CHAPTER 2. Time Value of Money 21


 Olivia Griffith
 1 years ago
 Views:
Transcription
1 CHAPTER 2 Time Value of Money 21
2 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22
3 Time lines i% CF 0 CF 1 CF 2 CF 3 Show the timing of cash flows Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period 23
4 Drawing time lines: $100 lump sum due in 2 years; 3year $100 ordinary annuity $100 lump sum due in 2 years i% 3 year $100 ordinary annuity i%
5 Drawing time lines: Uneven cash flow stream; CF 0 = $50, CF 1 = $100, CF 2 = $75, and CF 3 = $50 Uneven cash flow stream i%
6 What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%? Finding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods % 100 FV =? 26
7 Solving for FV: The arithmetic method After 1 year: FV 1 = PV ( 1 + i ) = $100 (1.10) = $ After 2 years: FV 2 = PV ( 1 + i ) 2 = $100 (1.10) 2 =$ After 3 years: FV 3 = PV ( 1 + i ) 3 = $100 (1.10) 3 =$ After n years (general case): FV n = PV ( 1 + i ) n 27
8 Solving for FV: The calculator method Solves the general FV equation Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.) INPUTS OUTPUT N I/YR PV PMT FV
9 What is the present value (PV) of $100 due in 3 years, if I/YR = 10%? Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding) The PV shows the value of cash flows in terms of today s purchasing power % PV =?
10 Solving for PV: The arithmetic method Solve the general FV equation for PV: PV FV = 1+ n ( i) n PV = FV 3 / ( 1 + i ) 3 = $100 / ( 1.10 ) 3 = $
11 Solving for PV: The financial tables PV = FV n II i PV = 3 FV 3 II 10 PV = $ =
12 Solving for PV: The calculator method Solves the general FV equation for PV Exactly like solving for FV, except we have different input information and are solving for a different variable INPUTS OUTPUT N I/YR PV PMT FV 212
13 Solving for N: If sales grow at 20% per year, how long before sales double? Solves the general FV equation for N Same as previous problems, but now solving for N INPUTS OUTPUT N I/YR PV PMT FV 213
14 Solving for N: with natural logarithm PV = 1 FV = 2 i = 20% ( ) n $ 1 = ( ) n = 2 ( 1.20) ln 2 nln = n0.18 = 0.69 n =
15 Solving for N: with financial tables PV = 1, FV = 2, i = 20% ( ) n $ 1 = ( ) n = 2 ( ) n 1.20 = 2 tables A1(20% and factor 2) between 3 and 4 years 215
16 interpolation y = 3 x 1 y = n y 2 = 4 x 1 x 2 = = 2 = n = 3 + = ( ) 3.79 years 216
17 Annuities & Perpetuities Annuity a series of fixed, equal payments for a specified number of periods Ordinary Annuity payments at the end of the period Annuity Due payments at the beginning of the period Perpetuity an Annuity forever 217
18 Difference between Ordinary Annuity and Annuity Due Ordinary Annuity i% Annuity Due PMT PMT PMT i% PMT PV PMT PMT FV 218
19 Future Value of an Annuity Solving for FV: 3year ordinary annuity of $100 at 10% $100 payments occur at the end of each period, but there is no PV. FVA ( 1+ i) n 1 = PMT = PMT i, n i ( ) n FVIFA = PMT III i FVA = 100 ( ) = 100 ( 3.310) =
20 Solving for FV: financial calculator 3year ordinary annuity of $100 at 10% $100 payments occur at the end of each period, but there is no PV. INPUTS OUTPUT N I/YR PV PMT FV
21 Solving for FV: 3year annuity due of $100 at 10% Now, $100 payments occur at the beginning of each period. Set calculator to BEGIN mode. INPUTS OUTPUT N I/YR PV PMT FV
22 Solving for FV: 3year annuity due of $100 at 10% Now, $100 payments occur at the beginning of each period. FVA FVA ( Due) = PMT ( 1+ i) i n 1 ( 1+ i) ( ) ( )( ) n Due = PMT FVIFA 1+ i = PMT III ( 1+ i) i, n i FVA FVA ( Due) = 100 ( ) ( ) ( Due) = 100( 3.310)( 1.10) =
23 Present value of an Annuity Solving for PV: 3year ordinary annuity of $100 at 10% $100 payments still occur at the end of each period, but now there is no FV. INPUTS OUTPUT N I/YR PV PMT FV 223
24 Solving for PV: 3year ordinary annuity of $100 at 10% $100 payments still occur at the end of each period, but now there is no FV. PVA PVA = = 1 PMT PMT 1 ( ) n ( ) n 1+ i 1+ i = PMT i ( 1+ i) ( ) n PVIFA = PMT IV i, n i 1 i n 3 PVA = 100 IV10 = =
25 Solving for PV: 3 year annuity due of $100 at 10% Again, $100 payments occur at the beginning of each period. Set calculator to BEGIN mode. INPUTS OUTPUT N I/YR PV PMT FV 225
26 Solving for PV: 3 year annuity due of $100 at 10% Again, $100 payments occur at the beginning of each period. PVA ( Due) = PMT( PVIFA )( 1 i) n i, n + PVA ( ) 3 Due = 100 IV ( ) 10 = =
27 What is the PV of this uneven cash flow stream? 0 10% = PV
28 Solving for PV: Uneven cash flow stream Input cash flows in the calculator s CFLO register: CF 0 = 0 CF 1 = 100 CF 2 = 300 CF 3 = 300 CF 4 = 50 Enter I/YR = 10, press NPV button to get NPV = $ (Here NPV = PV.) 228
29 Solving for I: What interest rate would cause $100 to grow to $ in 3 years? Solves the general FV equation for I. INPUTS OUTPUT 3 N I/YR PV PMT FV 229
30 Solving for I: What interest rate would cause $100 to grow to $ in 3 years? Solves the general FV equation for I. ( i) n FV = PV = ( + i) = ( 1+ i) 3 i = i = = 0.08 = 8% 230
31 Classifications of interest rates Nominal rate (i NOM ) also called the quoted or state rate. An annual rate that ignores compounding effects i NOM is stated in contracts. Periods must also be given, e.g. 8% Quarterly or 8% Daily interest i NOM = Rate/Period X # of Periods/Year i NOM = i PER xm 231
32 Classifications of interest rates Periodic rate (i PER ) amount of interest charged each period, e.g. monthly or quarterly i PER = i NOM / m, where m is the number of compounding periods per year. m = 4 for quarterly and m = 12 for monthly compounding 232
33 Classifications of interest rates Effective (or equivalent) annual rate (EAR = EFF%) the annual rate of interest actually being earned, taking into account compounding EFF% for 10% semiannual investment EFF% = ( 1 + i NOM / m ) m 1 = ( 1 + i PER ) m 1 = ( / 2 ) 2 1 = 10.25% An investor would be indifferent between an investment offering a 10.25% annual return and one offering a 10% annual return, compounded semiannually. 233
34 Why is it important to consider effective rates of return? An investment with monthly payments is different from one with quarterly payments. Must put each return on an EFF% basis to compare rates of return. Must use EFF% for comparisons. See following values of EFF% rates at various compounding levels. EAR ANNUAL = 10.00% EAR QUARTERLY = ( /4) 4 1 = 10.38% EAR MONTHLY = ( /12) 12 1 = 10.47% EAR DAILY (360) = ( /360) = 10.52% 234
35 When is each rate used? i NOM written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines. i PER Used in calculations and shown on time lines. If m = 1, i NOM = i PER = EAR. EAR Used to compare returns on investments with different payments per year. Used in calculations when annuity payments don t match compounding periods. 235
36 What is the FV of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? FV n = PV ( 1 + i m NOM ) m n = PV 1 ( + i ) PER number of periods FV FV FV FV 3S 3S 3Q 3Q = $100 ( 1 + ) 2 6 = $100 (1.05) = $ = $ = $100 (1.025) = $
37 Can the effective rate ever be equal to the nominal rate? Yes, but only if annual compounding is used, i.e., if m = 1. If m > 1, EFF% will always be greater than the nominal rate. 237
38 What s the FV of a 3year $100 annuity, if the quoted interest rate is 10%, compounded semiannually? 0 1 5% Payments occur annually, but compounding occurs every 6 months. Cannot use normal annuity valuation techniques. 238
39 Method 1: Compound each cash flow 0 1 5% FV 3 = $100(1.05) 4 + $100(1.05) 2 + $100 FV 3 = $
40 Method 2: Financial calculator Find the EAR and treat as an annuity. EAR = ( / 2 ) 2 1 = 10.25%. INPUTS OUTPUT N I/YR PV PMT FV
41 Find the PV of this 3year ordinary annuity. Could solve by discounting each cash flow, or Use the EAR and treat as an annuity to solve for PV. INPUTS OUTPUT N I/YR PV PMT FV 241
42 Loan amortization Amortization tables are widely used for home mortgages, auto loans, business loans, retirement plans, etc. Financial calculators and spreadsheets are great for setting up amortization tables. EXAMPLE: Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments. 242
43 Step 1: Find the required annual payment All input information is already given, just remember that the FV = 0 because the reason for amortizing the loan and making payments is to retire the loan. INPUTS OUTPUT N I/YR PV PMT FV 243
44 Step 1: Find the required annual payment n = 3 i / yr = 10% PV = 1,000 annuity factor V n i = ( ) n 1+ i i ( 1+ ) n i 1 annual payment A n 3 = 1,000 V10 = 1, =
45 Step 2: Find the interest paid in Year 1 The borrower will owe interest upon the initial balance at the end of the first year. Interest to be paid in the first year can be found by multiplying the beginning balance by the interest rate. INT t = Beg bal t (i) INT 1 = $1,000 (0.10) = $
46 Step 3: Find the principal repaid in Year 1 If a payment of $ was made at the end of the first year and $100 was paid toward interest, the remaining value must represent the amount of principal repaid. PRIN= PMT INT = $ $100 = $
47 Step 4: Find the ending balance after Year 1 To find the balance at the end of the period, subtract the amount paid toward principal from the beginning balance. END BAL = BEG BAL PRIN = $1,000  $ = $
48 Constructing an amortization table: Repeat steps 1 4 until end of loan Year BEG BAL PMT INT PRIN END BAL 1 $1,000 $402 $100 $302 $ TOTAL 1, ,000  Interest paid declines with each payment as the balance declines. 248
49 Illustrating an amortized payment: Where does the money go? $ Interest Principal Payments Constant payments. Declining interest payments. Declining balance. 249
Ehrhardt Chapter 8 Page 1
Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
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 informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
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 informationChapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS
Chapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS 71 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 $10,000(1.10) 5 $10,000(FVIF 10%, 5 ) $10,000(1.6105) $16,105. Alternatively, with a financial calculator enter the
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 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 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 informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationChapter 28 Time Value of Money
Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit $100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:
More informationCh. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,
Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flowseither payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash
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 informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
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 informationPRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.
PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values
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 informationUNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis
This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, endofchapter problems, and endofchapter
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 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 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 informationFinQuiz Notes 2 0 1 4
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
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 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 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 informationCalculator (HewlettPackard 10BII) Tutorial
UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT Calculator (HewlettPackard 10BII) Tutorial To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key s primary function
More informationCHAPTER 2. Time Value of Money 61
CHAPTER 2 Tme Value of Moey 6 Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 62 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationEXAM 2 OVERVIEW. Binay Adhikari
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
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 informationBUSI 121 Foundations of Real Estate Mathematics
Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia Outline Introduction Cash Flow Problems Cash Flow
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationSolutions to Problems
Solutions to Problems P41. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,
More informationHewlettPackard 10BII Tutorial
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, 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 informationFinance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.
Chapter 1 Finance 331 What is finance?  Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: 
More informationHOW TO CALCULATE PRESENT VALUES
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGrawHill/Irwin Copyright 2014 by The McGrawHill Companies, Inc. All rights reserved.
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 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 informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
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 informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More informationFinQuiz Notes 2 0 1 5
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
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 informationChapter 5 Time Value of Money
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 of Cash Flows 7. Other Compounding
More informationFINANCIAL CALCULATIONS
FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N
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 informationWeek 4. Chonga Zangpo, DFB
Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer
More informationChapter 4 Time Value of Money
Chapter 4 Time Value of Money Solutions to Problems P41. LG 1: Using a Time Line Basic (a), (b), and (c) Compounding Future Value $25,000 $3,000 $6,000 $6,000 $10,000 $8,000 $7,000 > 0 1 2 3 4 5 6 End
More informationChapter 3. Present Value. Answers to Concept Review Questions
Chapter 3 Present Value Answers to Concept Review Questions 1. Will a deposit made in an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one
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 informationTHE TIME VALUE OF MONEY
QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost
More informationChapter 1: Time Value of Money
1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting
More informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationTexas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
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 information3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
More informationChapter 02 How to Calculate Present Values
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 informationChapter 4. Time Value of Money
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationTime 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 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 informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationReal estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions
Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 31 a) Future Value = $12,000 (FVIF, 9%, 7 years) = $12,000 (1.82804) = $21,936 (annual compounding) b) Future Value
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
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 informationHewlettPackard 10B Tutorial
To begin, look at the face of the calculator. Every key (except one, the gold shift key) on the 10B has two functions: each key's primary function is noted in white on the key itself, while each key's
More informationChapter 3 Present Value
Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value
More informationUsing Financial Calculators
Chapter 4 Discounted Cash Flow Valuation 4B1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your HewlettPackard or Texas Instruments BA II Plus financial calculator
More informationSolutions Manual. Corporate Finance. Ross, Westerfield, and Jaffe 9 th edition
Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders
More informationTT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007
TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how
More informationHewlettPackard 17BII Tutorial
To begin, look at the face of the calculator. Most keys on the 17BII have two functions: a key's primary function is noted in white on the key itself, while the key's secondary function is noted in gold
More informationKey Concepts and Skills
Chapters 5 and 6 Calculators Time Value of Money and Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2013 by The McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able
More informationFINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes
FINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes The concept of timevalueofmoney is important to know, not only for this class, but for your own financial planning. It is a critical
More informationTexas Instruments BAII PLUS Tutorial
To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in
More informationIntroduction. Turning the Calculator On and Off
Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationTime Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...
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 informationTexas Instruments BAII PLUS Tutorial
Omar M. Al Nasser, Ph.D., MBA. Visiting Assistant Professor of Finance School of Business Administration University of HoustonVictoria Email: alnassero@uhv.edu Texas Instruments BAII PLUS Tutorial To
More informationChapter 4: Time Value of Money
Chapter 4: Time Value of Money BASIC KEYS USED IN FINANCE PROBLEMS The following two key sequences should be done before starting any "new" problem: ~ is used to separate key strokes (3~N: enter 3 then
More informationCompounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.
Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has builtin preset assumptions
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More informationChapter 5 & 6 Financial Calculator and Examples
Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationhp calculators HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow
HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow Discounting a Single Sum Discounting and Compounding Discounting a Series of Sums
More informationThe Interest Rate: A loan, expressed as a percentage of the amount loaned per year.
Interest Rates Time Value of Money The Interest Rate Simple Interest Amortizing a Loan The Interest Rate: A loan, expressed as a percentage of the amount loaned per year. Interest rate is the "price" of
More informationTime Value of Money PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA
Time Value of Money 1 PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA Learning objectives 2 Understand the Concept of time value of money. Understand the relationship between present and
More informationChapter 8. Present Value Mathematics for Real Estate
Chapter 8 Present Value Mathematics for Real Estate Real estate deals almost always involve cash amounts at different points in time. Examples: Buy a property now, sell it later. Sign a lease now, pay
More informationMHSA 8630  Healthcare Financial Management Time Value of Money Analysis
MHSA 8630  Healthcare Financial Management Time Value of Money Analysis ** One of the most fundamental tenets of financial management relates to the time value of money. The old adage that a dollar in
More informationTime Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam
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 informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
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 signin bonus for your new job? 1. $15,000 cash upon signing the
More information3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.
Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the
More informationTime Value Conepts & Applications. Prof. Raad Jassim
Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on
More informationPresent Value and Annuities. Chapter 3 Cont d
Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects
More information