Let the face value of commercial paper be denoted by F.V., net amount realised from the commercial paper be NAR, maturity period of commercial paper be MP. The effective pre - tax cost of commercial paper shall be :
\(\dfrac{(F.V. - NAR)}{NAR} \times \dfrac{360}{MP}\)
Option 4 — \(\dfrac{(F.V. - NAR)}{NAR} \times \dfrac{360}{MP}\) is correct.
Commercial paper is an unsecured, short-term promissory note issued at a discount and redeemed at face value. The issuer receives only the net amount realised (NAR) but must repay the full face value (F.V.) at maturity, so the discount (F.V. – NAR) is the effective cost of borrowing.
The formula is built in three logical steps:
| Step | Meaning |
|---|---|
| \(F.V. - NAR\) | The discount — the rupee cost of the borrowing |
| \(\dfrac{F.V. - NAR}{NAR}\) | Cost expressed as a rate on the funds actually received |
| \(\times \dfrac{360}{MP}\) | Annualises the periodic cost (MP = maturity in days, 360-day year) |
Why the other options are wrong: Option 1 gives only the absolute discount, not a rate. Option 2 divides by MP instead of annualising, understating the cost. Option 3 multiplies by 360 but omits the maturity period, so it is not annualised correctly.
Takeaway: Effective pre-tax cost = discount over net proceeds, annualised by \(\dfrac{360}{MP}\).
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