Trade credit cost of a firm

CFA Level I
#1

in the trade credit cost formula for a firm, I do not get why you divide the discount rate by (1 - discount rate). In the formula.

Could someone explain the intuition behind this reasoning?

Thanks!

#2

not sure if this helps…

you gave someone a discount of x%. That was a trade credit. You spent (1-X)% and gave them X%. So trade credit cost = X/(1-X).

#3

Schweser notes give an intuitive explanation (which is very much in line with the explanation above by cpk123 ):

The formula for the cost of trade credit is very similar to converting HPY to an effective annual return, where the term:

disc.rate/(1-disc.rate)

is the holding period return to the firm of taking advantage of a discount. Say you are supposed to pay $100 and get a 2% discount, then you end up paying $98 and “gain” $2. Then we compute:

0.02/(1-0.02)=2/(100-2)=0.02041

Which is our return on an “investment” of $98 (from the perspective of the buying firm, who has to pay). Of course this only holds, IF we actually use the discount. Obviously for the cost of trade credit, we then want to know what the cost is of not taking the discount, and thus we do the whole annualizing afterwards.