Financial & Accounting
Zero-Coupon Commercial Paper: PRICEDISC, YIELDDISC, RECEIVED & INTRATE Formulas
Price discounted money-market bills and commercial paper per $100 par (PRICEDISC), compute true money-market investment yield (YIELDDISC & INTRATE), and determine maturity redemption value (RECEIVED).
Bank discount rate on par vs true investment yield on purchase outlay
Short-term zero-coupon commercial paper, banker’s acceptances, and money-market bills are quoted on a bank-discount rate d applied to maturity par R rather than purchase price P: over DSM = maturity - settlement days on day-count basis B (360 for Actual/360 or 365 for Actual/365), PRICEDISC = R * (1 - d * DSM / B).
Because the investor actually deploys less than par (P < R), true money-market yield YIELDDISC (and INTRATE) divides the dollar discount R - P by purchase outlay P: YIELDDISC = ((R - P) / P) * (B / DSM). Conversely, investing cash amount Inv at discount rate d matures to RECEIVED = Inv / (1 - d * DSM / B).
| Money-Market Metric | Closed-Form Equation | 90-Day Paper (d = 5.20%, Actual/360) | Economic Interpretation |
|---|---|---|---|
| PRICEDISC (per $100 par) | 100 * (1 - d * DSM / B) | $98.70 | $1.30 discount deducted upfront |
| YIELDDISC / INTRATE | ((100 - P) / P) * (B / DSM) | 5.2685% | True return on $98.70 invested |
| RECEIVED ($987,000 outlay) | Inv / (1 - d * DSM / B) | $1,000,000.00 | Par payout redeemed at maturity |
Discounted Security Price per $100 Par (PRICEDISC)
Computes clean discounted purchase price per B4 ($100) redemption value over DSM = B3 - B2 days on day-count basis B6 (360 or 365).
=IF(OR(B3 <= B2, B5 < 0, B6 <= 0), "Invalid Terms", ROUND(B4 * (1 - B5 * (B3 - B2) / B6), 4))Money-Market Yield (YIELDDISC / INTRATE) & Maturity Proceeds (RECEIVED)
Computes the true annualized money-market yield earned when buying at discounted price P and holding to maturity.
=LET(dsm, B3 - B2, price, B4 * (1 - B5 * dsm / B6), ROUND(((B4 - price) / price) * (B6 / dsm), 6))Try the example
Use the original values or change them to test your understanding.