Original practice · fully worked
Original variant: duration of a three-cash-flow scholarship note
A scholarship trust owns a note that pays 30 at the end of years 1 and 2, then 1,030 at the end of year 3. At a 5% annual effective yield, calculate the note’s Macaulay duration.
- A
2.71 years - B
2.83 years - C
2.91 years - D
2.96 years - E
3.00 years
Answer and calculation
The note price is 945.54 and the weighted numerator is 2752.25; their quotient is 2.9108 years. The duration rounds to 2.91 years, so choice C is correct.
Setup
Setup
List the three dated payments and use the 5% yield to compute their present-value weights.
CF1=30,CF2=30,CF3=1030,i=0.05 Model
Model
Macaulay duration is the payment-time average under those weights, so divide the time-weighted present value by price.
P=t=1∑3CFt(1.05)−t,DM=P∑t=13tCFt(1.05)−t Compute
Compute
The note price is 945.54 and the weighted numerator is 2752.25; their quotient is 2.9108 years.
P=945.5350,∑tPV(CFt)=2752.2514,DM=2.9108 Answer
Answer
The duration rounds to 2.91 years, so choice C is correct.
DM=2.91 years(C) Calculator reproduction
BA II Plus keystrokes
- CF; 2nd CLR WORK; 0 CF0; 30 C01; 2 F01; 1030 C02; 5 I; CPT NPV945.54Use the worksheet price as the denominator; compute the time-weighted numerator separately.
