Bond Pricing - Annual Coupon
Price a corporate bond with annual coupon payments.
Problem Scenario
A 5-year corporate bond has a face value of $1,000, a coupon rate of 7%, and the market yield is 9%.
Given Data
Requirements
- Calculate the bond price
- Determine if it trades at premium or discount
Solution
Step 1:
Annual coupon = 0.07 × 1000 = $70.
Step 2:
PV of coupons = 70 × [(1 - 1.09^-5)/0.09] = 70 × 3.8897 = 272.28.
Step 3:
PV of face value = 1000/1.09^5 = 1000/1.5386 = 649.93.
Step 4:
Bond price = 272.28 + 649.93 = 922.21.
Final Answer
Price ≈ $922.21. Trades at a discount because coupon rate (7%) < YTM (9%).
Key Takeaways
- ✓Discount bonds have coupon rate < YTM
- ✓Break the bond into coupon annuity + lump sum
Common Errors to Avoid
- ✗Using coupon rate to discount instead of YTM
- ✗Forgetting the face value at maturity
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FAQs
Common questions about this problem type
Halve the coupon and YTM, double the number of periods.
Compare the coupon rate to YTM. If coupon rate > YTM, the bond trades at a premium (above par). If coupon rate < YTM, it trades at a discount (below par). If they are equal, price equals par.