Worked solution · Exam FM
This Exam FM sample reference tests Bond Valuation. Because the bond sells at a premium, the earliest permitted call is worst for the investor; solving the six-year call price with i = 0.96r gives i = 14.32%, choice E.
Independent solution
Setup
A premium bond gives the investor the lowest yield when the premium is returned over the shortest allowed period.
Model
Use the year-six call date and replace coupon rate r by i divided by 0.96.
Compute
The resulting price equation isolates the six-year discount factor and gives annual yield 0.1432.
Answer
The worst-case yield is 14.32%, corresponding to choice E.
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Original practice · fully worked
A 1,000 redemption bond pays 140 annually and sells for 1,050. It may be called at par after years 5, 7, or 9 and otherwise matures after year 12. Which redemption date produces the investor's yield to worst?
The corresponding yields rise from 12.59% at year 5 to 13.15% at year 12, so the year-5 call produces yield to worst, choice A.
Setup
Price the bond separately to each possible redemption date using its promised coupons through that date.
Model
Solving the year-five and year-seven equations shows yield increasing with the call horizon.
Compute
The year-nine and maturity yields are higher still, so the minimum is the year-five yield.
Answer
The investor's yield to worst occurs if the bond is called in year 5, corresponding to choice A.
Calculator reproduction
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Drill the method: Exam FM Bond Valuation, Pricing, and Yields problems
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