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["1.  ITT 6-year Bonds",{"$nulls":3},"ytm:",0.033," cc","6-year T-Note cc ytm:",null,0.016]
[null,"Coupon:",0.05]
[null,"Time-line of bond's cash flows:"]
[null,"Time (Years):",0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6]
[null,"Promised CF:",null,{"$f":"50*$C$2","v":2.5},{"$f":"50*$C$2","v":2.5},2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,{"$f":"100*(1+$C$2/2)","v":102.49999999999999}]
[null,"df:",null,{"$f":"EXP(-D4*$F$1)","v":0.9836353793906724},{"$f":"EXP(-E4*$F$1)","v":0.967538559589032},0.9517051581364622,0.9361308642916188,0.9208114378568045,0.9057427080235485,0.8909205722370781,0.8763409950793732,0.8620000071704987,0.8478937040879159,0.8340182453034796,0.8203698531378311]
[null,"PV:",null,{"$f":"D5*D6","v":2.459088448476681},{"$f":"E5*E6","v":2.41884639897258},2.3792628953411556,2.3403271607290472,2.302028594642011,2.264356770058871,2.2273014305926955,2.190852487698433,2.155000017926247,2.1197342602197895,2.085045613258699,84.08790994662768]
[null,null,{"$f":"SUM(D7:O7)","v":109.02975402454389}]
[]
[]
[null,"Credit Spread:",{"$f":"F1-J1","v":0.017}," 170 basis points"]
[]
[null,"Hazard rate:",{"$f":"0.5*C11","v":0.0085},"  85 basis points.  Our rule of thumb is that 1/2 of the credit spread is compensation for expected loss (and therefore is the hazard rate), and the remaining half is the risk premium."]
[{"$nulls":3},"  '==> Risk premium:",null,{"$f":"C11-C13","v":0.0085}]
[null,"6-year survival probability:",null,{"$f":"EXP(-6*C13)","v":0.950278670532427}]
[null,"So the probability that the bond will be worth 0 at any time prior to maturity is:",{"$nulls":5},{"$f":"1-D15","v":0.04972132946757302}]
[]
[null,"Expected return on the bond is computed by adding the risk premium to the term-matched Treasury yield:",{"$nulls":7},{"$f":"J1+F14","v":0.0245},"  (As long as everything is expressed on a cc basis.)"]
[null,"  Alternately, we can compute the expected return by subtracting the hazard rate from the bond's ytm:",{"$nulls":7},{"$f":"F1-C13","v":0.0245},"  (As long as everything is expressed on a cc basis.)"]
[null,"    This is important.  It shows the rate  of return that an investor in the bond expects to earn if she hold the bond to maturity."]
[null,"        It also is the pre-tax cost of debt to the borrower.  The reason for this is that the borrower doesn't pay in the event of default. And those cases are reflected by the hazard rate."]
[null,"             The expected return does not include the hazard rate.  (This is the reason that the expected return on a natural disaster catastrophe bond is the riskfree rate.)"]
[]
[]
["2. L3Harris",3,"year bond, annual coupon payments",null,null,0.06," coupon rate","  cc ytm on US Treasury:",null,0.03]
[null,null,"Hazard rate:",0.008]
[]
[]
[null,"Time-line of bond's cash flows:"]
[null,"Time (Years):",0,1,2,3]
[null,"Promised CF:",null,{"$f":"100*$F$25","v":6},{"$f":"100*$F$25","v":6},{"$f":"100*(1+$F$25)","v":106}]
[null,"Surv Prob:",null,{"$f":"EXP(-D30*$D$26)","v":0.9920319148370607},{"$f":"EXP(-E30*$D$26)","v":0.9841273200552851},0.9762857097579093]
[null,"E(CF):",null,{"$f":"D31*D32","v":5.952191489022364},{"$f":"E31*E32","v":5.90476392033171},103.48628523433838]
[]
["There are 2 natural ways to compute the bond's value.  The first is to discount the bond's promised cash flows at its ytm."]
[null,"We find the bond's cc ytm by adding the Treasury rate to the hazard rate plus the risk premium."]
[null,"We know that the risk premium is equal to the hazard rate using our rule of thumb.  Therefore we have:",{"$nulls":7},"Bond's cc ytm"]
[{"$nulls":9},"Treasury",{"$f":"J25","v":0.03},"  Compensation for time"]
[{"$nulls":9},"+ hazard rate",{"$f":"D26","v":0.008},"  Compensation for expected loss"]
[{"$nulls":9},"+ Risk Premium",{"$f":"D26","v":0.008},"  Compensation for fact that losses are correlated with the state of the economy."]
[{"$nulls":9},"  = ytm",{"$f":"K38+K39+K40","v":0.046}]
[null,"df(@bond's ytm):",null,{"$f":"EXP(-D30*$K$41)","v":0.9550419621907147},{"$f":"EXP(-E30*$K$41)","v":0.9121051495450904},0.8710986917457983,{"$nulls":5},"The expected return on the bond is:"]
[null,"PV:",null,{"$f":"D31*D42","v":5.730251773144288},{"$f":"E31*E42","v":5.472630897270542},92.33646132505463,{"$nulls":5},"  the bond's ytm minus its hazard rate:",null,null,{"$f":"K41-K39","v":0.038}]
[null,null,{"$f":"SUM(D43:F43)","v":103.53934399546947},{"$nulls":8},"- or - Treasury yield + Risk premium:",null,null,{"$f":"K38+K40","v":0.038}]
[]
[]
["-----   OR ----"]
[]
[null,"Discount the bond's  expected cash flows at the cc Treasury ytm + the bond's risk premium:"]
[null,"df(@UST ytm+ RP):",null,{"$f":"EXP(-D30*($K$38+$K$40))","v":0.9627129408911995},{"$f":"EXP(-E30*($K$38+$K$40))","v":0.9268162065593822},0.8922579558824083]
[null,"PV:",null,{"$f":"D33*D50","v":5.730251773144288},{"$f":"E33*E50","v":5.472630897270542},92.33646132505461]
[null,null,{"$f":"SUM(D51:F51)","v":103.53934399546944}]
[]
[]
[]
[]
["3. Weyerhauser"]
[null,"2-year 7.5% notes, selling for par.",null,null,"   Treasury yield:",null,0.04," cc"]
[]
[null,"Obtain cc ytm:","Semi-annually compounded ytm:",null,null,0.075,null,{"$f":"LN((1+F60/2)^2)","v":0.07362794624543284}]
[{"$nulls":7},"Verify:",{"$f":"EXP(H60)","v":1.0764062500000002}]
[{"$nulls":8},{"$f":"(1+F60/2)^2","v":1.0764062500000002}]
[]
[null,"Credit Spread:",{"$f":"H60-G58","v":0.03362794624543284}]
[null,"     haz rate:",{"$f":"0.5*C64","v":0.01681397312271642}]
[null,"    risk prem:",{"$f":"C64-C65","v":0.01681397312271642}]
[null,"Discussion: We are not told anything about the timing of the bond's cash flows so by convention, coupon payments are paid every 6 months.  This is not something that we can assume away."]
[null,"Time Line:"]
[null,"  Time (Yrs):",null,0.5,1,5,2]
[null,"  Promised Cash Flow:",null,{"$f":"50*$F$60","v":3.75},{"$f":"50*$F$60","v":3.75},3.75,{"$f":"100*(1+$F$60/2)","v":103.75000000000001}]
[null,"  Survival Probability:",null,{"$f":"EXP(-$C$65*D69)","v":0.9916282533272602},{"$f":"EXP(-$C$65*E69)","v":0.983326592796873},0.9193670217101845,0.9669311881015072]
[null,"  Expected (Cash Flow):",null,{"$f":"D70*D71","v":3.718605949977226},{"$f":"E70*E71","v":3.6874747229882736},3.4476263314131916,100.31911076553139]
[]
[null,"The expected return on a corporate bond equals the ytm minus the hazard rate:",{"$nulls":5},{"$f":"H60-C65","v":0.056813973122716424}]
[null,".  --  Alternately, it is the Treasury ytm + the risk premium:",{"$nulls":5},{"$f":"G58+C66","v":0.056813973122716424}]