This Exam FM sample reference tests Growing Perpetuities. Separating the first 15 level payments from the deferred growing perpetuity and solving the value equation gives k = 1.889%, choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AUsing 1.66% understates the growing tail. The first growing payment is 2500 times 1 plus k, not 2500.
BThe value 1.74% is not obtained when the tail is valued at time 17 and then discounted by v to the 17th power.
CThe value 1.78% results from premature rounding of the deferred tail or annuity factor. Retaining v to the 17th power gives 1.889%.
DThe value 1.83% is too low because it effectively shifts the growing perpetuity one period farther from the valuation date.
Original practice · fully worked
Original variant: growing grants beside a capital outlay
An endowment has 50,000 today. It must make a one-time capital outlay of 12,000 at time 6. It will also fund annual grants forever, with the first grant at time 3 and each later grant 1.2% larger. At a 4% annual effective return, determine the first grant.
A 1,052
B 1,138
C 1,227
D 1,315
E 1,402
Variant answer in brief
After reserving for the time-6 outlay, the remaining fund supports a first growing grant of 1,227.03, choice C.
Setup
Setup
Let X be the grant at time 3. Reserve the present value of the separate capital outlay before valuing the growing grants.
i=0.04
g=0.012
v=(1.04)−1
Model
Model
The growing perpetuity is worth X divided by i minus g at time 2, one period before the first grant.
50000=12000v6+v20.04−0.012X
Compute
Compute
The capital outlay requires 9,483.77 today. Solving for the first grant gives 1,227.03.
PVoutlay=12000v6=9483.77
X=(50000−9483.77)(0.028)v−2=1227.03
Answer
Answer
The first perpetuity grant is about 1,227, which is choice C.
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