Practice Problem – Bond YTM

Practice Question

Intro to Finance
Bond Valuation
Yield to Maturity
Short Answer

Bond X is a ten-year semi-annual coupon bond, which was issued at par 5 years ago. The yield to maturity 5 years ago was 6%. How much does Bond X worth currently when the yield to maturity is 8% now. Face value = $1,000.

Answer +
918.890
Explanation +
Step 1: Identify Known Values
  • Face value \( F = 1{,}000 \)
  • Coupon rate = 6% → annual coupon = \( 60 \), semi-annual = \( 30 \)
  • YTM now = 8% annually → semi-annual rate \( r = 0.04 \)
  • Remaining periods \( n = 5 \text{ years} \times 2 = 10 \)
Step 2: Present Value of Coupons
\[ PV_{\text{coupons}} = 30 \times \left( \frac{1 - (1 + 0.04)^{-10}}{0.04} \right) \] \[ PV_{\text{coupons}} = 30 \times 8.1109 = 243.33 \]
Step 3: Present Value of Face Value
\[ PV_{\text{face}} = \frac{1{,}000}{(1.04)^{10}} = \frac{1{,}000}{1.48024} = 675.56 \]
Step 4: Add Present Values
\[ PV_{\text{total}} = 243.33 + 675.56 = 918.89 \]
Final Answer

The current value of Bond X is $918.89.