# Present Value

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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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##### Solution Summary

The solution uses the example given in the question to demonstrate present value concepts using perpetuity.

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(a) Formula for Present Value of a Perpetuity = Yearly Payment X (1/i)

= 250,000 x (1/.05)

= 5,000,000

Thus 250,000 per year at a 5% opportunity rate is possible with an initial ...

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