4. (Endowment Problem) (25 Pts) UMS, an elite private school in Texas, currently has an
endowment of 1.7 billion dollars. The university has agreed to fund new academic initiatives over
the next 10 years by taking a draw from the endowment at the end of each year, beginning one
year from now (at the end of year 1). The university will calculate the draw using a formula based
on the year-end value of the endowment. The table below summarizes how large a draw the
university will take based on the endowment's year-end value.
Amount of Endowment (year-end)
Draw (%) of Endowment
$1,500,000,000 -- $2,000,000,000
$2,000,000,000 -- $2,500,000,000
Assume the university has fairly conservative investments with a mean annual (or one-year)
return of 6% and a standard deviation of 5%, and assume future returns are normally distributed.
Based on a simulation model with N = 10,000 trials, answer following questions:
(a) What is the average endowment balance at the end of year 10,
immediately after taking the
final year-ending draw?
(b) How many total dollars, on average, are drawn from the endowment over the ten year period
(include the final draw at the end of year 10)? Do not discount!
(c) What is the probability that the final year's draw is at the maximum 3% level?
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