http://altoidnerd.wordpress.com/2013/11/07/when-should-i-sell-my-bitcoin-mining-hardware-bitcoin-mining-hardware-resale-value-vs-projected-return/
It should be educational, as long as I hope it doesn't discourage you from mining! I still mine myself, because getting involved with bitcoin in all ways is best.
Cheers
There are some errors in the calculation in that blog.
First, the daily mining income is computed by taking ones fraction of the network hashrate compared to the total hashrate and multiplying that with the amount of coins generated per day. However, for this last term, the target-rate of 1 block per 10 minutes is used. In the scenario of exponentially increasing difficulty (which is assumed later on), a rate of (1 + D) blocks per 10 minutes should be assumed (where D is the fractional difficulty increase per adjustment).
Since the global network hashrate is an estimate at best, a more accurate way to estimate personal mining income is to look at the average time to find a block for given hashrate and difficulty, which is:
time = difficulty * 2^32 / hashrate (source: https://en.bitcoin.it/wiki/Difficulty)
The amount of coins mined per day at current difficulty is then:
coins/day = 25 * 24 * 3600 * hashrate / (difficulty * 2^32)
Next, the length of each difficulty-cycle depends on the size of the adjustment. If the difficulty goes up with 20%, that means blocks were found 20% too quickly for the last 2016 blocks, so those 2016 blocks were mined in 14 / 1.2 = 11.67 days. This changes the outcome of the summation of the geometric series.
If we take X as the amount of coins mined per day at current difficulty and D the fractional difficulty increase per cycle (so 20% -> D = 0.2), we see that the length of each cycle will be 14 / (1 + D) days. During the first cycle, we mine X * 14 / (1 + D) coins. Each next cycle, this goes down by a factor 1 / (1 + D), so we obtain the sum (n from 0 to infinity):
Sum( X * 14 / (1 + D) * (1 / (1 + D))^n )
= X * 14 / (1 + D) * Sum( (1 / (1 + D))^n )
= X * 14 / (1 + D) * [ 1 / (1 - 1 / (1 + D)) ] (using the sum formula for a geometric series)
= X * 14 / (1 + D) * [ 1 / (D / (1 + D) ) ]
= X * 14 / (1 + D) * (1 + D) / D
= X * 14 / D
So when you count in the fact that difficulty adjustments come faster with higher difficulty, the expression for the total amount mined becomes quite simple: 14 / D times the daily income. So with an increase of 25% per adjustment, a miner will at most mine 56 times what it mines today in its lifetime.
There are obvious flaws with the current model of infinite exponential growth, but for the short term it's actually a pretty good approximation.
Was I close? I (should have) admitted the whole thing is an approximation i empirically found to be correct.