A bond of face value ₹1000 has a coupon rate 10% per annum paid semi-annually & matures in 4 years. If present value of a bond is ₹1100 , then yield to maturity is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7.14% per annum
$\text{Face value} = 1000,\quad \text{Coupon rate} = 10\% \Rightarrow \text{annual coupon} = 100$
$\text{Semi-annual coupon} = 50,\quad n = 4 \times 2 = 8$
$\text{Let semi-annual yield} = r \Rightarrow \text{YTM} = 2r$
$1100 = 50 \cdot \frac{1 - (1+r)^{-8}}{r} + 1000(1+r)^{-8}$
$\text{Trial } r = 0.04:$
$1100 \approx 50 \cdot \frac{1 - (1.04)^{-8}}{0.04} + 1000(1.04)^{-8} = 1067.3$
$\text{Trial } r = 0.035:$
$1100 \approx 50 \cdot \frac{1 - (1.035)^{-8}}{0.035} + 1000(1.035)^{-8} = 1102.85$
$\text{Interpolating } r \approx 0.0355$
$\text{YTM} = 2r = 2 \times 0.0355 = 0.071$
$\text{Yield to maturity} \approx 7.1\%$