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Which one is correct "cost" or "costed"

The website, englisch-hilfen, says that the word "cost" does not change in three different tense form (past, present, and past participle). However, the dictionary has used the word "have costed" in their explanation. So which one is correct?

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    Note that your dictionary assigns the form costed to the past and past participle only for definitions 10, 11, 12, which have the derivative sense "determine the cost". In effect, it's a different verb.
    – StoneyB on hiatus
    Commented May 2, 2016 at 7:14
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    I suggest using a better dictionary, such as Oxford Online or the Oxford learner's version.
    – Alan Carmack
    Commented May 3, 2016 at 1:14

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Both cost and costed can be used; it depends on the sense in which you use them.

if you use the verb cost as a linking verb to imply to have an amount of money as a price, then it doesn't change in all the tense forms i.e. the present, past, past participle. For example, it costs/cost/has cost me five dollars.

However, if you use 'cost (out)' as an action verb to mean to determine or estimate how much something will cost you, then you can use costed as past tense and past participle. For examples:

We haven't yet costed (out) the proposal.

The project was costed (out) at $2.5 million.

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