Original practice · fully worked
Original variant: exact-match cost for a city arts obligation
A city arts office owes 800 in one year and 1,200 in two years. It can buy one-year zeros yielding 4% and two-year notes with 1,000 face, annual coupons 80, and yield 5.5%. Fractional notes are allowed. Find the current cost of an exact match.
- A
1,760.00 - B
1,810.00 - C
1,846.16 - D
1,900.00 - E
1,950.00
Answer and calculation
The year-two liability needs 10/9 notes; filling the year-one residual with zeros gives total cost 1,846.16, choice C.
Setup
Setup
The note is the only asset paying at year two, so its quantity is fixed by that liability first.
1080B=1200⟹B=10/9 Model
Model
Its year-one coupons reduce the redemption amount required from one-year zeros.
Z+80B=800⟹Z=711.111 Compute
Compute
Discounting the residual zero and pricing the fractional notes at 5.5% gives 1,846.158.
C=1.04Z+B(1.05580+1.05521080) Answer
Answer
The exact-match portfolio costs 1,846.16, corresponding to choice C.
C=1846.16(C) 