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Answer: USD 95.33
## Explanation To estimate the expected value of the zero-coupon bond one year from now: **Step 1: Calculate discount rates for each rating scenario** - Risk-free rate = 4% - AA spread = 40 bps = 0.40% → Discount rate = 4% + 0.40% = 4.40% - A spread = 80 bps = 0.80% → Discount rate = 4% + 0.80% = 4.80% - BBB spread = 150 bps = 1.50% → Discount rate = 4% + 1.50% = 5.50% **Step 2: Calculate bond values one year from now** Since it's a 2-year zero-coupon bond, one year from now there will be 1 year remaining to maturity: - AA rating: Value = 100 / (1 + 0.044) = 100 / 1.044 = 95.79 - A rating: Value = 100 / (1 + 0.048) = 100 / 1.048 = 95.42 - BBB rating: Value = 100 / (1 + 0.055) = 100 / 1.055 = 94.79 **Step 3: Calculate expected value** Expected Value = (Probability × Value) for each scenario: - AA: 5% × 95.79 = 4.7895 - A: 85% × 95.42 = 81.107 - BBB: 10% × 94.79 = 9.479 Total Expected Value = 4.7895 + 81.107 + 9.479 = 95.3755 ≈ USD 95.33 Therefore, the expected value is USD 95.33.
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A two-year zero-coupon bond issued by corporate XYZ is currently rated A. One year from now XYZ is expected to remain at A with 85% probability, upgraded to AA with 5% probability, and downgraded to BBB with 10% probability. The risk free rate is flat at 4%. The credit spreads are flat at 40, 80, and 150 basis points for AA, A, and BBB rated issuers, respectively. All rates are compounded annually. Estimate the expected value of the zero-coupon bond one year from now (for USD 100 face amount).
A
USD 92.59
B
USD 95.33
C
USD 95.37
D
USD 95.42
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