"simple past tense" vs "present perfect"

I have a question regarding the usage of "simple past tense" vs "presen perfect tense" . Sometimes I see they are both possible to talk about a finished action. I know we cannot use "present perfect tense" to talk about a finished action that have mentioned time frame. But my question is different. Suppose, something happened yesterday but I do not want to mention the time rather I want to describe what happened. In this kind of situation which tense is appropriate?

Here's the context:

• I bought/have bought a mobile. It has a stunning look and takes nice pictures. I am very happy with it.

Please note that I bought the phone yesterday. I know if I used yesterday in that sentence I had to use "simple past tense". But as I have not mentioned any time frame, Can I use both the tenses?

Please also note that I just suddenly start a conversation with "I bought a mobile", with no preamble.