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A company is offering a cash discount of 2.5% to receivables if they agree to pay debts within one month. The usual credit period take is 3 months.
What is the effective annualized cost of offering the discount and should it be offered, if the bank would loan the company at 18% pa?
My answer:
Assuming an invoice of $100.
Without discount 3 months $100
With discount 1 month $97.503 months – 1 month = 2 months
$100 – $97.50= $2.502.50/97.50 * 100 * 12/2= 15.38%
Study Text says the answer is 16.38%.
Where did I go wrong?
The interest for 2 months is 2.50/97.50 x 100 = 2.56%
To turn it into an annual rate, the simple way is simply to multiply by 6 (which is what you have done) which does give 15.36%
However, strictly, to turn it into an annual rate we should compound and it means that the annual rate is (1 + r)^6 – 1 (where r is the 2 month rate).
So…..1.0256^6 – 1 = 0.1638 or 16.38%‘Simple’ discount have only been asked twice (for very few marks) and both times the examiner accepted either of the two answers above. Strictly the second answer (the one in your study text) is more correct.
Ok. Thanks a million.
I passed F5 with 69% (Just got my results).
Thanks for all the help.
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