Worked solution · Exam FM
This Exam FM sample reference tests Coupon Bond Price Relations. The zero price implies v to the n equals 0.89. Substituting a coupon rate equal to half the yield into the second price equation gives face value 941.80, choice B.
Independent solution
Setup
Let F be the second bond's face value, i its annual yield, and v the annual discount factor.
Model
The second bond's annual coupon is Fi divided by 2. Price its coupons and redemption at the common yield.
Compute
Use i times a-angle-n equals one minus v to the n, then insert 0.89.
Answer
The second face value is approximately 942, choice B.
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Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A 1,000 redemption-value zero-coupon bond with maturity n sells for 760. Another bond has the same maturity, yield, and redemption value. Its annual coupon rate equals 40% of that yield. Determine the second bond's price without solving for n or the yield.
The zero price makes one minus v to the n equal 0.24. Coupons add 40% of the 240 discount, or 96, to the zero price. The result is 856, choice C.
Setup
Normalize the zero-bond price by its 1000 redemption value.
Model
The annual coupon is 0.4 times 1000i. Use i times a-angle-n equals one minus v to the n.
Compute
Replace the annuity term by the maturity discount.
Answer
The coupon bond price is 856, choice C.
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