Við metum kostnaðinn.

Yes — við can be either:

• the pronoun we
• or a preposition with meanings like with, against, by, depending on context

In Við metum kostnaðinn, it means we because it is the subject of the verb metum.

So here the structure is:

• Við = subject
• metum = verb
• kostnaðinn = object

As a preposition, við would normally be followed by a noun phrase, for example við húsið.

The dictionary form is meta.

Metum is the 1st person plural present tense form, so it means we estimate / we assess / we evaluate, depending on context.

A useful way to think of it is:

• að meta = to estimate / assess / evaluate
• við metum = we estimate / assess / evaluate

In this sentence, -um marks the verb as 1st person plural in the present tense.

So:

• ég met = I estimate
• þú metur = you estimate
• hann/hún/það metur = he/she/it estimates
• við metum = we estimate

So the ending tells you that the subject is we.

No. Meta is a flexible verb and can mean things like:

• estimate
• assess
• evaluate
• value

The exact English translation depends on context.

So Við metum kostnaðinn could be understood as:

• We estimate the cost
• We assess the cost
• We evaluate the cost

If the meaning has already been given to you, that is the best translation for this specific sentence, but it is good to know that meta is broader than just one English verb.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word.

So instead of a separate word like English the, Icelandic often uses a suffix:

• kostnaður = cost
• kostnaðurinn / kostnaðinn = the cost

The exact form changes with case, which is why you do not always see the same ending.

Because this noun is the direct object of the verb meta, and that means it appears in the accusative case.

The dictionary form is kostnaður.
But when it becomes a direct object, it changes form:

• kostnaður = cost, in the nominative
• kostnað = cost, in the accusative
• kostnaðinn = the cost, in the accusative definite

So kostnaðurinn would be the nominative definite form, but this sentence needs the accusative definite form kostnaðinn.

It is accusative singular definite.

Why?

• meta takes a direct object
• direct objects are often in the accusative in Icelandic
• kostnaðinn is the thing being estimated/assessed

So:

• subject: Við = nominative
• verb: metum
• object: kostnaðinn = accusative

Við is in the nominative case because it is the subject of the sentence.

That is the normal case for the subject of a finite verb in Icelandic.

So:

• Við = nominative subject
• kostnaðinn = accusative object

Usually, no. Icelandic normally keeps the subject pronoun in ordinary statements.

So the normal sentence is:

• Við metum kostnaðinn.

Leaving out við would usually sound incomplete, unusual, or like a different structure depending on context.

Unlike some languages, Icelandic is generally not a language where subject pronouns are regularly dropped just because the verb ending shows the person.

This is the most basic and neutral order: subject + verb + object.

But Icelandic also has verb-second word order in main clauses, which means the finite verb often comes second even if something else is placed first.

For example:

• Við metum kostnaðinn. = neutral
• Núna metum við kostnaðinn. = Now we estimate the cost

So the sentence you have is the straightforward default pattern, but other word orders are possible depending on emphasis and sentence structure.