Bond Valuation Exam Training
Bond questions on exams follow a handful of patterns: price a bond, adjust for semiannual coupons, decide whether it trades at a premium or discount, and sometimes solve for the yield. Once you set up the periods and the rate correctly, the math is the same every time.
What you will learn
- How to adjust coupons, rate and periods for semiannual bonds
- How to check your answer with the premium or discount rule
- How to approach yield to maturity questions on a calculator
- Common exam traps: annual vs semiannual, and coupon rate vs YTM
The formulas
- C
- Annual coupon payment
- r
- Annual yield to maturity (quoted APR)
- T
- Years to maturity
- F
- Face value
- Annual coupon
- Both semiannual coupons added together
Worked example
A 10-year, $1,000 bond pays an 8% coupon semiannually. The market yield is 6% (annual, compounded semiannually). What is its price?
- Semiannual coupon = 80 ÷ 2 = 40; periodic rate = 6% ÷ 2 = 3%; periods = 10 × 2 = 20
- PV of coupons = 40 × [1 − 1 ÷ 1.03²⁰] ÷ 0.03 ≈ 595.10
- PV of face value = 1,000 ÷ 1.03²⁰ ≈ 553.68
- Price ≈ 595.10 + 553.68 = 1,148.77
- Check: coupon 8% is above yield 6%, so a premium price above $1,000 makes sense
Answer: The bond is worth about $1,148.77 (rounded to the cent).
Common questions
How do you price a bond with semiannual coupons?
Halve the annual coupon, halve the annual yield, and double the number of years to get the number of periods. Then price it as usual: present value of the coupon annuity plus present value of the face value. Forgetting one of the three adjustments is the most common mistake.
How do you calculate yield to maturity on an exam?
There is no simple algebraic formula, so you solve for the rate that makes the present value of cash flows equal the price. On a financial calculator, enter N, PMT, PV (as a negative) and FV, then compute I/Y. For semiannual bonds, double the result.
How can I quickly check a bond price answer?
Compare the coupon rate with the yield. If the coupon is higher, the price should be above face value; if lower, below face value; if equal, exactly at face value. If your answer breaks this rule, recheck the rate and number of periods.
What types of bond valuation questions come up most on finance exams?
Typical questions ask you to price a bond, price it with semiannual coupons, find the yield to maturity or current yield, identify premium versus discount bonds, and explain how prices react when market rates change. Zero-coupon bonds also appear often.