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
Answer and calculation
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.
C≈27130(C) 