# At a price of 102462 the bond yields 102 convertible

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At a price of 1,024.62, the bond yields 10.2% convertible semi-annually.Exercise (4.5)What is the price of the bond in(4.4)if the required yield is 9.8%convertible semi-annually?Answer:1050.98In Example(4.4), the redemption value (1,100) is different from the face value(1,000).If an exam problem doesnotspecify a separate redemption value, youcan assume that the bonds will be redeemed at par.Note that raising the redemption value to 1,100 resulted in a price above 1,000.It is natural to ask what redemption value would give a price of 1,000.Example (4.6)Suppose that the company issuing the bonds of Example(4.1)wants toincrease the redemption value to keep the price at 1,000 for a requirednominal yield of 10.2% We can find the required redemption value onthe BA II Plus.Set N=20, I/Y=5.1, PMT=50, PV =1,000, and CPT FV= 1,033.42.The required redemption value is 1,033.42.Exercise (4.7)What redemption value would assure a price of 1,000 for the abovebonds if the required nominal yield were 10.1%?Answer: 1016.62An investor who wishes to buy a bond is usually quoted a market price for thebond. In that case, the investor would like to know the bond’s yield at that price.Example (4.8)A 1,000 par value bond with a term of 10 years and a coupon rate of 10%payable semi-annually is offered at a price of 990. We can find the yieldper semi-annual period on the BA II Plus.Set N=20, PV =990, PMT=50, FV=1,000, and CPT I/Y=5.08.This gives a nominal yield convertible semi-annually of5.08%210.16%.Downloaded by li li ([email protected])lOMoARcPSD|4343609
Page M4-4Module 4 – BondsACTEX LearningExam FM – Financial MathematicsDinius, Hassett, Ratliff, Garcia, & SteebyExercise (4.9)A 1,000 par value bond with a term of 10 years and a coupon rate of 10%payable semi-annually is offered at a price of 1,020. Find the impliedyield (convertible semi-annually).Answer: 9.68%You may have observed by now that we have solved all the problems to thispoint using the financial calculator and have not introduced any mathematicalnotation or formulas. It is important to recognize when exam problems can besolved easily and directly like this. As always, there are formulas and notationto learn, and some problems will require their use. The key variables are:F= par value (or face value)r=coupon rateper coupon period(e.g., per semi-annual period)Fr =coupon amountC =redemption (maturity) value (=Fin most cases)n= number of coupon periods to redemptionP= pricei=yieldper coupon periodiv11iThe most basic formula for the pricePis:(4.10)If the bond is redeemed at par, thenFC, and we can writenin iPFr aFv.Since1ninin ivFvFFiFFi ai, we can derive the following formula for abond’s price in terms of its premium or discount:(4.11)We illustrate this with another example.Example (4.12)Consider again a 1,000 par value bond redeemable at par in 10 years witha nominal coupon rate of 10% payable semi-annually. This bond hasF=1,000,r=0.05 andn=20. We have already shown in Example(4.2)thatthe price of this bond at a yield of 10.2% is 987.64. We can check thisusing the above formula with0.051i.

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