Worked solution · Exam FM
This Exam FM sample reference tests Bond Valuation. Quarterly coupon is 87.50 and yield is 1.4%; expressing the second and third book values in terms of redemption C makes third-period premium amortization 39.0667 − 0.00625C, so C = 5,150, choice A.
Independent solution
Setup
Convert both the annual coupon and nominal yield to quarterly amounts.
Model
Premium amortization in a coupon period equals coupon minus interest on the prior book value.
Compute
Writing the prospective book value after two payments as coupon and redemption components gives a linear equation in C.
Answer
The redemption value is 5,150, corresponding to choice A.
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Original practice · fully worked
A 15-year bond has face 5,000, redemption 5,200, and 7% annual coupons paid quarterly. It yields 5.6% nominal convertible quarterly. Determine premium amortized in the third coupon payment.
A prospective book-value schedule gives third-period premium amortization 6.56, choice C.
Setup
Price the bond at issue using quarterly coupon and yield.
Model
Roll the book value forward through the first two coupon payments.
Compute
The third coupon less interest on the second book value is 6.5632.
Answer
Premium amortized in the third payment is 6.56, corresponding to choice C.
Calculator reproduction
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Drill the method: Exam FM Bond Valuation, Pricing, and Yields problems
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