Concept explainers
Perpetuities You have just read an advertisement stating, “Pay us $100 a year for 10 years and we will pay you $100 a year thereafter in perpetuity.” If this is a fair deal, what is the rate of interest?
To determine: The rate of interest.
Answer to Problem 27PS
The rate of interest is 7.18%.
Explanation of Solution
Determine the rate of interest
The PV of $100 a year for 10 year is calculated as,
The PV of $100 a year forever is calculated as,
Combine Equation (1) and (2),
By solving for r using trial and error method, we get r as 7.18%.
Therefore the rate of interest is 7.18%.
Want to see more full solutions like this?
Chapter 2 Solutions
Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- Under what interest rates would you prefer a perpetuity that pays $2 million a year to a one- time payment of $40 million?arrow_forwardYou want to buy a piece of land and the owner would sell it to you for $20,000 cash. Alternatively, he would let you pay for it with five annual installments of $5,000 each, the first one due right now. What is the implied interest rate here?arrow_forwardQ4. A local bank advertises the following deal: "Pay us $100 at the end of each year for 10 yearsand then we will pay you (or your beneficiaries) $100 at the end of each year forever."A. Calculate the present value of your payments to the bank if the interest rate is 8.25%.B. What is the present value of a $100 perpetuity deferred for 10 years if the interest rate is8.25%?C. Is this a good deal?arrow_forward
- Suppose you are going to receive $5,000 per year for 8 years. The appropriate interest rate is 10 percent. What is the present value of the payments if they are in the form of an ordinary, a. anhuity? b. What is the present value if the payments are an annuity due?arrow_forwardwhat is the present value of a loan that calls for the payment of $500 per year for six years if the discount rate is 10 percent and yne forst payment will be made one year from now ? how would your answer change if $500 per year occured for ten years ?arrow_forwardjust say it option. Question 1) You took 100.000 TL car loan from a bank. You will repay the loan to the bank in 4 years with a compound interest of 12% per month in 48 equal installments. In this case, how much of the first installment payment is interest and how much is the principal payment? Please choose one: А. 1630, 1000 В. 1000, 1630 С. 1430, 1200 D. 1200, 1430 Question2) If payments are made every 6 months, calculate the interest for the following situations? 9% annual compounded quarterly interest Quarter 3%, quarterly compounded interest 8.8% per annum, quarterly compounded interest Please choose one: А. 9.15%, 3.09%, 9.06% B. 9.55%, 3.09%, 8.8% C. 4.55%, 6.099%, 4.48% D. 9.45%, 6.09, 9.16% E. 9.1%, 12.18%, 8.96arrow_forward
- A local bank advertises the following deal: Pay us $100 at the end of each year for 10 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever. Calculate the present value of your payments to the bank if the interest rate is 8.25%. Annuity Formula: *Note: Equal amounts w/a finite period; $100, 10 years PV = C x (1 - 1 / (1 + r)t / r r = 8.25% C = 100.00 T = 10 100 x (1 - 1 / (1 + .825)10 / .825 100 x (1 - .002439 / .825 100 x (1 - .002439 / .825 100 x .997561 / .825 100 x 1.209164 PV = 120.92 What is the present value of a $100 perpetuity deferred for 10 years if the interest rate is 8.25%. Perpetuity Formula: *Note: Equal amounts w/ an infinite period; $100 PV = C / r r = 8.25% C = 100.00 PV = 100 / 8.25 PV = 121.21 Is this a good deal? I would go with option A over option B. I’m investing less with option A at $120.92.arrow_forwardYou have an opportunity to buy a perpetuity that pays $69 a year forever starting a year from now for $1100. What interest rate makes this a fair price? Instruction: Round to three decimal places.arrow_forwardSuppose you take out a $117,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 5%. To keep things simple, we will assume you make payments on the loan annually at the end of each year. a. What is your annual payment on the loan? b. Construct a mortgage amortization. c. What fraction of your initial loan payment is interest? d. What fraction of your initial loan payment is amortization? e. What is the total of the loan amount paid off after 10 years (halfway through the life of the loan)? f. If the inflation rate is 3%, what is the real value of the first (year-end) payment? g. If the inflation rate is 3%, what is the real value of the last (year-end) payment? h. Now assume the inflation rate is 6% and the real interest rate on the loan is unchanged. What must be the new nominal interest rate? i-1. Recompute the amortization table. i-2. What is the real value of the first (year-end) payment in this high-inflation scenario? j. What is the real value of the last…arrow_forward
- Suppose you are going to receive Rs. 63,800 per year for five years. The appropriate interest rate is 7.3 What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due? Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are an annuity due? Which has the highest present value, the ordinary annuity or annuity due? Which has the highest future value? Will this always be true? Note- Answer all the parts of the questionarrow_forwardWhat’s the present value of a perpetuity that pays $1,000 per year beginning1 year from now, if the appropriate interest rate is 5%? What would the valuebe if payments on the annuity began immediately? ($20,000, $21,000.Hint: Just add the $1,000 to be received immediately to the value of theannuity.)arrow_forwardA local bank advertises the following deal: “Pay us $100 a year for 10 years and then we will pay you (or your beneficiaries) $100 a year forever.” Is this a good deal if the interest rate available on other deposits is 8 percent? 2. Consider an APR of 12% with monthly compounding. What is the EAR (effective annual rate)?arrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
- Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningCorporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author: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 ProfessorPublisher:McGraw-Hill Education