You decide to give SCU an endowment as a lump sum of $1,000,000. Youwould like to specify that this will pay out an income stream of $R per year, with anannual increase of $1000 per year, continuing forever. Assume that you can lock in an5.interest rate of 5%. What value of R would match your lump sum donation of$1,000,000?

Present Value of Perpetuity = 1,000,000 Income Stream = R Annual Increase in Annuity = 1000 per year…

Answered: You decide to give SCU an endowment as…

Financial Accounting Intro Concepts Meth/Uses

14th Edition

ISBN:9781285595047

Author:Weil

Publisher:Weil

ChapterA: Appendix - Time Value Of Cash Flows: Compound Interest Concepts And Applications

Section: Chapter Questions

Problem 23E

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1. You decide to give SCU an endowment that will pay out $50 K per year forever,with a continuously compounded annual increase of 3%. Assuming that you canlock in an interest rate of 5%, gure out how much this endowment would cost.What is the total value of this income stream? 4. Let's revisit the income stream from your endowment to SCU in the rst prob-lem, which is $50 K per year with 3% continuously compounded annual increase.Instead of the 5% investment rate we used in Problem 1, compute the presentvalue of this income stream (lasting forever) assuming a constant interest rater. What is the present value of the income stream ifr= 0:02. For which values of r is the present value finite?
1. You decide to give SCU an endowment that will pay out $50 K per year forever,with a continuously compounded annual increase of 3%. Assuming that you canlock in an interest rate of 5%, gure out how much this endowment would cost.What is the total value of this income stream? 2.Suppose Aunt Grace wanted to give annual increases of $2,000 per year. How would this change the computations above? Give values for the amount Aunt Grace would have to pay to fund the income stream for 25 years, 50 years, 100years, 200 years, and forever. (Hint: You need only integrate by parts once.) 3. In addition to the $1 M already deposited there by Aunt Grace, how much would Aunt Margaret have to add to the fund to enableit to pay out an income stream ofR(t) = 60 +t forever?
1. You decide to give SCU an endowment that will pay out $50 K per year forever, with a continuously compounded annual increase of 3%. Assuming that you can lock in an interest rate of 5%, figure out how much this endowment would cost. What is the total value of this income stream? 2. Suppose Aunt Grace wanted to give annual increases of $2,000 per year. How would this change the computations above? Give values for the amount AuntGrace would have to pay to fund the income stream for 25 years, 50 years, 100years, 200 years, and forever. (Hint: You need only integrate by parts once.) 3. You take all the information about Aunt Grace's gift to your not-quite-so-wealthy Aunt Margaret. In addition to the $1 M already deposited there byAunt Grace, how much would Aunt Margaret have to add to the fund to enable it to pay out an income stream of R(t) = 60 +t forever? 4. Let's revisit the income stream from your endowment to SCU in the first problem, which is $50 K per year with 3% continuously…
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