Any pricing will be removed by the mods - if you spot any hit the report post button! This allows fair competition for people wanting the job.
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To the OP it's not at your discretion to decide the budget on the time - budget is for monetary purposes only.
You'd pay a doctor £50 on a visit whether you're there for 1 minute or an hour, you'd pay a mechanic to fix a problem with a car for parts plus labour - and you can't tell a mechanic how long it takes to fix something, even if you feel it's simple ... and so on.
It might take 3 hours to draw the outline for your piece, it might take 30 minutes! Nobody could guestimate that without seeing it, and it's all dependent on experience.
And your logo will need to come with many versions which take to setup.
You'll need a
4 colour process logo
2/3 colour version in spot colours
Single colour black and white (not grayscale)
All of the above in high resoltuion version and vector versions in
AI format
EPS format (for antiquated workflows *glances at quark users*)
TIFF/PSD format
And you'll also require all of the above in versions for
Web
Microsoft Office
You'd be looking at about 20-30 versions of your logo in various formats and sizes.
This is why it takes longer to do - this is why you need an expert designer who knows the system.
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Don't forget you'll need your logo to be compatible for different printing processes and electronic distribution, such as web, litho, flexo, screen printing, embroidery, faxing, emailing and many other iterations.
You may also need your logo be designed so that it's a good
FavIcon! Or is legible at small sizes in print and on an App for Android or iPhone.
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Sure you can go ahead and get a logo done for £50 - but you get what you pay for.
Pay a real designer who knows what they're doing and save yourself £££ and time down the road. If you don't pay for it now you'll pay much for it later.