Worked solution · Exam FM
This Exam FM sample reference tests Bond Pricing and Yields. Subtracting the two bond prices cancels the common redemption C. The coupon advantage contributes 15 times the 40-period annuity factor, and the extra redemption contributes K times the discount factor; solving gives K = 250.01, choice E.
Independent solution
Setup
Use half-year periods at yield 3.5%; the coupon amounts are 75 and 60.
Model
Subtract the prices so the unknown common redemption component cancels.
Compute
The coupon present-value difference is 320.33 and v to the fortieth is 0.25257247; hence K = 250.01.
Answer
The redemption increment is approximately 250, selecting choice E.
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Original practice · fully worked
Two twelve-year bonds yield 6% nominal annually convertible semiannually and have the same price. Bond X pays 35 each half-year and redeems 1,000. Bond Y redeems 1,100. Calculate Bond Y's level half-year coupon.
Equal prices require Bond Y's coupon shortfall to offset the present value of its extra 100 redemption. Solving the 24-period price difference gives coupon 32.10, choice B.
Setup
Write both prices at the 3% half-year yield.
Model
Equate prices and isolate the unknown coupon.
Compute
The required coupon is 32.0953 each half-year.
Answer
Bond Y's half-year coupon is 32.10, selecting choice B.
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Drill the method: Exam FM Bond Valuation, Pricing, and Yields problems
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