Working Backwards from Future Needs

If your organisation has 20,000 members in the year 2009, bringing in £200,000 per year, and it will need to spend £550,000 in 2013, then in 2013 you will need 55,000 members, (unless you are absolutely sure of developing alternative sources of income). Can this be achieved?

2010 2011 2012 2013
Start of year 18,000 34,200 48,780 61,902
Add in year 20,000 20,000 20,000
Total at end 38,000 54,200 68,780
which will give you a margin of error of better thatn 10%. Over four years this would be most welcome!
This is a simplified example with no account taken of inflation or other changes in the economy, or increases in membership fees or average donations. New members arriving during 2013 have also been ignored, and, for clarity it was assumed people all leave at the end of the year.
So the investment now needed is enought to bring in 20,000 new mwmbers earch year plus the full costs of servicing those members and appealing to them for extra funds. Is this available?
If a member stays with you for six years on average, and contribures £30 per year on average, in total they are worth (6 x £30) = £180 over their ‘lifetime’ with you. If the newsletter costs £4 per head per year and all other servicing costs £3 per head per year then the member would cost (6x£7) = £42 over their ‘lifetime’. So each member is worth (£180-£42) = £138 to you.
If an advertisement campaign costs £10,000 and brings in 100 members with an average donation of £18 your immediate loss will be £8,200. Over, say, the next six years these members will bring in (100 x £138) = £13,800 showing a long-term profit of £5,600. The question we must now ask is, ‘Is this too close for comfort?’.
If, instead 200 people joined, the immediate loss would be (£10,00 – (200x£18)) = £6,400, but over six years they would bring in (200 x £138) = £27,600 and yield a profit of £21,200. Is this more acceptable?
If, say, 400 people joined, the immediate loss would be (£10,000 – (400 x £18)) = £2,800, but over six years they would bring in (400 x £138) = £55,200 and generate a profit of £52,400. Do you have a more profitable and secure way of raising funds?