"I will have read that book by Wednesday."
Translation:Do středy tu knihu přečtu.
It is grammatically correct and it is a translation of this sentence. It is not grammaticalized to a full new perfect tense, but the words do have that meaning. I am not sure if it is originally a syntactic germanism or not (certainly not anglicism, it is too old for that).
There is an interesting comparison between Czech and English in V. Mathesius - A Functional Analysis of Present Day English on a General Linguistic Basis:
This is the well-known difference between the English preterite and the present perfect (I saw — / have seen). In Czech this difference usually remains unexpressed as can be shown by Tak jsem si včera roztrhl kalhoty [Yesterday I tore my trousers] and Podívej se, jak jsem si roztrhl kalhoty [Look, I have torn my trousers].
Only colloquial Czech has started to develop a special “perfect” type with the verb mít [to have]: Mám kalhoty roztržené [I-have trousers torn]. It is to be stressed that the Present Day English observes the difference between the preterite and the present perfect very strictly.
I am not sure if it is still colloquial only. The SSČ dictionary shows this without any such remark.
I did not read the above book, I have just find the above part when searching something a few days ago.
Sorry for creating confusion. I was referring to the original exercise (budu mít … přečtenou), which resembles the German future 2 (future perfect). Of course you are right that Mám kalhoty roztržené corresponds to the German perfect, which is very common, contrary to future 2. And yes, the German perfect is superseding the preterite, at least in oral usage.
I have to admit that I had never met the Czech mít perfect before but of course my Czech is very elementary.