FNCE90065 Chap.7 Loans, Bonds and Effective Rates
Loans, Bonds and Effective Rates
Loans and bonds package dated contractual cash flows. This chapter values bond coupons as an annuity and face value as a single maturity payment, using the market yield rather than the coupon rate for discounting. It explains premium, par and discount prices, converts payment frequency consistently and distinguishes yield to maturity from realised holding-period return.
The fastest reasonableness test compares coupon rate with market yield before calculation.
What this chapter covers
- 01
Coupon rate multiplied by face value determines the contractual coupon
- 02
Market yield discounts the remaining bond cash flows
- 03
Bond price equals coupon-annuity value plus principal present value
- 04
Coupon above yield implies a premium; coupon below yield implies a discount
- 05
Payment frequency changes coupon, periodic yield and number of periods together
- 06
Longer maturity and lower coupons generally increase interest-rate sensitivity
Worked example · free
Price a fixed-coupon bond
- 1Calculate the annual coupon as $50.
- 1Value the three coupons as an annuity at the 6 percent market yield.
- 1Coupon present value is approximately $133.65.
- 1Principal present value is approximately $839.62.
- 1Total price is approximately $973.27, below par because coupon rate is below yield.
Key terms
- Coupon rate
- Coupon rate is the contractual annual coupon expressed as a percentage of face value.
- Face value
- Face value is the principal amount promised at bond maturity and used to calculate coupons.
- Market yield
- Market yield is the return currently required on comparable bond cash flows.
- Premium bond
- A premium bond trades above face value because its coupon is attractive relative to market yield.
- Discount bond
- A discount bond trades below face value because its coupon is low relative to market yield.
Loans, Bonds and Effective Rates FAQ
Why do bond prices fall when yields rise?
A fixed-coupon bond promises the same cash flows regardless of the new market yield. When investors require a higher return, those payments are discounted more heavily and their present value falls. The inverse relationship is curved because discounting is nonlinear.
What is the difference between coupon rate and yield?
Coupon rate determines the contractual coupon from face value. Market yield is the discount rate investors require and therefore determines current price. When coupon rate exceeds yield the bond trades above par; when coupon rate is below yield it trades below par.
How do I set up a semiannual bond?
Divide the annual coupon into two payments, convert the quoted yield to a half-year rate under the stated convention, and double the number of years to obtain periods. Do not divide face value; it remains one principal payment at maturity.
Exam move
Begin every bond question by predicting premium, par or discount from coupon rate versus yield. Draw coupon dates and the principal payment, then separate the valuation into coupon annuity and face-value present value. For semiannual questions, write coupon, yield and period count on three separate conversion lines. Stress-test price by increasing yield and confirming that value falls.
Keep yield to maturity and realised return distinct: realised return can change with sale price, reinvestment and holding period even when the initial yield was calculated correctly. Construct a bond setup box with face value, annual coupon rate, payment frequency, quoted yield, remaining years and settlement date.
Convert the coupon into cash per period, the yield into a periodic discount rate and years into total periods before writing the valuation equation. If the coupon rate equals the yield, use par as a benchmark; if the yield is higher, predict a discount, and if lower, predict a premium. Split every price into an annuity component and a principal component so a missing face-value repayment is obvious.
Revalue the same bond after one payment and explain both the passage-of-time effect and any yield-change effect. Create a small price-yield table and verify the curve slopes downward and bends rather than forming a straight line. Compare a short and long maturity bond after the same yield change to practise duration intuition without needing a duration formula.
For effective rates, follow one written conversion chain: quoted annual rate to periodic rate, periodic growth factor to effective annual rate. Never compare rates with different compounding frequencies before conversion. Add one holding-period problem in which the bond is sold before maturity. Include coupon income, sale price and purchase price, then distinguish this realised return from the original yield to maturity.
Conclude each drill with a reasonableness sentence covering price direction, premium or discount status and the cash-flow date used for principal. Include a zero-coupon bond beside the coupon bond to isolate the principal discounting logic. Compare their responses to the same yield movement and connect the stronger long-maturity response to cash arriving later.
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