Homework Help is Here – Start Your Trial Now!
Business
Finance
5. The present value of a perpetuity that will pay out $10 K per year forever is $250 K. Assuming that the interest rate is constant, find the rate.

5. The present value of a perpetuity that will pay out $10 K per year forever is $250 K. Assuming that the interest rate is constant, find the rate.

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
See similar textbooks
icon
Related questions
Question

Question 5 if the picture please. 

**Exercises** 1. You decide to give SCU an endowment that will pay out $50K 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 Aunt Grace would have to pay to fund the income stream for 25 years, 50 years, 100 years, 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 $1M already deposited there by Aunt 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 $50K per year with a 3% continuously compounded annual increase. Instead of the 5% interest rate we used in Problem 1, compute the present value of this income stream (lasting forever) assuming a constant interest rate of \( r \). a. What is the present value of the income stream if \( r = 0.02 \)? For which values of \( r \) is the present value finite? 5. The present value of a perpetuity that will pay out $10K per year forever is $250K. Assuming that the interest rate is constant, find the rate.
Transcribed Image Text:**Exercises** 1. You decide to give SCU an endowment that will pay out $50K 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 Aunt Grace would have to pay to fund the income stream for 25 years, 50 years, 100 years, 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 $1M already deposited there by Aunt 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 $50K per year with a 3% continuously compounded annual increase. Instead of the 5% interest rate we used in Problem 1, compute the present value of this income stream (lasting forever) assuming a constant interest rate of \( r \). a. What is the present value of the income stream if \( r = 0.02 \)? For which values of \( r \) is the present value finite? 5. The present value of a perpetuity that will pay out $10K per year forever is $250K. Assuming that the interest rate is constant, find the rate.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Database design
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Essentials Of Investments
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
FUNDAMENTALS OF CORPORATE FINANCE
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:
9781260013962
Author:
BREALEY
Publisher:
RENT MCG
Financial Management: Theory & Practice
Financial Management: Theory & Practice
Finance
ISBN:
9781337909730
Author:
Brigham
Publisher:
Cengage
Foundations Of Finance
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS