A donor wishes to endow a scholarship at a certain university. The endowment may

Question

A donor wishes to endow a scholarship at a certain university. The endowment may be made by a lump-sum deposit to a special foundation set up by the university for such purposes. The foundation director believes that its funds will earn at least 8% interest per year, tax free, for indefinite future.

The scholarship is to provide $5,000 the first year increasing by $500 each year thereafter to a maximum of $10,000 per year. On the assumption that the scholarship will start at the end of the first year and continue forever, what endowment must the donor make? (Hint: this is a capitalized cost problem that has an infinite life)

Explanation / Answer

As Initial Scollarship is 5000 & increase by 500 per year. So it will become 10000 in 10 Yrs. Post that, it will remain at 10000 for ever

So PV of Perpetity at Y10 = P/i = 10000/8% = $125,000

Now we have Initial Payout at 5000 & increase by 500 for 10 yrs is like initial zero & then a Gradient of 500 every year for 10 Yrs & then Y10 = 125000

So PV of This= 5000+500(A/G,8%,10)+125000*(P/F,8%,10)

= 5000+500*3.8713+125000*0.4632

= 64836

Su Lump sum payment reqd is $64,836

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