# Math Help - Pro-rated percentage increase formula - help.

1. ## Pro-rated percentage increase formula - help.

I need some help creating a formula to calculate a percentage increase for an incomplete pro-rated agreement.... Ok, that probably doesn't explain much! Let's try again:

I recently agreed to do a pre-determined volume of bulk work over the next year at a discount. To keep things simple, I offered a 40% discount from my regular rates on the assumption that I would be paid for all the jobs on a monthly basis. However, there is the chance that my contract could be terminated early. In such a case, I want to be paid a pro-rated percentage on the volume of work completed so far. For example, if I had completed 50% of the work and was fired, then the client would only get a 20% discount for all the work done up to that point.

The formula that I came up with goes like this (let's assume there are 300 jobs in total and I completed 150, or half, before the client cancelled the contract): 150/300*40%=20%. So in this case, because the client had essentially only paid me for half of the original full bulk contract, they would only be entitled to a 20% discount from the normal rates (rather than the 40% discount which applied only to a full bulk contract).

NOW, this is all nice and we can do the reverse math by multiplying the original price by 20%, BUT I've already offered a pricing list which has all the discounted (40%) prices. Essentially, I want to offer the client a formula that they can apply to the discounted rates that they would have paid up to whatever point I would theoretically get terminated (that is, the full amount of money I had collected upto that point) so they can easily determine how much they owe me for the early termination. I can't simply multiply the already discounted rates by 20%, for instance... I hope this makes sense. Ideas anyone?

By the way: if this post belongs in another thread/forum topic, please let me know which and I'll move it.

Thank you!

2. Originally Posted by pr71
I need some help creating a formula to calculate a percentage increase for an incomplete pro-rated agreement.... Ok, that probably doesn't explain much! Let's try again:

I recently agreed to do a pre-determined volume of bulk work over the next year at a discount. To keep things simple, I offered a 40% discount from my regular rates on the assumption that I would be paid for all the jobs on a monthly basis. However, there is the chance that my contract could be terminated early. In such a case, I want to be paid a pro-rated percentage on the volume of work completed so far. For example, if I had completed 50% of the work and was fired, then the client would only get a 20% discount for all the work done up to that point.

The formula that I came up with goes like this (let's assume there are 300 jobs in total and I completed 150, or half, before the client cancelled the contract): 150/300*40%=20%. So in this case, because the client had essentially only paid me for half of the original full bulk contract, they would only be entitled to a 20% discount from the normal rates (rather than the 40% discount which applied only to a full bulk contract).

NOW, this is all nice and we can do the reverse math by multiplying the original price by 20%, BUT I've already offered a pricing list which has all the discounted (40%) prices. Essentially, I want to offer the client a formula that they can apply to the discounted rates that they would have paid up to whatever point I would theoretically get terminated (that is, the full amount of money I had collected upto that point) so they can easily determine how much they owe me for the early termination. I can't simply multiply the already discounted rates by 20%, for instance... I hope this makes sense. Ideas anyone?

By the way: if this post belongs in another thread/forum topic, please let me know which and I'll move it.

Thank you!

You and I are going to run a little risk here: I run the risk of dealing with this applied-maths

problem whereas I'm definitey more pure-maths oriented, and you run the risk

that what I do here is trash:

I think that what you want to know is what discount must you offer (and what formula

to produce) to your clients if your contract is terminated after some fraction of the

original one year, so it is simply a rule of three (or whatever this is called in engish):

if by the whole work (1) you give 40% discount, then for a proportion of r (r < 1) of this

work, you must give $40\cdot r%$ discount...

Thus, if your work is terminated after a portion r of that 1 year, you must charge

$\displaystyle{x-\frac{40r}{100}x=(1-0.4r)x$ , where x = the original price for

the whole one year work without discount.

Tonio

3. Originally Posted by tonio

Thus, if your work is terminated after a portion r of that 1 year, you must charge

$\displaystyle{x-\frac{40r}{100}x=(1-0.4r)x$ , where x = the original price for

the whole one year work without discount.
Thanks Tonio. Excuse my ignorance, but what am I solving for? I'm not a math student... this is an actual business problem I'm currently having during contracts negotiation. Can you please show me how to use this formula, an example? Thanks!

4. Originally Posted by pr71
I recently agreed to do a pre-determined volume of bulk work over the next year at a discount. To keep things simple, I offered a 40% discount from my regular rates on the assumption that I would be paid for all the jobs on a monthly basis. However, there is the chance that my contract could be terminated early. In such a case, I want to be paid a pro-rated percentage on the volume of work completed so far. For example, if I had completed 50% of the work and was fired, then the client would only get a 20% discount for all the work done up to that point.
Completing 50% means 6 months (you did state over the next year...), and you
have been paid on a regular basis for these 6 months, after allowing 40%...
So I fail to see what you're asking...

5. Perhaps pr71 is asking how to incorporate some limitations on the current price list (which has 40% off for all jobs) in case the contract is terminated earlier than [agreed? expected? not clear]. I am in business, so I'd prefer another method - to give a full price list and then a system of volume discounts granted after the client met some volume targets for the year. But, you gave them the 40% discounted prices already. Now what you can do is to include a clause in the contract that the attached prices are discounted by 40% and are only applicable if [contract is completed... bla bla bla...) and otherwise the 'full' prices are applicable (or with 20% discount, if you wish). In such case, upon termination of the contract, you'd recalculate the total contract value at full/20% off price and submit a new bill.

By the way, if it's a business problem you are trying to solve here, we need much more information than was given. Based on the sketch of the situation, I gave my opinion above.