This Exam FM sample reference tests Cash-Flow and Risk Matching. Exact matching is cheapest with the one-year bond for the first liability and the higher-yield two-year zero for the second, giving 25,000/1.0675 + 20,000/1.05² = 41,560, choice C.
How to solve this Cash-Flow and Risk Matching question
Setup
Setup
Match the two liability dates independently because securities can be purchased in arbitrary quantities.
C1=1.067525000
Model
Model
For each required date, choose the available asset that supplies that dated cash flow at the lowest current cost without creating an unmatched earlier coupon.
C2=1.05220000
Compute
Compute
The one-year par bond covers year one, while the two-year zero covers year two more cheaply than the lower-yield coupon bond.
C=C1+C2=41560
Answer
Answer
Adding their purchase costs gives approximately 41,560, which is choice C.
C≈41560(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the dated cash-flow matrix and present-cost comparison; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the dated cash-flow matrix and present-cost comparison; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the dated cash-flow matrix and present-cost comparison; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the dated cash-flow matrix and present-cost comparison; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: minimum-cost scholarship disbursement ladder
A scholarship fund owes 12,000 after one year and 18,000 after two years. It may buy one-year zeros yielding 5%, two-year zeros yielding 6%, or two-year notes at par that pay 7% annual coupons. Fractional notes are allowed. Determine the least cost of an exact cash-flow match.
A 26,900
B 27,000
C 27,130
D 27,449
E 28,000
Variant answer in brief
Maximizing the 7% notes and filling the year-one residual with a zero costs about 27,130, choice C.
Setup
Setup
Each two-year note supplies both a first-year coupon and a final coupon-plus-redemption payment.
1070J=18000⟹J=16.82243
Model
Model
Because the note yield exceeds the zero yields and it sells at par, use notes until their year-two cash flow reaches that liability.
H+70J=12000⟹H=10822.43
Compute
Compute
The note coupons leave a year-one residual of 10,822.43, which is funded by a one-year zero.
C=1000J+1.05H=27129.51
Answer
Answer
The combined purchase cost is 27,129.51, rounding to 27,130 in choice C.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
