Practice Question
The £40 par value bond with maturity in two years and £5 semi-annual coupon is trading for £50. If the Yield to maturity is 7%, the bond is:
To determine whether the £40 par value bond with maturity in two years and £5 semi-annual coupon trading for £50 is over-valued, fairly-valued, or under-valued given a yield to maturity (YTM) of 7%, we need to calculate the bond's present value (PV) and compare it to its trading price.
Step-by-Step Solution:
1. Define Variables:
- Face Value (F): £40
- Coupon Payment (C): £5 (semi-annual)
- Yield to Maturity (YTM): 7% annually (3.5% semi-annually)
- Number of Periods (n): 2 years × 2 = 4 semi-annual periods
- Market Price (P): £50
2. Calculate Present Value of Coupon Payments:
\[ PV_{\text{coupons}} = C \times \left( \frac{1 - (1 + k)^{-n}}{k} \right) \]
\[ PV_{\text{coupons}} = £5 \times \left( \frac{1 - (1 + 0.035)^{-4}}{0.035} \right) = £5 \times 3.7177 = £18.5885 \]
3. Calculate Present Value of Face Value:
\[ PV_{\text{face}} = F \times (1 + k)^{-n} = £40 \times (1 + 0.035)^{-4} = £40 \times 0.8714 = £34.856 \]
4. Calculate Total Present Value:
\[ PV_{\text{total}} = PV_{\text{coupons}} + PV_{\text{face}} = £18.5885 + £34.856 = £53.4445 \]
5. Compare to Market Price:
- Trading Price: £50
- Calculated Present Value: £53.4445
Conclusion: Since the calculated present value (£53.4445) is higher than the trading price (£50), the bond is under-valued. Therefore, the correct answer is:
Answer: C) Under-valued