Original practice · fully worked
Original variant: least-cost funding for an arts venue
An arts venue must pay 600 in one year and 900 in two years. It can buy one-year zeros yielding 5%, two-year zeros yielding 6%, or units of a note priced at 500 that pay 40 in year one and 540 in year two. Fractional units are allowed. Find the least current cost of an exact match.
- A
1,300.00 - B
1,325.50 - C
1,341.27 - D
1,360.00 - E
1,390.00
Answer and calculation
Using 5/3 notes exhausts the second-year liability; the residual one-year zero makes total cost 1,341.27, choice C.
Setup
Setup
Represent residual liability coverage by zero-coupon redemption amounts after selecting J note units.
H+40J=600,I+540J=900 Model
Model
The exact-match equations express both zero holdings as linear functions of J, making current cost linear as well.
C=1.05H+1.062I+500J Compute
Compute
The negative cost slope favors the largest feasible note position; the year-two constraint limits it to five-thirds units.
dJdC=−1.0540−1.062540+500<0,J=900/540 Answer
Answer
Those notes plus a one-year zero cost 1,341.27 in total, which is choice C.
C=1341.27(C) 