Worked solution · Exam FM
This Exam FM sample reference tests Midterm Bond Book Value. The post-nth-coupon book value prices the remaining n semiannual coupons. Eliminating the unknown coupon from that equation and the purchase price gives v to the n = 3.6844/4.4913, hence n = 10, choice B.
Independent solution
Setup
There are 2n semiannual coupons in an n-year bond. Let x be the coupon and v = 1/1.02.
Model
At the midpoint after coupon n, exactly n coupons remain.
Compute
Split the original 2n-period price into the first n coupons and the midpoint value, then eliminate x.
Answer
The term is 10 years, choice B.
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Error diagnosis
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Original practice · fully worked
A 1,000 face-value bond has 7 years remaining immediately after its sixth semiannual coupon. Its book value at that date is 970 and its yield is 2% effective per half-year. Determine the annual coupon rate, payable semiannually.
Fourteen coupons remain. Solving 970 as the prospective value gives a half-year coupon of 17.5219, or an annual coupon rate of 3.5044%, choice C.
Setup
Seven remaining years mean fourteen semiannual coupon periods.
Model
Let C be the half-year coupon and write the prospective book-value equation.
Compute
Solve for C and convert two coupons per year into an annual rate on face.
Answer
The annual coupon rate is approximately 3.50%, choice C.
Calculator reproduction
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