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KIC000004

# KIC000004 - Valuation of Defaultable Therefore the PV oj...

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Valuation of Defaultable Bonds - continued Therefore, the PV oj the e~p..aed ""sh flo ...... discounted at tl1e fair Im",,,,l "'Ie r is: (l_d(-ld(~+_C~+, .. +__ C_+_R_J+ (I+r) (IH);' (l+r/- 1 (l+r)T (l_d/(_C_+~+ +_C__ + C+P J (l+r) (l+r)l -," (l+rl- 1 (l+r{ Valuation of Defaultable Bonds - continued After lots of algebra, we can sfm plify the previous expression to: p = (1- d)C + dR [1- (~)T] + F(~)T r w d l+r l+r When d=O, we are dealing with a Treasury. We know that r '" y In thai case and we are back to our other formula: 5 Bond Valuation - example 50 1 t 1 1,050 u..mple: two bond, with the ,arne promised <:ad,flows, one USTn!a,ury and 0"'" ''''''porale, 2 ~i1rs to m~turlty hee (Par) value = \$1,000 10% ilnnua' coupon rate semi-annual coupon paV"'ents _ USTeea,urv bond with dl.wunl rate = 3% P'" semerter. 2 _ Corporate bond with default probability ,,11% per ,eme!;!;er, "'toyeryv~lue R",400and iI discount l"iIte ~ 3.5% per semener, p =~+~+~+ 1,050=107434 1,03 1.00' 1.00' 1.03' ' - p= {1-0.0l)X50+0,OIX400[,_( 1-0,01 )']+I,OOJ 1-00])' :1,030.77 0035+0.01 1+0.035 "~1+0.035

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Defaultable Bond Yield-to-Maturity (YTM) In the previous slides our goal was to find the price of a bond given the discount for its expected cash flows.
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