This Exam FM sample reference tests Macaulay Duration. The weighted quotient is 5.5554 years. Rounding to two decimals gives 5.56 years. The result agrees with the published answer key, choice C.
Because the bond is bought at par, its yield per half-year equals its coupon rate per half-year, 3.8%. There are fourteen coupon dates.
j=0.076/2=0.038,n=14
Model
Model
Macaulay duration is the present-value-weighted average payment time. The numerator weights each semiannual coupon by its time and weights redemption by seven years; the denominator is the bond price.
DM=190a14∣j+5000v1495(Ia)14∣j+7(5000)v14
Compute
Compute
The weighted quotient is 5.5554 years. Rounding to two decimals gives 5.56 years.
DM=5.5554 years
Answer
Answer
The calculation gives 5.56 for macaulay duration, matching published choice C.
DM=5.56(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (5.16) does not match the checked macaulay duration result (5.56); no distinct standard one-step error is identifiable.
BChoice B (5.35) does not match the checked macaulay duration result (5.56); no distinct standard one-step error is identifiable.
DChoice D (5.77) does not match the checked macaulay duration result (5.56); no distinct standard one-step error is identifiable.
EChoice E (5.99) does not match the checked macaulay duration result (5.56); no distinct standard one-step error is identifiable.
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
Variant answer in brief
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.
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