MODULE 2. Finance An Introduction


 Kory Byrd
 2 years ago
 Views:
Transcription
1 MODULE 2 Finance An Introduction The functions of finance in an organization is interlinked with other managerial responsibilities and in many instances, the finance manager could also done the role of a managing director. For the smooth functioning as well as to achieve excellence, organizations have to concentrate on the financial impact of a decision and its consequences. This also helps the organization to aim at a desired competency level against its competitors. Basic Concept In Finance In organizations, flow of money occurs at various points of time. In order to evaluate the worth of money, the financial managers need to look at it from a common platform, namely one time duration. This common platform enables a meaningful comparison of money over different time periods. An important principle in financial management is that the value of money depends on when the cash flow occurs which implies Rs.100 now is worth more than Rs.100 at some future time.
2 Time Value Of Money Time Value Of Money The TimeValue Of Money Money like any other desirable commodity has a price. If you own money, you can, 'rent' it to someone else, say a banker, who can use it to earn income. This 'rent' is usually in the form of interest. The investor's return, which reflects the timevalue of money, therefore indicates that there are investment opportunities available in the market. The return indicates that there is a riskfree rate of return rewarding investors for forgoing immediate consumption compensation for risk and loss of purchasing power.
3 Time Value Of Money Risk: An amount of Rs.100 now is certain, whereas Rs.100 receivable next year is less certain. This 'uncertainty' principle affects many aspects of financial management and is termed as risk value of money. Inflation: Under inflationary conditions, the value of money, expressed in terms of its purchasing power over goods and services, declines. Hence Rs.100 possessed now is not equivalent to Rs.100 to be received in the future. Personal consumption preference: Most of us have a strong preference for immediate rather than delayed consumption. As a result we tend to value the Rs.100 to be received now more than Rs.100 to be received latter. Future Value Vs. Present Value Future value (FV) and present value (PV) adjust all cash flows to a common time. This is relevant when we want to compare the cash flows occurring at different periods of time. Either in terms of projects, performance or turnover, the cash flows accrue to the company at different stages. The evaluation of all these cash flows are true when they are all brought to the same base period. Computing Present Value In financial parlance, a value of currency is not kept idle. The amount, if invested would certainly bring additional returns in the future. This future expectation from the present investment is termed as the future value.
4 Let us assume x amount is invested now and the investor expects r% to accrue on the investment one year ahead. This is translated into present and future values as follows: PV = Rs. x FV = Rs. x + (r * x) Computing Future Value Example Let us assume Rs.1,000 is invested now and the investor expects 5% to accrue on this investment one year ahead. This is translated into present and future values as follows: PV = Rs.1,000 FV = Rs.1,000 + (.05 * 1,000) = Rs.1,050. Computing Future Value This can be restated as FV = PV * (1+r) This relationship leads to the following concept of discounting the future value to arrive at the present value i.e., PV = FV / (1 + r) This is the formula for equating the future value that is associated at the end of 1st year. Now the concept of time over a longer duration can be easily brought into the above equation, where 'n' defines the time duration after which the cash flows are expected.
5 Computing Present Value Example Let us assume that Rs.1,000 is to be received at the end of 1 year from now and the investor expects 5% rate of return on this investment. Here FV = Rs.1,000 Hence the present value is computed as: PV = FV / (1 + r) = Rs.1000 / (1.05) = Rs.952. Value With And Without Compounding Interest without compounding is a simple interest formula i.e., Pnr/100 Where: P is the principle, n is the number of years and r is the interest rate. Interest with annual compounding adds the interest received earlier to the principle amount and increases the final amount that is received from the investment. Hence, the FV of an investment for a two year duration with annual compounding would be: FV = PV * (1+r)* (1+r) = PV * (1+r)^2. Hence Present Value is: PV = FV / (1+r)^2. This equation can be generalized for 'n' years as: PV = FV / (1 + r)^n
6 Future Value With And Without Compounding Compound Value In compounding, it is assumed that a certain sum accrues at the end of a time duration, which is again reinvested. In short, when a sum is invested in a year, it will yield interest and the interest is reinvested for the next year and so on till the time when withdrawal is made. The 3 year or 4 year bank deposit is a typical example of this annual interest compounding. Here: FV = Principal + interest FV = P(1+r)^n
7 The term (1+r)^n is the compound value factor (CVF) of a lump sum of Re.1, and it always has a value greater than 1 for positive r, indicating that CVF increases as r and n increase. Compound Value Example Assume a lump sum of Rs.1,000 is deposited in a bank fixed deposit for 3 years for an interest rate of 10% per annum. FV = Principal + interest FV = P(1+r)^n FV = 1000 x (1+.10)^3 = 1000 x = Rs.1,331. Compounding In Less Than A Duration Usually, it is common practice to compound the interest on a yearly basis. But, there are instances when compounding is done on a halfyearly, quarterly, monthly or a daily basis. The halfyearly interest rates indicate that interest is payable semiannually, i.e., interest is received r%/2 twice every year. When the principle of compounding is applied, this implies that the r%/2 received twice an year will yield an actual rate which is higher than the declared (r%) rate. This actual rate is called the effective annual rate. For instance, let us take an illustration of a banker declaring a 10% p.a. interest payable semiannually. This implies that at the end of the year the amount received for every one rupee will be 1 * (1+[10%/2]) * (1+[10%/2]) i.e., (1.05) * (1.05) = (1.05)^2 =
8 The Effective interest rate is 10.25% Effective Interest Rate The effective interest rate in the previous example was computed as =.1025 and in percentage terms it will be 10.25%. The effective rate of interest is hence 10.25% and not 10%. This can be expressed through the following formula: FV = PV (1+ r/m)^(m*n) where m is the number of times within a year interest is paid. When halfyearly interest payments are made 'm' will be 12/6 i.e., 2. When quarterly interest payments are made 'm' will be 12/3 i.e., 4. When monthly compounding is done then 'm' will be 12/1 i.e., 12. Compounding on a daily basis, 'm' will be 365/1 i.e., 365. This is referred to as multiperiod compounding. Continuous Compounding Sometimes compounding may be done continuously. For example, banks may pay interest continuously; they call it continuous compounding. It can be mathematically proved that the continuous compounding function will reduce to the following: FV = PV x {e^x} When x = (r * n) and e is mathematically defined as equal to Continuous Compounding Example The present value of an investment is Rs.1,000. At 10% p.a. interest rate at the end of 5 years, the future value of this investment with continuous compounding will be: FV = 1,000 x {e^.5} = Rs.1, When x = (r * n =.1 x 5 =.5) and e is mathematically defined as equal to
9 Similarly, the present value of a future flow of Rs.100 at 10% p.a. interest rate to be received 5 years hence with continuous compounding will be PV = FV / {e^.5} = 100 / {e^.5} = Rs Annuity There can be a uniform cash flow accrual every year over a period of 'n' years. This uniform flow is called "Annuity". An annuity is a fixed payment (or receipt) each year for a specified number of years. The future compound value of an annuity as follows: FV = A {[(1+r)^n  1]/ r} The term within the curly brackets {} is the compound value factor for an annuity of Re.1, and A is the annuity. The present value of an annuity hence will be PV = A {[11/(1+r)^n]/r} Annuity Example The Future value of Rs.10 received every year for a period of 5 years at an assumed interest rate of 10% per annum will be FV = 10 {[(1+0.1)^51]/ 0.1} = Rs The Present value of Rs.100 to be received every year in the next five years at an assumed interest rate of 10% per annum will be
10 PV =100{[11/(1+0.1)^5]/0.1}=Rs Resent Value Of Perpetuity Perpetuity is an annuity that occurs indefinitely. In perpetuity, time period, n, is so large (mathematically n approaches infinity) that the expression (1+r)^n in the present value equation tends to become zero, and the formula for a perpetuity simply condenses into: PV = A/r rate. where A is the annuity amount occurring indefinitely and r is the interest
11 Regular Annuity Vs. Annuity Due When an annuity's cash payments are made at the end of each period, it is referred as regular annuity. On the other hand, the annual payments/receipt can also be made at the beginning of each period. This is referred to as annuity due. Lease is a contract in which lease rentals (payment) are to be paid for the use of an asset. Hire purchase contract involves regular payments (installments) for acquiring (owning) an asset. A series of fixed payments starting at the beginning of each period for a specified duration is called an annuity due. Annuity Due The formula for computing value of an annuity due is: FV = A[(1 + r) + (1+r)^2+ (1+r)^ (1+r)^n1] FV = A {[(1+r)^(n1) 1] / r} Hence, PV = A {[11/(1+r)^n]/r } * (1+r) PV = A(PVRA,r)*(1+r) Where PVAR is present value of regular annuity and r is the interest rate. Annuity Due Example The future value of Rs.10 received in the beginning of each year for a 5 year duration at an assumed rate of 10% p.a. will be: FV = 10 {[(1+0.1)^(51) 1] / 0.1} = Rs The present value of Rs.100 received in the beginning of each year for 5 years at an assumed interest rate of 10% p.a. will be: PV = 100 {[11/(1+1.1)^5]/0.1 } x (1+0.1)= Rs
12 Multi Period Annuity Compounding The compound value of an annuity in case of the multiperiod compounding is given as follows: FV = A {[(1+r/m)^(n x m)] 1 } /(r/m) PV = A {1 [1/(1+r/m)^(n x m)]} / (r/m) In all instances, the discount rate will be (r/m) and the time horizon will be equal to (n x m). PRESENT VALUE OF A GROWING ANNUITY An annuity may not be a constant sum through the time duration, it may also grow at a rate of g% every year. This is referred as a growing annuity. When there is a growth for specific number of years, the present value of an annuity is stated using the following formula: Present Value Of A Growing Annuity Example An annuity of Rs.100 is expected to grow at a rate of 2% every year. Assuming the interest rate as 10% per annum the present value for this growing annuity for a 5 year duration will be: PV = 100 x {(1/0.08)[(1/0.08)*(1.02)^5/(1.1)^5]} = Rs
13 FUTURE VALUE OF A GROWING ANNUITY Future value of a growing annuity can be defined by the following formula: Future Value Of A Growing Annuity  Example Future value of an annuity of Rs.10 growing at 2% every year with an assumed rate of interest at 10% for five years is computed as: FV = 10 x {[1.1^5/0.08][1.02^5/0.08]} = Rs Present Value Of A Growing Annuity Perpetuity In financial decisionmaking there are number of situations where cash flows may grow at a compound rate. Here, the annuity is not a constant amount A but is subject to a growth factor 'g'. When the growth rate 'g' is constant, the formula can be simplified very easily. The calculation of the present value of a constantly growing perpetuity is given by the following equation: PV = A/(1+r) + A(1+g)/(1+r)^2 + A(1+g)^2/(1+r)^ This equation can be simplified as: PV = A / (r  g) Present Value Of A Growing Annuity Perpetuity In financial decisionmaking there are number of situations where cash flows may grow at a compound rate. Here, the annuity is not a constant amount A but is subject to a growth factor 'g'. When the growth rate 'g' is constant, the formula can be simplified very easily. The calculation of the present value of a constantly growing perpetuity is given by the following equation:
14 PV = A/(1+r) + A(1+g)/(1+r)^2 + A(1+g)^2/(1+r)^ This equation can be simplified as: PV = A / (r  g) Present Value Of Example A Growing Annuity Perpetuity The present value of an annuity of Rs.10 growing at 2% every year with an assumed rate of interest of 10% to perpetuity is: PV = A / (r  g) PV = 10 / ( ) = Rs.125.
Introduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationThe Institute of Chartered Accountants of India
CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able
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 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 information2 Time Value of Money
2 Time Value of Money BASIC CONCEPTS AND FORMULAE 1. Time Value of Money 2. Simple Interest 3. Compound Interest 4. Present Value of a Sum of Money 5. Future Value It means money has time value. A rupee
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 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 informationTIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!
TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on
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 informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
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 informationBasic Concept of Time Value of Money
Basic Concept of Time Value of Money CHAPTER 1 1.1 INTRODUCTION Money has time value. A rupee today is more valuable than a year hence. It is on this concept the time value of money is based. The recognition
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 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 (Nonannual Payments)... 4 3. Conversion of Annual into
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 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 C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
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 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 informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
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 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 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 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 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 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 informationLO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.
LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please
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 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 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 informationBasic financial arithmetic
2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals
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 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 informationSample problems from Chapter 10.1
Sample problems from Chapter 10.1 This is the annuities sinking funds formula. This formula is used in most cases for annuities. The payments for this formula are made at the end of a period. Your book
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 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 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 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 informationChapter 1 The Measurement of Interest
Interest: the compensation that a borrower of capital pays to a lender of capital for its use. It can be viewed as a form of rent that the borrower pays to the lender to compensate for the loss of use
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
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 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 informationCOMPOUND INTEREST AND ANNUITY TABLES
COMPOUND INTEREST AND ANNUITY TABLES COMPOUND INTEREST AND ANNUITY TABLES 8 Percent VALUE OF AN NO. OF PRESENT PRESENT VALUE OF AN COM AMORTIZ ANNUITY  ONE PER YEARS VALUE OF ANNUITY POUND ATION YEAR
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 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 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 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 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 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 information( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100
Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded
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 $5,000 per month in retirement.
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More information1 Interest rates, and riskfree investments
Interest rates, and riskfree investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 ($) in an account that offers a fixed (never to change over time)
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 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 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 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 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 informationFinancial and Investment Mathematics. Dr. Eva Cipovová Department of Business Management Email: evacipovova@gmail.com
Financial and Investment Mathematics Dr. Eva Cipovová Department of Business Management Email: evacipovova@gmail.com Content 1. Interest and annual interest rate. Simple and compound interest, frequency
More informationAccounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money
Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate WynnWilliams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest
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 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 informationChapter 8. 48 Financial Planning Handbook PDP
Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for
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 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 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 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 informationSolutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at
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. appendix B NATURE OF INTEREST
appendix B Time value of money LEARNING OBJECTIVES After studying this appendix, you should be able to: Distinguish between simple and compound interest. Solve for future value of a single amount. Solve
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 informationStock valuation. Price of a First period's dividends Second period's dividends Third period's dividends = + + +... share of stock
Stock valuation A reading prepared by Pamela Peterson Drake O U T L I N E. Valuation of common stock. Returns on stock. Summary. Valuation of common stock "[A] stock is worth the present value of all the
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 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 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 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 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 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 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 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 informationTime Value of Money Concepts
BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction.
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
More informationMATHEMATICS OF FINANCE AND INVESTMENT
MATHEMATICS OF FINANCE AND INVESTMENT G. I. FALIN Department of Probability Theory Faculty of Mechanics & Mathematics Moscow State Lomonosov University Moscow 119992 g.falin@mail.ru 2 G.I.Falin. Mathematics
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
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 informationWarmup: Compound vs. Annuity!
Warmup: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years
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 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 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 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 informationMBA Finance PartTime Present Value
MBA Finance PartTime 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 informationIf Alfred s endowment was payable in five years time what sum should be payable to make both of equal value?
FUTURE VALUE OF A SINGLE SUM Question 1 Alfred and George are brothers. They have both been given an endowment of 5,000 by Great Uncle Edward. George will receive his money immediately whilst Alfred must
More informationConstruction Economics & Finance. Module 6. Lecture1
Construction Economics & Finance Module 6 Lecture1 Financial management: Financial management involves planning, allocation and control of financial resources of a company. Financial management is essential
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 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 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 information