Original practice · fully worked
Original variant: duration of the second bond in a wetlands reserve
A wetlands reserve owes 50,000 in four years and values cash flows at 8%. It holds 10,000 today in a bond of modified duration 2.0 and invests the rest of the liability present value in a second bond. What modified duration must the second bond have?
- A
3.50 - B
4.00 - C
4.34 - D
4.75 - E
5.00
Answer and calculation
Matching the four-year liability's modified duration with market-value weights gives 4.34 for the second bond, choice C.
Setup
Setup
Compute the liability's current value and convert its four-year Macaulay duration to modified duration.
PVL=50000(1.08)−4=36751.49,DL=4/1.08=3.70370 Model
Model
The second bond's market value is the liability value less the 10,000 already invested.
36751.49DL=10000(2)+(26751.49)D2 Compute
Compute
Equating the asset and liability duration numerators gives 4.34057 for the unknown measure.
D2=4.34057 Answer
Answer
The required modified duration is 4.34 years, which is choice C.
D2=4.34(C) 