A bond can make every promised payment while its market price falls. Discounted cash flow valuation explains that result by separating the bond's cash payments from the return buyers require.
When you compare bonds for a customer, first identify what the borrower promises to pay and when. A bond is a debt security: you lend money to an issuer, which promises specified payments. Par value, also called face value, is the principal amount the issuer promises to repay. It also provides the base for coupon interest.
The coupon rate determines annual interest as a percentage of par. Annual coupon interest equals coupon rate multiplied by par value. A 5% bond with $1,000 par pays $1,000 × 0.05 = $50 annually. With two equal payments, each coupon is $50 ÷ 2 = $25.
Your purchase price does not change those contractual coupons. A fixed-rate bond trades at a discount when its coupon rate is below the market's required yield, at a premium when above it. It trades at par when the two are equal.
Common mistakes
- Applying coupon to market price. A 5% coupon on $1,000 par pays $50 annually, even if you pay $900. The $45 answer uses the wrong base.
- Mixing annual and half-year inputs. A 6% nominal annual yield means 3% per half-year. Discounting both semiannual payments at 6% understates value.
- Treating duration as a dollar loss. Modified duration of 6 with a 0.5-percentage-point yield increase implies roughly −6 × 0.5% = −3%, not a $6 loss.
Bottom line
- Annual coupon interest equals coupon rate multiplied by par value.
- Discounted cash flow values coupons and principal using rates matched to their timing, risk and payment frequency.
- YTM uses maturity payments; YTC uses an assumed call date and call price, and either yield may be higher.
- For a callable bond, quote the customer the lower of YTC and YTM, the yield to worst.
Exam shortcut
Before calculating, circle what the question wants: cash income, price, yield, sensitivity or shares. That choice determines which inputs belong in the calculation. Draw the payment dates for valuation questions. Put coupons on each date and principal or call price on the final assumed date. For semiannual cash flows, halve the coupon and nominal annual yield, then double years. Convert basis points before using duration.
The full lesson (about 2,723 words, 18 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.
Learning objectives
- B3
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