Explanation:
To determine which bond price is higher, we need to calculate the present value of the bond's cash flows using both spot rate sequences.
Bond Details:
$100$2 (2% of $100)$2 at Year 1, $2 at Year 2, $102 at Year 3 (coupon + principal)Price Calculation using Sequence 1:
Price₁ = $2/(1.02) + $2/(1.035)² + $102/(1.047)³
= $1.9608 + $1.8669 + $89.0147
= $92.8424
Price Calculation using Sequence 2:
Price₂ = $2/(1.047) + $2/(1.035)² + $102/(1.02)³
= $1.9102 + $1.8669 + $96.1169
= $99.8940
Comparison:
Price₁ = $92.84 < Price₂ = $99.89
Key Insight:
The bond price is lower when discounting with higher spot rates for later cash flows. In Sequence 1, the 3-year spot rate (4.7%) is much higher than in Sequence 2 (2.0%). Since the largest cash flow ($102) occurs at Year 3, the higher discount rate in Sequence 1 significantly reduces the present value of this cash flow, making the overall price lower.
Therefore, the price using Sequence 1 is less than the price using Sequence 2.
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An analyst gathers the following information about spot rates:
| Time to Maturity | Sequence 1 | Sequence 2 |
|---|---|---|
| 1 year | 2.0% | 4.7% |
| 2 years | 3.5% | 3.5% |
| 3 years | 4.7% | 2.0% |
For a 3-year, 2% annual coupon payment bond, the price using Sequence 1 is:
A
less than the price using Sequence 2.
B
the same as the price using Sequence 2.
C
greater than the price using Sequence 2.