Upon the untimely and tragic death of their wealthy uncle, his heirs wanted to m

Question

Upon the untimely and tragic death of their wealthy uncle, his heirs wanted to memorialize him with a named donation to the local hospital. They offered the hospital a choice of 60,000 annual payments forever or a lump sum payment of 700,000 today: What should be the decision if the hospital thinks it could earn an average of 5% annually on this donation? 9%? 13%?

(I am just unsure of what I am supposed to do for this question. Am I simply taking the percentage asked of the 60,000? Any help would be greatly appreciated!)

Explanation / Answer

We need to find the Present Values of $ 60000 under the 3 interest rates(5%,9% & 13% ) and compare with the lumpsum of $ 700000 today & accept whichever is higher. Present Value of annuity forever is   Present value of perpetuity whose formula= Annuity/Interest rate PV of perpetuity $ 60000 @ 5% = 60000/0.05= 1200000 PV of perpetuity $ 60000 @ 9% = 60000/0.09= 666667 PV of perpetuity $ 60000 @ 13% = 60000/0.13= 461538 As PV of perpetuity $ 60000 @ 5% =$ 1200000 is > the lumpsum of $ 700000 today & the PVs under the other 2 rates of 9%&13% are less than $ 700000 Annual donations of $ 60000 can be accepted and invested @ 5% interest

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