# How Do They Arrive At This Simple Formula For Cost of Funds Against Discounts?

#### abrogard

##### New member
There is this formula I can't understand. It finds for you whether it is better to pay a debt early and take the discount for early payment or to wait until the last minute to pay.

Setting, as I understand it, the benefit from the reduced debt amount - i.e. debt minus discount - against your own Cost of Funds, i.e. the interest you'd have to pay for that period at your interest rate.

And this is it: " % value of discount = % prompt payment discount X 365
100 - % prompt pay discount Credit days forgone.

So if we have: Cost of funds: %10
Discount for prompt: 2%
Prompt payday; 10 days.
Credit term: 30 days.
therefore days forgone: 20 days.

the formula becomes : 2/100-2 x 365/20

= 2/98 x 365/20

= 37.24%

which is greater than the 10% cost of funds therefore take the discount.

I understand virtually nothing and am seeking help. Because I don't seem to be able to nut it out.

Why not, I think in the first instance, find the difference between money saved on the debt and the interest cost on the debt for that 20 day period?

Money saved on the debt is easy, it is given: 2% You've saved an overall 2% of the debt.

Cost for 20 days on that debt would be 10% p.a. rate / 365 x 20, wouldn't it? = 0.547% my calculator says. Which seems about right to me.

So you're obviously heaps ahead with the discount.

That's my thinking. But for decades ( or centuries? ) financial gurus have gone the other way so I must be wrong. Back to the formula and I can't understand.

Take the first term. discount/100-discount. i.e. 2/98. What has happened here? What does this mean? Why are we doing this?

It looks to me like calculating a percentage. What percentage is 8 of 57? I do it like that, don't I? 8/57 and get 0.147 which I can either read as a percentage or multiply by 100 and say that's the percentage. 14.7 I've never quite understood those two ways of going, either.

So if it is a percentage it doesn't make sense to me. What's it matter what percentage 2 is of 98?

Then the second and last term: 365/days forgone: 365/20 = 18.25.

That's the number of 'forgone' periods there are in a year. Why do we care about that? Multiply that by what percentage 2 is of 98 ??

I'm obviously a slow and poor thinker and very confused.

It'd be wonderful if someone could dispel the cloud of confusion in my head. 