FINM1001 Chap.4 Valuing Debt Instruments
Valuing Debt Instruments
Price promised cash flows on the coupon clock
A coupon bond combines a finite annuity of coupon payments with one face-value payment at maturity. A zero-coupon bond contains only the maturity payment. Both are present-value problems; the specialised notation simply organises their cash-flow shapes.
Quoted coupon rates determine coupon dollars from face value.
Required yield discounts the promised cash flows at the current market price. For semiannual coupons, divide the annual coupon dollars and a nominal annual yield by two, then count half-year periods. Face value is not divided because it is paid once at maturity.
The premium, par and discount relationship provides a pre-calculation check.
Coupon rate above yield implies a premium because contractual interest exceeds the market requirement. Equal rates imply par. Coupon rate below yield implies a discount because a lower price must supplement the small coupons and raise total return to the required yield.
Read zero-coupon quotation conventions carefully
A zero-coupon price is face value discounted from maturity.
The periodic rate still depends on the stated quotation basis. Longer maturity yields may be given as annual effective rates, while short discount instruments can use nominal quotations over days. Use the convention supplied by the course question instead of importing one basis into every instrument.
Reasonableness checks are powerful. At a positive yield, a zero-coupon price should be below face value.
Holding yield fixed, its value rises toward face value as maturity approaches. For a coupon bond, recompute at yield equal to coupon rate and confirm the price becomes par. These checks reveal omitted principal, wrong period counts and frequency mismatches.
A complete answer shows coupon amount, periodic yield, number of periods and face value before the valuation line.
It finishes by naming the dollar price and whether the bond trades at a premium, par or discount. That interpretation is part of the finance reasoning, not optional commentary.
What this chapter covers
- 01
Coupon cash flows
- 02
Periodic yield
- 03
Bond pricing
- 04
Premium and discount
- 05
Zero-coupon debt
Worked example · free
Price a semiannual coupon bond
- 1Convert the coupon to dollars per half-year.
- 1Convert yield and count half-year periods.
- 1Discount coupons and face value.
- 1Check the result against par.
Key terms
- Coupon payment
- The contractual periodic interest cash flow calculated from face value, coupon rate and payment frequency.
- Face value
- The principal amount promised at maturity and used as the base for calculating coupon payments.
- Bond premium
- A price above face value, typically occurring when the coupon rate exceeds the required yield under standard positive-yield conditions.
- Zero-coupon bond
- A debt instrument with no periodic coupons whose value comes from discounting a single face-value payment at maturity.
Valuing Debt Instruments FAQ
Why are coupon and yield divided by frequency?
Coupons occur on the shorter payment clock, so both coupon dollars and the nominal quoted yield must be expressed per coupon period before discounting every promised payment.
Why is face value not divided?
Face value is one contractual payment at maturity rather than an annual quotation. It is discounted once over the full number of coupon periods to the selected valuation date.
How can I predict premium or discount?
Compare coupon rate with required yield. Coupon above yield suggests premium, equality suggests par, and coupon below yield suggests discount under the standard coupon-date valuation setup.
What is the main zero-coupon trap?
Students often ignore the quotation basis. Identify whether the yield is effective or nominal and match the rate and period count to maturity before discounting face value.
Exam move
Rebuild every bond as a cash-flow timeline. Practise converting quotations, pricing coupons and principal separately, and predicting the side of par before using a calculator. Reconcile price with the sources of return: coupon cash flows and any difference between purchase price and face value received at maturity. A discount compensates for coupons below the market requirement; a premium offsets coupons above it.
Create pairs of otherwise identical bonds and change only yield, coupon rate, maturity or payment frequency. Predict price direction before recalculating and record which cash-flow channel caused it. When a question values a bond between coupon dates or under a stated day-count convention, follow the specific method supplied rather than silently extending the standard coupon-date formula.
Retain the separation between promised cash flows and market-required yield. Confusing them can produce a plausible par price for every bond, erasing the economic purpose of valuation. During a speed set, write coupon per period, yield per period and number of periods in a small input box. Check the finished price against par before interpreting it; the coupon-yield comparison should explain the direction immediately.
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