Discount bonds and reconcile settlement prices

Learning goals

• Explain present-value engine using mechanisms and limitations.
• Explain price relationships using mechanisms and limitations.
• Explain settlement and comparables using mechanisms and limitations.

Draft · approximately 35 minutes, excluding further revision.

Present-value engine

Bond value discounts every remaining payment at compatible periodic rates; annual yield and payment frequency must be reconciled before calculation.

For an option-free fixed-rate bond, a higher required yield lowers price when cash flows stay unchanged; convexity makes this relationship nonlinear.

Price relationships

A coupon above the yield generally produces a premium price on a coupon date; coupon below yield produces a discount under standard fixed-payment assumptions.

Between coupon dates, full price includes accrued interest while the quoted clean price excludes it; apply the contractual day-count convention.

Settlement and comparables

Matrix pricing estimates a less-traded bond’s yield or price from comparable credit, maturity and structure; interpolation does not eliminate issuer-specific risk.

Pull to par describes price convergence toward repayment as maturity approaches when yield and promised cash stay unchanged; default or yield changes can overwhelm it.

Fractional settlement and matrix interpolation

A bond pays3 per half-year on face100. At settlement exactly halfway between coupons, the next coupon is0.5 periods away and two payments remain:3 and103. Nominal annual YTM6% compounded semiannually gives periodic3%. Full price=3/1.03^0.5+103/1.03^1.5=101.4889; accrued coupon=1.5 under the stated equal-half convention, so clean price99.9889. Actual accrued days require the contract day count.

Suppose comparable credit/structure bonds yield4% at two years and5% at four years. Linear maturity interpolation gives4.5% at three years. Price the target’s own dated cash flows at that estimate, then assess issuer-specific and liquidity differences. Interpolating yield is an assumption, not the same as interpolating price or constructing a complete arbitrage-free curve.

Formula and assumptions

Full price=Σ CFt/(1+y/m)^(mt); full=clean+accrued

Original applied case: Discount bonds and reconcile settlement prices

1. A two-year bond pays 5 annually and 100 principal; required annual yield is 6%.
2. Price=5/1.06+105/1.06²=98.1666 on a coupon date.
3. The discount is consistent with coupon below yield; it is not proof of imminent default.

Errors to catch

• Do not assume: Annual yield can be used as a semiannual rate unchanged.
• Do not assume: Fixed-rate bond prices rise whenever yields rise.
• Do not assume: A coupon above yield always implies a discount.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov