syuttyouhi ga takai desu.

It is read:

しゅっちょうひ が たかい です。

Breakdown:

• 出張 = しゅっちょう = business trip
• 費 = ひ = expense / cost
• 高い = たかい = high / expensive
• です = polite sentence ending

So 出張費 means business trip expenses or business trip cost.

が marks the thing being described by the adjective.

In this sentence:

• 出張費が高いです = The business trip expenses are high / expensive.

You can think of it as:

• As for what is high? → the business trip expenses

With adjectives like 高い, が often marks what has that quality.

Yes, 出張費は高いです is also possible, but the nuance changes.

• 出張費が高いです
  Focuses more on the fact that the business trip expenses are high.
• 出張費は高いです
  Makes business trip expenses the topic, often with a slight contrast, like As for business trip expenses, they’re high.

In many everyday situations, both can work. Learners often see が here because it directly marks what is being described.

高い is an い-adjective.

For い-adjectives, you do not add だ in normal speech.
The polite form is simply:

• 高い → plain
• 高いです → polite

So:

• 出張費が高い。 = plain
• 出張費が高いです。 = polite

高いだ and 高いですだ are incorrect.

Not exactly.

In this sentence, です mainly adds politeness.
The adjective 高い already carries the meaning is high / is expensive.

So:

• 高い already means something like is expensive
• です just makes it polite

That is different from English, where you need is:

• English: The expense is high
• Japanese: 出張費が高い (already complete)

Here it means expensive or costly.

高い can mean both:

• high for height, level, price, etc.
• expensive for things that cost a lot

Because 出張費 is a cost, the natural meaning is:

• business trip expenses are expensive
• or more natural English: business trip expenses are high

Japanese usually does not require articles like the or a, and it often does not use a separate word for are / is in adjective sentences.

So:

• 出張費 can mean business trip expenses, the business trip expenses, or business trip cost, depending on context
• 高い already covers the idea of are high / are expensive

Japanese relies much more on context than English does.

No, normally Japanese is written without spaces:

出張費が高いです。

Spaces are often added only in teaching materials to make the parts easier to see.

Yes, it is grammatically natural and understandable.

It means something like:

• Business trip expenses are high.
• The cost of a business trip is high.

Depending on context, a speaker might also say:

• 出張費は高いです。
• 出張の費用は高いです。

But 出張費が高いです is a perfectly fine sentence.

The structure is:

noun + が + い-adjective + です

In this case:

• 出張費 = noun
• が = subject marker
• 高い = い-adjective
• です = politeness

This is a very common pattern in Japanese, for example:

• 値段が高いです。 = The price is high.
• 山が高いです。 = The mountain is high.
• 気温が高いです。 = The temperature is high.