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# Calculating the Present Value of an Endowment

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A wealthy philanthropist has established the following endowment for a hospital. The details are as follows: a cash deposit of \$ 8 M one year from now; an annual cash deposit of \$3M per year for the next five years. The first \$3M will start today; at the end of 5 years, the hospital will also receive a lump sum payment of \$18M. Assuming the cost of money is 3%, what is the value of this endowment in today's dollars? Show your work.

https://brainmass.com/math/calculus-and-analysis/calculating-present-value-endowment-506805

#### Solution Preview

Let us calculate Present value of \$8 M deposited one year from now
Future Value of deposit = FV = \$8,000,000
Number of periods = n = 1
Discount rate = i = 3%
PV1=FV/(1+i)^n = 8000000/(1+3%)^1 = ...

#### Solution Summary

Solution describes the steps to estimate the present value of given future deposits. Calculations are carried out with the help of suitable algebraic formulas.

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## Present Value Analysis

You became incredibly wealthy one day and a huge contributing factor to your success was the education that you'd received at York/Atkinson. As a way to thank the school you set up an endowment today in the amount of \$5,000,000. But you don't just hand over \$5,000,000 just like that!!! You stipulate that York use the funds to provide scholarships to ADMS3530 students totaling \$250,000 annually. The scholarships are to commence one year from today and are to continue for as long as ADMS3530 is around (in effect for ever!!!). The market interest rate for the foreseeable future is expected to be 5% per annum compounded annually.

(a) Based on the above information will York be able to meet your stipulation by providing ADMS3530 students with annual scholarships totaling \$250,000 forever? Provide supporting analysis.

(b) What if your endowment was \$4,000,000 instead of \$5,000,000 would York still be able to meet your stipulation? If not what would be the maximum annual scholarship payout? Provide supporting analysis.

(c) As we all know the cost of education keeps going up and up. To accommodate these inflationary pressures you ask that the \$250,000 scholarship grow at a constant rate of 1% annually. Would York be able to fund this scholarship for ever with your \$5,000,000 endowment? If not what would be the maximum annual scholarship? Provide supporting analysis.

(d) What would your endowment have to be to accommodate annual scholarships of \$300,000 with a constant growth rate of 1% annually? Provide supporting analysis.

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