Practice Problem – Coupon Payments

Practice Question

Bond Valuation
Coupon Payments
Short Answer

Gator Inc. has outstanding bonds with $1,000 par value, and they mature in five (5) years. Their yield to maturity is 9% with semi-annual compounding, and the current market price is $853.61. What is the bond’s annual coupon interest rate?

Answer +
Correct Answer: 5.3%
Explanation +

Step 1: Define the variables

  • Par value \( (FV) = \$1{,}000 \)
  • Market price \( (PV) = \$853.61 \)
  • Yield to maturity (YTM) = 9% annually, compounded semi-annually
  • Years to maturity = 5
  • Periods = 5 × 2 = 10
  • Semi-annual rate \( r = \frac{9\%}{2} = 4.5\% \)

Step 2: Use the bond pricing formula

Bond price is given by: \[ PV = \sum_{t=1}^{N} \frac{PMT}{(1 + r)^t} + \frac{FV}{(1 + r)^N} \] Using a financial calculator or spreadsheet, solve for \( PMT \) that satisfies: \[ 853.61 = \frac{PMT}{(1 + 0.045)^1} + \cdots + \frac{PMT}{(1 + 0.045)^{10}} + \frac{1000}{(1 + 0.045)^{10}} \]

Step 3: Solve for PMT

Using calculator or Excel: \[ PMT \approx 26.50 \]

Step 4: Convert to annual coupon

  • Annual coupon payment = \( 26.50 \times 2 = 53 \)
  • Coupon interest rate = \( \frac{53}{1000} = 5.3\% \)

Final Answer: 5.3%