Lesson 1. Key Financial Concepts INTRODUCTION


 Melanie Sparks
 4 years ago
 Views:
Transcription
1 Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have some underlying financial implications, either direct or indirect. Also, financial concepts arise in the everyday management of your personal resources. It s important, therefore, to understand the basics of finance. For example, the time value of money and the analysis of financial statements are basic components of finance that will be used throughout the remainder of this course and in future finance classes. It s essential that you take the time to master these concepts. As you work your way through this course, you ll learn the importance of finance to the success of every entity, both personal and professional. In Lesson 1, you ll learn some important fundamentals of finance. Some of this material is analytical in nature, requiring you to understand some mathematical calculations. Example problems in both your textbook and study guide will help you to master these calculations. Some of the problems can be completed manually or with the help of tables; however, you ll find that some calculations are much easier to perform with the aid of a financial calculator. A financial calculator is a special type of calculator that s designed to perform specific financial functions. A financial calculator is a useful professional tool that can be used throughout this course and in future finance classes. If you prefer, use an electronic spreadsheet such as Microsoft Excel to perform financial calculations. Professionals in finance generally use electronic spreadsheets more than calculators, although they require more time to learn. Your textbook provides instructions for both financial calculators and spreadsheets. You ll find financial calculator instructions starting on pages 111; Appendix E, starting on page 587, provides instructions for using Excel. Either a financial calculator or an electronic spreadsheet is required to complete this course. Lesson 1 7
2 OBJECTIVES When you complete this lesson, you ll be able to Explain the importance of financial decision making to the business community Describe the importance of financial statement analysis Explain the concepts of compounding and future value Discuss the concepts of discounting and present value Calculate the present value and future value of an annuity Read and understand the principal components of a balance sheet Perform ratio calculations to determine liquidity, activity, and profitability ASSIGNMENT 1 Read the following assignment. Then read pages 3 8 and in your textbook. Be sure to complete the selfcheck to gauge your progress. The Time Value of Money One of the most important concepts in the study of finance is the time value of money. As this phrase implies, this concept covers how time impacts the value of money. One dollar today isn t equal in value to one dollar 10 years from now. The difference in the value of these two dollars can be explained by the time value of money. The Future Value of a Dollar The future value of one dollar is the amount that one dollar will grow to at some point in the future. The process of compounding takes into account the earning of interest on interest, and is the process of finding the future value of some initial amount. 8 Financial Management
3 Let s look at an example problem. Example: Suppose you begin with $100 today and deposit it in an account that pays 10 percent annually. How much will you have in the account after 1 year? Solution: The calculation is relatively simple. In this example, you ve been given three variables. The present value (PV) is the amount you begin with, which is $100. The number of time periods (N) is 1 year. The interest rate (I) is 10 percent annually. The missing variable that you need to calculate is the future value (FV), which is the value of the investment at the end of 1 year. You would use the following formula to calculate the future value of the investment. FV = PV (1 + I.) N Substitute the known values of PV, I, and N into the formula and solve. FV = $100 ( percent) 1 FV = $100 ( ) 1 FV = $100 (1.10) 1 FV = $ FV = $110 Thus, the value of the $100 investment after 1 year will be $110. Now, let s consider the same problem over a 5year period. Example: Today, suppose that you deposit $100 into an account that pays 10 percent annually. How much will you have in the account after 5 years? Solution: In this problem, you re given the following variables: PV = $100 N = 5 years I = 10 percent annually You would again use the following formula to calculate the future value of the investment (FV). FV = PV (1 + I.) N Lesson 1 9
4 Substitute the known values of PV, I, and N into the formula and solve. FV = $100 ( percent) 5 FV = $100 ( ) 5 FV = $100 (1.10) 5 FV = $100 (1.6105) FV = $ Thus, the value of the $100 investment after 5 years will be $ In this example problem, note that the compounding process (the process of earning interest on interest) has produced total interest of $61.05, which is greater than the total simple interest of $50. The Present Value of a Dollar Finding the present value of a dollar is the opposite of calculating its future value. The present value of a dollar is the amount that a future dollar is worth today. You would calculate the present value when you need to determine how much money to invest today to obtain some future goal. Discounting is the process of finding the present value of some future amount. Let s look at another example problem. Example: Suppose you want to know how much money to invest today to reach a future goal of $100. You want to invest the money for 1 year in an account that pays 10 percent interest annually. Solution: This calculation is relatively simple. You ve been given the following three variables: future value (FV) = $100 number of time periods (N) = 1 year interest rate (I) = 10 percent annually 10 Financial Management
5 The missing variable that you need to calculate is the present value (PV), which is the amount of money you ll need to invest today to reach your future goal. You would use the following formula to calculate the present value of the investment. PV = FV [(1 + I.) N.] Next, substitute the known values of FV, I, and N into the formula and solve. PV = $100 [( percent) 1 ] PV = $100 [( ) 1 ] PV = $100 [1.101] PV = $ PV = $90.91 Thus, you ll need to invest $90.91 today to have $100 after one year. Now, consider the same problem over a fiveyear period. Example: Suppose you want to know how much money to invest today in order to reach a future goal of $100. You want to invest the money for 5 years in an account that pays 10 percent interest annually. Solution: In this problem, you re given the following three variables. FV = $100 N = 5 years I = 10 percent annually You would again use the following formula to calculate the present value of the investment (PV). PV = FV [(1 + I.) N ] Lesson 1 11
6 Substitute the known values of PV, I, and N into the formula and solve. PV = FV [( percent) 5 ] PV = $100 [( ) 5 ] PV = $100 [(1.10) 5 ] PV = $100 [1.6105] PV = $62.09 Thus, the process of discounting tells you that you ll need to invest $62.09 today. After 5 years of earning 10 percent interest annually, your investment will have a value of $100. The Future Value of an Annuity An annuity is a series of equal payments made at equal time intervals (for example, annually). An annuity that s paid annually is called an ordinary annuity. Let s look at some example problems that demonstrate how to calculate the value of an annuity. Note: The equations we provide in the study guide for calculating the time value of annuities take a different form than the equations in the textbook. We think you ll find that the study guide equations are simpler. Example: What will be the future value of an ordinary annuity after 3 years, if $100 is deposited annually and the account earns an interest rate of 10 percent annually? Solution: In this problem, you re given the following three variables. value of each payment (PMT) = $100 number of annuity payments (N) = 3 annual payments interest rate (I) = 10 percent annually The missing variable that you need to calculate is the future value of the annuity (FV), which is the value of the investment after 3 years. 12 Financial Management
7 You would use the following formula to calculate the future value of the investment (FV). FV = PMT [(1 + I.) N 1] I Substitute the known values of PMT, I, and N into the formula and solve. FV = $100 [( percent) 3 1] 10 percent FV = $100 [( ) 3 1] 0.10 FV = $100 [(1.10) 3 1] 0.10 FV = $100 [ ] 0.10 FV = $ FV = FV = $ Thus, the value of the annuity after 3 years will be $ The Present Value of an Annuity Now let s examine how to calculate the present value of an annuity, which is the amount of money you ll need to invest today to reach a future goal. Example: What is the present value of an annuity that will pay $100 a year, at the end of each of the next 3 years, at an interest rate of 10 percent annually? Solution: In this problem, you re given the following three variables. PMT = $100 N = 3 yearly payments I = 10 percent annually The missing variable that you need to calculate is the present value of the annuity (PV). You would use the following formula to calculate PV. PV = PMT {1 [1 (1 + I ) N ]} I Lesson 1 13
8 Substitute the known values of PMT, I, and N into the formula and solve. PV = $100 {[1 [1 ( percent) 3 ]} 10 percent PV = $100 {[1 [1 ( ) 3 ]} 0.10 PV = $100 {[1 [1 (1.10) 3 ]} 0.10 PV = $100 {[1 [ ]} 0.10 PV = $100 { } 0.10 PV = $ PV = PV = $ Thus, you ll need to invest $ today to receive payments of $100 per year for 3 years. Practice Problems Now, in this section, we ll examine some more practice problems. Work through each of the practice problems to make sure you understand the calculations that are represented. Example: At 5 percent interest compounded annually, how many years will be needed for an investment of $200 to grow to $255? Solution: In this problem, you re given the following three variables. FV = $255 PV = $200 I = 5 percent annually The missing variable that you need to calculate is the number of time periods (N). You would use the following formula to calculate N. FV = PV (1 + I ) N 14 Financial Management
9 Substitute the known values into the formula and solve for N. $255 = $200 (1 + 5 percent) N $255 = $200 ( ) N $255 = $200 (1.05) N $255 $200 = (1.05) N = (1.05) N log = N (log 1.05) = N ( ) = N 4.97 = N N = 5 years (rounded) Example: A widow currently has a $75,000 investment that yields 7 percent annually. Can she withdraw $15,000 a year for the next 10 years? Solution: This problem requires you to find the amount of money that can be withdrawn from her account annually. In other words, you re looking for the annuity payment for this investment. In this problem, you re given the following three variables. PV = $75,000 N = 10 yearly payments I = 7 percent annually The missing variable that you need to calculate is the value of each payment (PMT). You would use the following formula to calculate PMT. PV = PMT {1 [1 (1 + I ) N ]} I Lesson 1 15
10 Substitute the known values into the formula and solve for PMT. $75,000 = PMT {1 [1 (1 + 7 percent) 10 ]} 7 percent $75,000 = PMT {1 [1 ( ) 10 ]} 0.07 $75,000 = PMT {1 [1 (1.07) 10 ]} 0.07 $75,000 = PMT {1 [ ]} 0.07 $75,000 = PMT { } 0.07 $75,000 = PMT $75,000 = PMT $75, = PMT $10, = PMT No, she can withdraw only $10, per year for the next 10 years. Example: Imagine that you re 30 years old and inherit $75,000 from your grandfather. You want to invest your inheritance and increase the total amount to $100,000 after 4 years. What compound annual interest rate of return must you earn to achieve your goal? Solution: This problem requires you to find the interest rate that will produce a certain future value. You re given the following three variables: FV = $100,000 PV = $75,000 N = 4 You would use the following formula to calculate the interest rate (I). FV = PV (1 + I ) N 16 Financial Management
11 Substitute the known values into the formula and solve for I. $100,000 = 75,000 (1 + I.) 4 $100,000 75,000 = (1 + I.) = (1 + I.) 4 log = 4 log (1 + I.) = 4 log (1 + I.) = log (1 + I.) = 1 + I = I I = 7.5 percent (rounded) An interest rate of 6 percent will increase the amount of your inheritance to $100,000 after 4 years. Example: Suppose that you want an investment of $1,000 to double within a period of 3 years. At what annual rate of growth must your investment increase to achieve your goal? Solution: You need to find the interest rate that will cause your investment of $1,000 to double to $2,000 within 3 years. You re given the following three variables: FV = $2,000 PV = $1,000 N = 3 You would use the following formula to calculate the interest rate (I). FV = PV (1 + I ) N Lesson 1 17
12 Substitute the known values into the formula and solve for I. $2,000 = $1,000 (1 + I.) 3 $2,000 $1,000 = (1 + I.) 3 2 = (1 + I.) 3 log 2 = 3 log (1 + I.) = 3 log (1 + I.) = [3 log (1 + I.)] = log (1 + I.) 1.26 = 1 + I 0.26 = I I = 26 percent An interest rate of 26 percent will cause an investment of $1,000 to double within 3 years. Note that this answer will be the same no matter what value you choose for your present value. You can prove this to yourself if you wish by resolving the problem with a different present value. For example, try PV = $10,000 and FV = $20, Financial Management
13 SelfCheck 1 At the end of each section of Financial Management, you ll be asked to pause and check your understanding of what you ve just read by completing a SelfCheck. Writing the answers to these questions will help you review what you ve studied so far. Please complete SelfCheck 1 now. Indicate whether each of the following statements is True or False. 1. Compounding is the process of determining the amount of simple interest on an investment. 2. At an annual interest rate of 7 percent, it will take 16.2 years for an investment of $100 to triple to $ The future value of one dollar increases with lower interest rates. 4. The future value of one dollar increases with longer periods of time. 5. An ordinary annuity is a series of equal payments made at the beginning of each time period. Complete Problems 1, 2, 4, 5, 6, 7, 9, 12, 13, 14, 15, 18, and 19 on pages in the textbook. Check your answers with those on page 121. Lesson 1 19
first complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest.
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
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 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 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 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationCalculations for Time Value of Money
KEATMX01_p001008.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 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 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 informationMain TVM functions of a BAII Plus Financial Calculator
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
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 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 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 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 informationKey Concepts and Skills
McGrawHill/Irwin Copyright 2014 by the McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationTIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY
TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value
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 longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
More informationHow To Use Excel To Compute Compound Interest
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationIng. Tomáš Rábek, PhD Department of finance
Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received 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 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 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 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 informationIf I offered to give you $100, you would probably
File C596 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 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 informationTHE VALUE OF MONEY PROBLEM #3: ANNUITY. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
THE VALUE OF MONEY PROBLEM #3: ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction Earlier, we explained how to calculate the future value of a single sum placed on deposit
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 information#10. Timing is Everything. CPA... Imagine the possibilities!
#10 T I M E V A L U E O F M O N E Y Timing is Everything CPA... Imagine the possibilities! Intro Learning Activity Learning Objectives 1. Understand the time value of money. 2. Calculate the present value
More information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
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 informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationReview Page 468 #1,3,5,7,9,10
MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula
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 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 informationSolving Compound Interest Problems
Solving Compound Interest Problems What is Compound Interest? If you walk into a bank and open up a savings account you will earn interest on the money you deposit in the bank. If the interest is calculated
More informationImportant Financial Concepts
Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time
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 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 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 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 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 informationA = P (1 + r / n) n t
Finance Formulas for College Algebra (LCU  Fall 2013)  Formula 1: Amount
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 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 informationKey Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 11. Chapter 4
Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received
More informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
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 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 informationFinance Unit 8. Success Criteria. 1 U n i t 8 11U Date: Name: Tentative TEST date
1 U n i t 8 11U Date: Name: Finance Unit 8 Tentative TEST date Big idea/learning Goals In this unit you will study the applications of linear and exponential relations within financing. You will understand
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 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 information10.3 Future Value and Present Value of an Ordinary General Annuity
360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period
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 informationFIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1
FIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems  Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 31 a) Future Value = FV(n,i,PV,PMT)
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 informationContinuous Compounding and Discounting
Continuous Compounding and Discounting Philip A. Viton October 5, 2011 Continuous October 5, 2011 1 / 19 Introduction Most realworld project analysis is carried out as we ve been doing it, with the present
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 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 informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.
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 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 informationFinancial Management Spring 2012
31 Financial Management Spring 2012 Week 4 How to Calculate Present Values III 41 32 Topics Covered More Shortcuts Growing Perpetuities and Annuities How Interest Is Paid and Quoted 42 Example 33
More informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
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 informationLesson 4 Annuities: The Mathematics of Regular Payments
Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas
More informationOrdinary Annuities Chapter 10
Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate
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 informationActivity 3.1 Annuities & Installment Payments
Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.
More information5.1 Simple and Compound Interest
5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
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 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 information9.2 Summation Notation
9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a
More informationUnderstand the relationship between financial plans and statements.
#2 Budget Development Your Financial Statements and Plans Learning Goals Understand the relationship between financial plans and statements. Prepare a personal balance sheet. Generate a personal income
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 informationSection 4.2 (Future Value of Annuities)
Math 34: Fall 2015 Section 4.2 (Future Value of Annuities) At the end of each year Bethany deposits $2, 000 into an investment account that earns 5% interest compounded annually. How much is in her account
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 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 informationThis is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationThis lesson plan is from the Council for Economic Education's publication: Mathematics and Economics: Connections for Life 912
This lesson plan is from the Council for Economic Education's publication: Mathematics and Economics: Connections for Life 912 To purchase Mathematics and Economics: Connections for Life 912, visit:
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 informationFinance 3130 Sample Exam 1B Spring 2012
Finance 3130 Sample Exam 1B Spring 2012 True/False Indicate whether the statement is true or false. 1. A firm s income statement provides information as of a point in time, and represents how management
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 Revisited: Part 1 Terminology. Learning Outcomes. Time Value of Money
Time Value of Money Revisited: Part 1 Terminology Intermediate Accounting II Dr. Chula King 1 Learning Outcomes Definition of Time Value of Money Components of Time Value of Money How to Answer the Question
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 informationCheck off these skills when you feel that you have mastered them.
Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of
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 information5 More on Annuities and Loans
5 More on Annuities and Loans 5.1 Introduction This section introduces Annuities. Much of the mathematics of annuities is similar to that of loans. Indeed, we will see that a loan and an annuity are just
More informationANNUITIES. Ordinary Simple Annuities
An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities  Compounding periods and payment periods coincide. General Annuities  Compounding
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 informationThe Time Value of Money
C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
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 informationCHAPTER 6 Accounting and the Time Value of Money
CHAPTER 6 Accounting and the Time Value of Money 61 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary
More information