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Unformatted text preview: 82 9.25 9.50 9.56 10.41 9.86 11.04 9.75 10.00 10.16 11.72 DF 0.9195 0.8415 0.7662 0.6940 0.6250 0.5594 Payments Fixed Float 0.10 0.0875 0.10 0.0927 0.10 0.0982 0.10 0.1041 0.10 0.1104 0.10 0.1172 Present Fixed 0.0920 0.0842 0.0766 0.0694 0.0625 0.0559 Values Float 0.0805 0.0780 0.0753 0.0722 0.0690 0.0656 Sum of PV Payments = PV of Principal = 0.4406 0.5594 0.4406 0.5594 PV of All Cash Flows = 1.0000 1.0000 Swaps: R. J. Hawkins Econ 136: Financial Economics 15/ 19 Risky Debt: A simple example Consider a 1-year annually compounded zero-coupon bond If risk-free it has a price of Prf = 1 1+r Now complicate matters with default risk: 1 2 a default probability of Pdef a recovery rate of rrec Now risky it has a price of Prisky = Pdef × rrec 1 + (1 − Pdef ) × 1+r 1+r and a risky rate R and spread s via Prisky = Pdef (rrec − 1) + 1 1 1 ≡ = 1+r 1+R 1+r +s Fixed Income VI: R. J. Hawkins Econ 136: Financial Economics 3/ 22 Risky Debt: A simple example Consider a 1-year annually compounded zero-coupon bond A risk-free rate (flat term-structure) of 5%. A recovery-rate of 40%. The spread follows f...
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