Financial Markets and Valuation - Tutorial 1: SOLUTIONS. Present and Future Values, Annuities and Perpetuities
|
|
- Opal Simon
- 8 years ago
- Views:
Transcription
1 Financial Markets and Valuation - Tutorial 1: SOLUTIONS Present and Future Values, Annuities and Perpetuities (*) denotes those problems to be covered in detail during the tutorial session (*) Problem 1. (Ross, Westerfield & Jaffe) You have won the Florida state lottery. Lottery officials offer you the choice of the following alternative payouts: Alternative 1: $10,000 one year from now. Alternative 2: $20,000 five years from now. Which should you choose if the discount rate is a. 0%? b. 10%? c. 20%? d. What rate makes the options equally attractive to you? (a) PV(Alt. 1) = 10,000 < PV(Alt. 2) = 20,000 => Choose Alt.2 which has higher NPV (b) PV(Alt. 1) = 10,000/(1+0.10) = 9, < Alt. 2 = 20,000/( )^5 = 12, => Choose Alt.2 which has higher NPV (c) PV(Alt. 1) = 10,000/(1+0.20) = 8, > PV(Alt. 2) = 20,000/(1+0.20)^5 = => Choose Alt. 1 which has higher NPV (d) Equate 10,000/(1+r)=20000/(1+r)^5, to find r => (1+r)^4 = 2, r = 18.9% Problem 2. (Ross, Westerfield & Jaffe) Suppose you place $1000 in an account at the end of each of the next 4 years. If the account earns 12%, how much will be in the account at the end of 7 years? Solution : The $1,000 that you place in the account at the end of the first year will earn interest for six years. The $1,000 that you place in the account at the end of the second year will earn interest for five years, etc. Thus, the account will have a balance of $1,000 (1.12) 6 + $1,000 (1.12) 5 + $1,000 (1.12) 4 + $1,000 (1.12) 3 = $6, (*) Problem 3. (Ross, Westerfield & Jaffe) Assuming an interest rate of 10%, calculate the present value of the following streams of yearly payments: a. $1000 per year forever, with the first payment one year from today. b. $500 a year forever, with the first payment 2 years from today. c. $2,420 a year forever with the first payment 3 years from today. FMV/Tutorial 1 Solutions/Sept.-Oct
2 a. PV (today) = 1000/0.1 = $10,000 b. PV (today) = [500/0.1]/1.1=5,000/1.1 = $4, c. PV (today) = [2420/0.1]/(1.1)^2= $20,000 (*) Problem 4. (Ross, Westerfield & Jaffe) You are saving for your retirement. You have decided that one year from today you will place 2% of your annual salary in an account which will earn 8% p.a. Your salary is 50,000 today, but it will grow at 4% p.a. throughout your career. How much money will you have for your retirement which will begin in 40 years? You are going to put aside 2% of your annual salary (which grows at 4% per year). The first payment one year from today is 2% * 50,000 * 1.04 = 1,040. To find the Future Value in 40 years time, it is easier to first determine the present value of this growing annuity, using the Growing Annuity formula. 40 Present Value of these savings is PV = 1, = 20, And them to compound the PV for 40 periods, to determine the Future Value in 40 years time when you retire: FV = 20, * [(1.08)^40] = $440,011 (*) Problem 5. (Ross, Westerfield & Jaffe) What is the future value three years hence of $1,000 invested in an account with a stated annual interest of 8 percent, a. compounded annually? b. compounded semi-annually? c. compounded monthly? d. Why does the future values increase as the compounding period shortens? a. $1.000 (1.08) 3 = $1, b. $1,000 [1 + (0.08 / 2)] 2 3 = $1,000 (1.04) 6 = $1, c. $1,000 [1 + (0.08 / 12)] 12 3 = $1,000 ( ) 36 = $1, d. The future value increases because of the compounding. The account is earning interest on interest. Essentially, the interest is added to the account balance at the end of every compounding period. During the next period, the account earns interest on the new balance. When the compounding period shortens, the balance that earns interest is rising faster. (*) Problem 6. Societe Generale offers a 4.1% SAIR compounded quarterly, while BNP Paribas offers a 4.05% SAIR compounded monthly. Which bank offers the higher rate for your deposit? FMV/Tutorial 1 Solutions/Sept.-Oct
3 At SG the effective annual rate is (1 + r/4)^4-1 = ( /4)^4-1 = At BNP Paribas the effective annual rate is (1 + r/12)^12-1 = ( /12)^12-1 = => Societe Generale is better Problem 7. (Grindblatt & Titman) You are considering a new business venture and want to determine the present value of seasonal cash flows. Historical data suggests that quarterly flows will be $3,000 in quarter 1, $4,000 in quarter 2, $5,000 in quarter 3, $6,000 in quarter 4. The annualized rate is 10 percent, compounded annually. a. What is the PV if this quarterly pattern will continue into the future (that is, forever)? b. How would your answer change if same quarter growth is 1 percent per year in perpetuity? a. Treat each quarter s cash flow stream separately and them add up to have full PV. PV(CF 1 st quarter) = PV(3,000 in 1 st quarter) + PV(3,000 perpetuity in every 1 st quarter) = 3,000/[(1.10)^(1/4)] + [3,000/0.10]/[(1.10)^(1/4)] = $32,223 PV(CF 2 nd quarter) = 4,000/[(1.10)^(2/4)] + [4,000/0.10]/[(1.10)^(2/4)] = $41,952 PV(CF 3 rd quarter) = 5,000/[(1.10)^(3/4)] + [5,000/0.10]/[(1.10)^(3/4)] = $51,206 PV(CF 4 th quarter) = 6,000/[(1.10)] + [6,000/0.10]/[(1.10)] = $60,000 TOTAL PV = $185,381 b. Same as in a. but now each quarterly cash flow stream is a growing perpetuity. And need to take into account that first cash flow of the perpetuity is already after the 1% annual growth. PV(CF 1 st quarter) = PV(3,000) + PV(3,030 GROWING perpetuity in every 1 st quarter) = 3,000/[(1.10)^(1/4)] + [3,030/( )]/[(1.10)^(1/4)] = $35,803 PV(CF 2 nd quarter) = 4,000/[(1.10)^(2/4)] + [4,040/( )]/[(1.10)^(2/4)] = $46,614 PV(CF 3 rd quarter) = 5,000/[(1.10)^(3/4)] + [5,050/( )]/[(1.10)^(3/4)] = = $56,895 PV(CF 4 th quarter) = 6,000/[(1.10)] + [6,060/( )]/[(1.10)] = = $66,667 TOTAL PV = $205,979 FMV/Tutorial 1 Solutions/Sept.-Oct
4 Bonds (*) Problem 8. (Ross, Westerfield & Jaffe) A bond with the following characteristics is available. Principal: $1,000 Term to maturity: 20 years Coupon rate: 8 percent, annual payments Calculate the price of the bond if the stated annual interest rate is: a. 8 percent b. 10 percent c. 6 percent. a. Since the coupon rate coincides with the discount rate, the present value of the bond should be equal to the face value, i.e. the bond is traded at par. PV (8%) = (0.08)*1,000 * A (20 periods, 8%) + 1,000/(1+0.08)^20 = = 80* ,000* = = 1,000 = Face value b. Since the coupon rate is less than the discount rate, the present value of the bond is less than the face value, i.e. the bond is traded at a discount. PV (10%) = (0.08)*1,000 * A (20 periods, 10%) + 1,000/(1+0.10)^20 = = 80* ,000* = = < 1,000 c. Since the coupon rate exceeds the discount rate, the present value of the bond exceeds the face value, i.e. the bond is traded at a premium. PV (6%) = (0.08)*1,000 * A (20 periods, 6%) + 1,000/(1+0.06)^20 = = 80* ,000 * = = 1, > 1,000 (*) Problem 9. (Ross, Westerfield & Jaffe) You have just purchased a newly issued $1,000 5-year Vanguard Company bond at par. This 5-year bond pays $60 in interest semi-annually. You are also considering the purchase of another Vanguard Company bond that returns $30 in semi-annual interest payments and has six years remaining before it matures. This bond has a face value of $1,000. a. What is the effective annual return on the five-year bond? b. Assume that the rate you calculated in part (a) is the correct rate for the bond with six years remaining before it matures. What should you be willing to pay for that bond? c. How will your answer to part (b) change if the five-year bond pays $40 in semiannual interest? a. Since issued at par, the semi-annual coupon rate equals the semi-annual discount rate = 6% per semester or, equivalently, the annual coupon rate is 12% per year. To determine the effective annual discount rate (EAIR), we have to take care of the effect of first annual coupon being reinvested and earning interest. => 1 + EAIR = [( 1 + annual coupon rate / m ) ]^(m) FMV/Tutorial 1 Solutions/Sept.-Oct
5 where m=2 semesters per year => EAIR = [(1+0.12/2 )]^2 1 = 12.36% b. To determine the price of bond it s better to work with the effective semiannual rate of 6% (although the annual rate is 12.36% as shown in a). => PV (6-year bond) = 30 * A(12 periods, 6%) + 1,000/(1+0.06)^12 = = 30 * *0.497 = = = < 1,000 c. The new effective semi-annual discount rate is now 4% => PV (6-year bond) = 30 * A(12 periods, 4%) + 1,000/(1+0.04)^12 = = 30 * * = = = < 1,000 FMV/Tutorial 1 Solutions/Sept.-Oct
Time Value of Money (TVM)
BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is $1 now worth in the future? how much is $1 in the future worth now? Business planning
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationThe Time Value of Money
The Time Value of Money Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationHow to calculate present values
How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance
More informationTopics Covered. Ch. 4 - The Time Value of Money. The Time Value of Money Compounding and Discounting Single Sums
Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationFNCE 301, Financial Management H Guy Williams, 2006
Review In the first class we looked at the value today of future payments (introduction), how to value projects and investments. Present Value = Future Payment * 1 Discount Factor. The discount factor
More informationChapter 2 Present Value
Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted
More informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationPrepared by: Dalia A. Marafi Version 2.0
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
More informationTopics Covered. Compounding and Discounting Single Sums. Ch. 4 - The Time Value of Money. The Time Value of Money
Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationMODULE: PRINCIPLES OF FINANCE
Programme: BSc (Hons) Financial Services with Law BSc (Hons) Accounting with Finance BSc (Hons) Banking and International Finance BSc (Hons) Management Cohort: BFSL/13/FT Aug BACF/13/PT Aug BACF/13/FT
More informationPractice Set #1 and Solutions.
Bo Sjö 14-05-03 Practice Set #1 and Solutions. What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets
More informationBusiness 2019. Fundamentals of Finance, Chapter 6 Solution to Selected Problems
Business 209 Fundamentals of Finance, Chapter 6 Solution to Selected Problems 8. Calculating Annuity Values You want to have $50,000 in your savings account five years from now, and you re prepared to
More informationInternational Financial Strategies Time Value of Money
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
More informationNPV calculation. Academic Resource Center
NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationAppendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition
C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationCHAPTER 4. The Time Value of Money. Chapter Synopsis
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
More informationMGT201 Lecture No. 07
MGT201 Lecture No. 07 Learning Objectives: After going through this lecture, you would be able to have an understanding of the following concepts. Discounted Cash Flows (DCF Analysis) Annuities Perpetuity
More informationFINANCIAL MATHEMATICS FIXED INCOME
FINANCIAL MATHEMATICS FIXED INCOME 1. Converting from Money Market Basis to Bond Basis and vice versa 2 2. Calculating the Effective Interest Rate (Non-annual Payments)... 4 3. Conversion of Annual into
More informationBonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University
Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University
More informationHow To Calculate The Value Of A Project
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
More informationOklahoma State University Spears School of Business. Time Value of Money
Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. $15,000 cash upon signing the
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationCHAPTER 5 HOW TO VALUE STOCKS AND BONDS
CHAPTER 5 HOW TO VALUE STOCKS AND BONDS Answers to Concepts Review and Critical Thinking Questions 1. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used
More informationHP 12C Calculations. 2. If you are given the following set of cash flows and discount rates, can you calculate the PV? (pg.
HP 12C Calculations This handout has examples for calculations on the HP12C: 1. Present Value (PV) 2. Present Value with cash flows and discount rate constant over time 3. Present Value with uneven cash
More informationTopic 3: Time Value of Money And Net Present Value
Topic 3: Time Value of Money And Net Present Value Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk From Material by Pierre Mella-Barral MBA - Financial Markets - Topic 3 1 2. Present
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest
More informationHow To Read The Book \"Financial Planning\"
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationIf I offered to give you $100, you would probably
File C5-96 June 2013 www.extension.iastate.edu/agdm Understanding the Time Value of Money If I offered to give you $100, you would probably say yes. Then, if I asked you if you wanted the $100 today or
More informationSpotlight Quiz on Inflation, Index-Linking and Compounding
Spotlight Quiz on Inflation, Index-Linking and Compounding Frequency of payment A major UK bank has recently written to its customers along the following lines: Through talking to customers we have found
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1
C Time Value of Money C- 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C- 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationTIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this
More informationF V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ]
1 Week 2 1.1 Recap Week 1 P V = F V (1 + r) n F V = P (1 + r) n 1.2 FV of Annuity: oncept 1.2.1 Multiple Payments: Annuities Multiple payments over time. A special case of multiple payments: annuities
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationAPPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More informationTopics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
More informationFinancial Management Spring 2012
3-1 Financial Management Spring 2012 Week 4 How to Calculate Present Values III 4-1 3-2 Topics Covered More Shortcuts Growing Perpetuities and Annuities How Interest Is Paid and Quoted 4-2 Example 3-3
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationGREAT LAKES ADVISORS THE PENSION PROMISE SESSION THREE. A Presentation to the: National Conference on Public Employee Retirement Systems
GREAT LAKES ADVISORS THE PENSION PROMISE SESSION THREE Presenter: Kelly Weller Managing Director, Client Service (312) 353-3733 kweller@greatlakesadvisors.com A Presentation to the: National Conference
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationReview Solutions FV = 4000*(1+.08/4) 5 = $4416.32
Review Solutions 1. Planning to use the money to finish your last year in school, you deposit $4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen
More informationFI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY
FI 302, Business Finance Exam 2, Fall 2000 versions 1 & 8 KEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEYKEY 1. (3 points) BS16 What is a 401k plan Most U.S. households single largest lifetime source of savings is
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationContinue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
More informationHow To Value Cash Flow
Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value
More informationTopics Covered. Compounding and Discounting Single Sums. Ch. 4 - The Time Value of Money. The Time Value of Money
Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate Inflation & Time Value The Time Value of Money
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More information15.401. Lecture Notes
15.401 15.401 Finance Theory I Haoxiang Zhu MIT Sloan School of Management Lecture 2: Present Value Lecture Notes Key concept of Lecture 1 Opportunity cost of capital True or False? A company s 10-year
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationChapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1
Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationLearning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:
Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value
More informationToday s Plan. MBA Jump Start. Finance Day 3 Thomas Gilbert
MBA Jump Start Finance Day 3 Thomas Gilbert September 2013 Today s Plan Excel is a very important tool for finance (and also for the other courses) Model building Pricing Sensitivity analysis Today, we
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationCHAPTER 2. Time Value of Money 2-1
CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More informationANSWERS TO STUDY QUESTIONS
ANSWERS TO STUDY QUESTIONS Chapter 17 17.1. The details are described in section 17.1.1. 17.3. Because of its declining payment pattern, a CAM would be most useful in an economy with persistent deflation
More informationChapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
More informationI. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds
Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with Default-Free Bonds III. Duration: Details and Examples IV. Immunization
More informationCalculations for Time Value of Money
KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More informationBond Valuation. What is a bond?
Lecture: III 1 What is a bond? Bond Valuation When a corporation wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities called bonds. A bond
More informationChapter 3 Mathematics of Finance
Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationFinal Examination, BUS312, D1+ E1. SFU Student number:
Final Examination, BUS312, D1+ E1 NAME: SFU Student number: Instructions: For qualitative questions, point form is not an acceptable answer. For quantitative questions, an indication of how you arrived
More informationYield to Maturity Outline and Suggested Reading
Yield to Maturity Outline Outline and Suggested Reading Yield to maturity on bonds Coupon effects Par rates Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading
More informationBond Valuation. Chapter 7. Example (coupon rate = r d ) Bonds, Bond Valuation, and Interest Rates. Valuing the cash flows
Bond Valuation Chapter 7 Bonds, Bond Valuation, and Interest Rates Valuing the cash flows (1) coupon payment (interest payment) = (coupon rate * principal) usually paid every 6 months (2) maturity value
More information9. Time Value of Money 1: Present and Future Value
9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because
More informationExercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776
CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%
More informationHow to Calculate Present Values
How to Calculate Present Values Michael Frantz, 2010-09-22 Present Value What is the Present Value The Present Value is the value today of tomorrow s cash flows. It is based on the fact that a Euro tomorrow
More informationMBA Finance Part-Time Present Value
MBA Finance Part-Time Present Value Professor Hugues Pirotte Spéder Solvay Business School Université Libre de Bruxelles Fall 2002 1 1 Present Value Objectives for this session : 1. Introduce present value
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The
More informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More information