Explanation:
C is correct. First, the discount factors for the zero-coupon bonds must be calculated as the market price divided by the face value:
$97.8012 / 100 = 0.978012$$95.2375 / 100 = 0.952375$$92.3805 / 100 = 0.923805$These discount factors are then applied to the corresponding cash flows from the coupon-paying bond:
$67,500 \times 0.978012 = 66,015.81$$67,500 \times 0.952375 = 64,285.31$$4,567,500 \times 0.923805 = 4,219,479.34$Summing these present values: $66,015.81 + 64,285.31 + 4,219,479.34 = USD 4,349,780.46$
Therefore, the present value of the cash flows from the sovereign coupon bond is approximately USD 4,349,780, which matches option C. This technique uses the bootstrap method where zero-coupon bond prices provide the discount factors needed to price coupon-bearing bonds.
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Question 91: A fixed-income portfolio manager is using discount factors to price a sovereign bond. The bond is a coupon bond with the following cash flows:
The manager observes the following market price quotes for three zero-coupon bonds issued by the same country:
| Time to maturity (months) | Face value (USD) | Market price (USD) |
|---|---|---|
| 3 | 100 | 97.8012 |
| 6 | 100 | 95.2375 |
| 9 | 100 | 92.3805 |
Based on the discount factors of the zero-coupon bonds, what is the present value of the cash flows from the sovereign coupon bond?
A
USD 3,728,209
B
USD 4,059,055
C
USD 4,349,780
D
USD 4,436,915
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