate adjectives do not take the accusative -n. They agree in number, but not as objects.

So:

• la takso estas granda = correct
• la takso estas grandan = incorrect

If the noun were plural, then you would say:

• la taksoj estas grandaj

La shows that this is a specific assessment/estimate, something known from the context.

• la takso = the assessment / the estimate
• takso = an assessment / an estimate

So the sentence is talking about a particular one, not just any assessment in general.

Ĝin refers back to la takso.

The verb klarigi takes a direct object: you explain something. That object is marked with -n.

So:

• li klarigos ĝin = he will explain it

Here ĝin = la takso.

Because the two verbs describe different things:

• estas describes the state of the assessment: how large it is
• klarigos describes the later action: he will explain it

Esperanto chooses tense by meaning. The sentence says, in effect:

Whatever its size is, he will explain it.

If the speaker wanted a different time relationship, a different tense could be used, but this version is completely normal.

Yes. Kiel ajn granda estu la takso is also possible.

Using estu can sound a bit more formal, literary, or hypothetical, like whatever size the assessment may be.

So both are possible, with a slight difference in tone:

• Kiel ajn granda estas la takso... = straightforward, plain
• Kiel ajn granda estu la takso... = a bit more formal or abstract

Takso is a fairly broad word. Depending on context, it can mean things like:

• assessment
• estimate
• valuation
• rating
• appraisal

So the best English translation depends on the situation.

Also, it does not automatically mean tax. For tax, Esperanto usually uses imposto.

Not exactly. It is more concessive than conditional.

• Se la takso estas granda... = If the assessment is large...
• Kiel ajn granda estas la takso... = No matter how large the assessment is...

The second one means that the size does not change the result: he will explain it anyway.