A university has $16,000,000 invested in its endowment. The university wants to withdraw $800,000 from this endowment starting next year and continuing at annual intervals forever, with each subsequent payment growing at 4% per year. What rate of return does the endowment have to earn to sustain the desired withdrawals?
What will be an ideal response?
The present value of this growing perpetuity is $16,000,000. The equation for a growing perpetuity tells us that this present value equals the first payment divided by the difference between the rate of return and the growth rate of future payments:
PV = CF / (r - g)
$16,000,000 = $800,000 / (r - 0.04)
Solve for r to find the rate of return needed to generate the desired cash payouts.
(r - 0.04) = $800,000 / $16,000,000
r = 0.04 + 0.05 = 0.09 = 9%
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