Lets say that I have the average monthly searches, competition, top of page bid (low range) and top of page bid (high range) and also 10% CTR for a keyword.
How can I calculate the maximum and the minimum monthly budget for that keyword?
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Competition isn't entirely relevant as a separate factor (it does impact CPC and CTR, but you already have ideas for these).
Basic figures would be: Minimum: (Avg monthly searches / expected CTR) * Top of page (low range) Maximum: (Avg monthly searches / expected CTR) * Top of page (high range)
This would give you what you should expect to set as a monthly budget without limiting yourself. Then you also have how much you can spend, what you're expected return on ad spend would be, and whether you're refining your audience with negative keywords (almost every industry will have irrelevant searches on their most trafficked keywords, which will make the average monthly searches lower once removed).
Then you have to factor in that if you can get a good quality score (mostly on relevance of ad copy and landing page to the keyword in question), you won't have to bid as high to get the same position (quality score + bid = adrank, the higher the quality score, the lower the bid needs to be).
So, you can make some educated guesses as to a recommended budget, but I always tell my clients to start their budget at what they're willing to spend and then see how that works in reality. You can always change things after you've started.
A 10% CTR is quite high. From what we've seen on running Ads is that:
Branded terms (the company you're providing Ads services for) will receive high CTRs - around 20-40%
Emergency type phrases that deem people want to get service very quickly and don't want to look through the entire front page will receive 15 - 35% CTR. Examples, emergency plumbers, electricians, locksmiths.
For non-branded and non-emergency or urgent services you're more likely looking at 5-8% CTR