Present Value (PV) Tutorial


 Cody Singleton
 2 years ago
 Views:
Transcription
1 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, and assignments. PRESENT VALUE CONCEPTS There s an old saying, time is money. This saying reflects the notion that as time passes, the assets and liabilities we hold are changing, due to interest. Interest is the payment to the owner of an asset for its use by a borrower. The most common example of this type of asset is a savings account. As we keep a balance of cash in our account, it earns interest that is paid to us by the financial institution. An example of a liability is a car loan. As we carry the balance of the loan, we accumulate interest costs on this debt. We must ultimately repay this loan with interest. Present value computations are a means for us to estimate the interest component of holding assets or liabilities over time. The present value of an amount applies when we either lend or borrow an asset that must be repaid in full at some future date, and we want to know its worth today. The first section focuses on the present value of a single amount. The next section will focus on the present value of a series of amounts (or annuity). LO 1 Describe the earning of interest and the concept of present value. LEARNING OBJECTIVES LO 1 Describe the earning of interest and the concept of present value. LO 2 Apply present value concepts to a single amount by using interest tables. LO Apply present value concepts to an annuity by using interest tables. 1
2 2 Extend Your Knowledge 151 Present Value (PV) Tutorial PRESENT VALUE OF A SINGLE AMOUNT We graphically express the present value (p) of a single future amount (f ) received or paid at a future date in Exhibit PV15.1. EXHIBIT PV15.1 Present Value of a Single Amount f Time p Today Future LO 2 Apply present value concepts to a single amount by using interest tables. The formula to calculate the present value of this single amount is shown in Exhibit PV15.2 where: p present value; ƒ future value; i rate of interest per period; and n number of periods. EXHIBIT PV15.2 Present Value of a Single Amount Formula f p (1 i) n To illustrate the application of this formula, let s assume we need $220 one period from today. We want to know how much must be invested now, for one period, at an interest rate of 10% to provide for this $ For this illustration the p, or present value, is the unknown amount. In particular, the present and future values, along with the interest rate, are shown graphically as: f $220 (i 0.10) p? Conceptually, we know p must be less than $220. This is obvious from the answer to the question: Would we rather have $220 today or $220 at some future date? If we had $220 today, we could invest it and see it grow to something more than $220 in the future. Therefore, if we were promised $220 in the future, we would take less than $220 today. But how much less? To answer that question, we can calculate an estimate of the present value of the $220 to be received one period from now using the formula in Exhibit PV15.2 as: p f $220 $200 (1 i) n (1 0.10) 1 This means we are indifferent between $200 today or $220 at the end of one period. 1 Interest is also called a discount, and an interest rate is also called a discount rate.
3 Extend Your Knowledge 151 Present Value (PV) Tutorial 3 We can also use this formula to calculate the present value for any number of periods. To illustrate this calculation, we consider a payment of $242 at the end of two periods at 10% interest. The present value of this $242 to be received two periods from now is calculated as: p f $242 $200 (1 i) n (1 0.10) 2 These results tell us we are indifferent between $200 today, or $220 one period from today, or $242 two periods from today. The number of periods (n) in the present value formula does not have to be expressed in years. Any period of time such as a day, a month, a quarter, or a year can be used. But, whatever period is used, the interest rate (i) must be compounded for the same period. This means if a situation expresses n in months, and i equals 12% per year, then we can assume 1% of an amount invested at the beginning of each month is earned in interest per month and added to the investment. In this case, interest is said to be compounded monthly. A present value table helps us with present value calculations. It gives us present values for a variety of interest rates (i) and a variety of periods (n). Each present value in a present value table assumes the future value (f) is 1. When the future value (f) is different from 1, we can simply multiply present value (p) by that future amount to give us our estimate. The formula used to construct a table of present values of a single future amount of 1 is shown in Exhibit PV p (1 i) n EXHIBIT PV15.3 Present Value of 1 Formula This formula is identical to that in Exhibit PV15.2 except that f equals 1. Table 15B.1 (from Appendix 15B to Chapter 15, repeated at the end of this EYK) is a present value table for a single future amount. It is often called a present value of 1 table. A present value table involves three 2 factors: p, i, and n. Knowing two of these three factors allows us to calculate the third. To illustrate, consider the three possible cases. Case 1 (solve for p, knowing i and n). Our example above is a case in which we need to solve for p when we know i and n. To illustrate how we use a present value table, let s again look at how we estimate the present value of $220 (f ) at the end of one period (n) where the interest rate (i) is 10%. To answer this we go to the present value table (Table 15B.1) and look in the row for one period and in the column for 10% interest. Here we find a present value (p) of based on a future value of 1. This means, for instance, that $1 to be received one period from today at 10% interest is worth $ today. Since the future value is not $1, but is $220, we multiply the by $220 to get an answer of $200. Case 2 (solve for n, knowing p and i). This is a case in which we have, say, a $100,000 future value (f ) valued at $13,000 today ( p) with an interest rate of 12% (i). In this case we want to know how many periods (n) there are between the present value and the future value. A case example is when we want to retire with $100,000, but have only $13,000 earning a 12% return. How long will it be before we can retire? To answer this, we go to Table 15B.1 and look in the 12% interest column. Here 2 A fourth is f, but as we already explained, we need only multiply the 1 used in the formula by f.
4 4 Extend Your Knowledge 151 Present Value (PV) Tutorial we find a column of present values (p) based on a future value of 1. To use the present value table for this solution, we must divide $13,000 (p) by $100,000 (f ), which equals This is necessary because a present value table defines f equal to 1, and p as a fraction of 1. We look for a value nearest to (p), which we find in the row for 18 periods (n). This means the present value of $100,000 at the end of 18 periods at 12% interest is $13,000 or, alternatively stated, we must work 18 more years. Case 3 (solve for i, knowing p and n). This is a case where we have, say, a $120,000 future value (f ) valued at $60,000 (p) today when there are nine periods (n) between the present and future values. Here we want to know what rate of interest is being used. As an example, suppose we want to retire with $120,000, but we only have $60,000 and hope to retire in nine years. What interest rate must we earn to retire with $120,000 in nine years? To answer this, we go to the present value table (Table 15B.1) and look in the row for nine periods. To again use the present value table we must divide $60,000 (p) by $120,000 (f ), which equals Recall this is necessary because a present value table defines f equal to 1, and p as a fraction of 1. We look for a value in the row for nine periods that is nearest to (p), which we find in the column for 8% interest (i). This means the present value of $120,000 at the end of nine periods at 8% interest is $60,000 or, in our example, we must earn 8% annual interest to retire in nine years. CHECKPOINT 1. A company is considering an investment expected to yield $70,000 after six years. If this company demands an 8% return, how much is it willing to pay for this investment? Do Quick Study question: QS PV151 LO 3 Apply present value concepts to an annuity by using interest tables. PRESENT VALUE OF AN ANNUITY An annuity is a series of equal payments occurring at equal intervals. One example is a series of three annual payments of $100 each. The present value of an ordinary annuity is defined as the present value of equal payments at equal intervals as of one period before the first payment. An ordinary annuity of $100 and its present value ( p) is illustrated in Exhibit PV15.4. EXHIBIT PV15.4 Present Value of an Ordinary Annuity $100 $100 $100 Time p Today Future (n 1) Future (n 2) Future (n 3) One way for us to calculate the present value of an ordinary annuity is to find the present value of each payment using our present value formula from Exhibit PV15.3. We then would add up each of the three present values. To illustrate, let s look at three $100 payments at the end of each of the next three periods with an interest rate of 15%. Our present value calculations are: p $100 $100 $100 $ (1 0.15) 1 (1 0.15) 2 (1 0.15) 3
5 Extend Your Knowledge 151 Present Value (PV) Tutorial 5 This calculation also is identical to calculating the present value of each payment (from Table 15B.1) and taking their sum or, alternatively, adding the values from Table 15B.1 for each of the three payments and multiplying their sum by the $100 annuity payment. A more direct way is to use a present value of annuity table, Table 15B.2. If we look at Table 15B.2 where n 3 and i 15%, we see that the present value is This means the present value of an annuity of 1 for three periods, with a 15% interest rate, is A present value of annuity formula is used to construct Table 15B.2. It can also be constructed by adding the amounts in a present value of 1 table. To illustrate, we use Tables 15B.1 and 15B.2 to confirm this relation for the prior example. From Table 15B.1 From Table 15B.2 i 15%, n i 15%, n i 15%, n Total i 15%, n We can also use business calculators or spreadsheet computer programs to find the present value of an annuity. CHECKPOINT 2. A company is considering an investment paying $10,000 every six months for three years. The first payment would be received in six months. If this company requires an annual return of 8%, what is the maximum amount it is willing to invest? Do quick study questions: QS PV152, QS PV153, QS PV154 SUMMARY OF EYK 151 LO 1 Describe the earning of interest and the concepts of present value. Interest is payment to the owner of an asset for its use by a borrower. Present value calculations are a means for us to estimate the interest component of holding assets or liabilities over a period of time. LO 2 Apply present value concepts to a single amount by using interest tables. The present value of a single amount to be received at a future date is the amount that can be invested now at the specified interest rate to yield that future value. LO 3 Apply present value concepts to an annuity by using interest tables. The present value of an annuity is the amount that can be invested now at the specified interest rate to yield that series of equal periodic payments. GUIDANCE ANSWERS TO CHECKPOINT 1. $70, $44,114 (using Table 15B.1, i 8%, n 6). 2. $10, $52,421 (using Table 15B.2, i 4%, n 6).
6 6 Extend Your Knowledge 151 Present Value (PV) Tutorial QUICK STUDY QS PV151 Present value of an amount LO 2 Kim Flaherty is considering an investment that, if paid for immediately, is expected to return $140,000 five years hence. If Flaherty demands a 9% return, how much is she willing to pay for this investment? QS PV152 Present value of an annuity LO 3 Beene Distributing is considering a contract that will return $150,000 annually at the end of each year for six years. If Beene demands an annual return of 7% and pays for the investment immediately, how much should it be willing to pay? QS PV153 Interest rate on an investment LO 2 Ken Francis has been offered the possibility of investing $2,745 for 15 years, after which he will be paid $10,000. What annual rate of interest will Francis earn? QS PV154 Number of periods of an investment LO 2 Megan Brink has been offered the possibility of investing $6,651. The investment will earn 6% per year and will return Brink $10,000 at the end of the investment. How many years must Brink wait to receive the $10,000? EXERCISES Exercise PV151 Interest rate on an investment LO 3 Betsey Jones expects an immediate investment of $57,466 to return $10,000 annually for eight years, with the first payment to be received in one year. What rate of interest will Jones earn? Exercise PV152 Number of periods of an investment LO 3 Keith Riggins expects an investment of $82,014 to return $10,000 annually for several years. If Riggins is to earn a return of 10%, how many annual payments must he receive? Exercise PV153 Present value of an annuity LO 3 Sam Weber financed a new automobile by paying $6,500 cash and agreeing to make 40 monthly payments of $500 each, with the first payment to be made one month after the purchase. The loan bears interest at an annual rate of 12%. What was the cost of the automobile? Exercise PV154 Present value of bonds LO 2,3 Spiller Corp. plans to issue 10%, 15year, $500,000 par value bonds payable that pay interest semiannually on June 30 and December 31. The bonds are dated December 31, 2014, and are to be issued on that date. If the market rate of interest for the bonds is 8% on the date of issue, what will be the cash proceeds from the bond issue? Exercise PV155 Present value of an amount LO 1,2,3 McAdams Company expects to earn 10% per year on an investment that will pay $606,773 six years hence. Use Table 15B.1 to calculate the present value of the investment.
7 Extend Your Knowledge 151 Present Value (PV) Tutorial 7 Exercise PV156 Present value of an amount and annuity LO 2,3 Calculate the amount that can be borrowed under each of the following circumstances: a. A promise to pay $90,000 in seven years at an interest rate of 6%. b. An agreement made on February 1, 2014, to make three payments of $20,000 on February 1 of 2015, 2016, and The annual interest rate is 10%. Exercise PV157 Present value of an amount LO 2 On January 1, 2014, a company agrees to pay $20,000 in three years. If the annual interest rate is 10%, determine how much cash the company can borrow with this promise. Exercise PV158 Present value of an amount LO 2 Find the amount of money that can be borrowed with each of the following promises: Single Future Number Interest Case Payment of Years Rate a. $40, % b. 75, % c. 52, % d % e. 63, % f. 89, % Exercise PV159 Present values of annuities LO 3 C&H Ski Club recently borrowed money and agreed to pay it back with a series of six annual payments of $5,000 each. C&H subsequently borrowed more money and agreed to pay it back with a series of four annual payments of $7,500 each. The annual interest rate for both loans is 6%. a. Use Table 15B.1 to find the present value of these two annuities. (Round amounts to the nearest dollar.) b. Use Table 15B.2 to find the present value of these two annuities. Exercise PV1510 Present value with semiannual compounding LO 1,3 Otto Co. borrowed cash on April 30, 2014, by promising to make four payments of $13,000 each on November 1, 2014, May 1, 2015, November 1, 2015, and May 1, a. How much cash is Otto able to borrow if the interest rate is 8%, compounded semiannually? b. How much cash is Otto able to borrow if the interest rate is 12%, compounded semiannually? c. How much cash is Otto able to borrow if the interest rate is 16%, compounded semiannually?
8 8 Extend Your Knowledge 151 Present Value (PV) Tutorial TABLE 15B.1 Present Value of 1 Due in n Periods Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% TABLE 15B.2 Present Value of an Annuity of 1 per Period Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15%
Time Value of Money CAP P2 P3. Appendix. Learning Objectives. Conceptual. Procedural
Appendix B Time Value of Learning Objectives CAP Conceptual C1 Describe the earning of interest and the concepts of present and future values. (p. B1) Procedural P1 P2 P3 P4 Apply present value concepts
More informationModule 8: Current and longterm liabilities
Module 8: Current and longterm liabilities Module 8: Current and longterm liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationPREVIEW OF CHAPTER 62
61 PREVIEW OF CHAPTER 6 62 Intermediate Accounting IFRS 2nd Edition Kieso, Weygandt, and Warfield 6 Accounting and the Time Value of Money LEARNING OBJECTIVES After studying this chapter, you should
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 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 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 1. Compound Interest
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
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 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 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 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 informationA = P (1 + r / n) n t
Finance Formulas for College Algebra (LCU  Fall 2013)  Formula 1: Amount
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 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 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 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 informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
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 informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
More informationCorporate Finance Fundamentals [FN1]
Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose
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 information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationThe Time Value of Money/ Present Values Appendix C
The Time Value Money/ Present Values Appendix C THIS IS ABOUT THE BASICS You should become familiar with the concept present values and the basics how they work using the tables. This is NOT intended to
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 informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
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 informationIntroduction 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 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 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 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 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 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 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 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 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 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 informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
More information14 ARITHMETIC OF FINANCE
4 ARITHMETI OF FINANE Introduction Definitions Present Value of a Future Amount Perpetuity  Growing Perpetuity Annuities ompounding Agreement ontinuous ompounding  Lump Sum  Annuity ompounding Magic?
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 informationThe following is an article from a Marlboro, Massachusetts newspaper.
319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston  Last week
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 informationEXERCISE 64 (15 20 minutes)
EXERCISE 64 (15 20 minutes) (a) (b) (c) (d) Future value of an ordinary annuity of $4,000 a period for 20 periods at 8% $183,047.84 ($4,000 X 45.76196) Factor (1 +.08) X 1.08 Future value of an annuity
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 (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 informationVilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis
Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................
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 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 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 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 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 informationExercise 1 for Time Value of Money
Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing
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 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 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 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 informationDeterminants of Valuation
2 Determinants of Valuation Part Two 4 Time Value of Money 5 FixedIncome Securities: Characteristics and Valuation 6 Common Shares: Characteristics and Valuation 7 Analysis of Risk and Return The primary
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 5 Discounted Cash Flow Valuation
Chapter Discounted Cash Flow Valuation Compounding Periods Other Than Annual Let s examine monthly compounding problems. Future Value Suppose you invest $9,000 today and get an interest rate of 9 percent
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 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 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 informationApplying Time Value Concepts
Applying Time Value Concepts C H A P T E R 3 based on the value of two packs of cigarettes per day and a modest rate of return? Let s assume that Lou will save an amount equivalent to the cost of two packs
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 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 informationthe Time Value of Money
8658d_c06.qxd 11/8/02 11:00 AM Page 251 mac62 mac62:1st Shift: 6 CHAPTER Accounting and the Time Value of Money he Magic of Interest T Sidney Homer, author of A History of Interest Rates, wrote, $1,000
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 informationBonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University
Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University
More 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 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 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 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 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 information4 Annuities and Loans
4 Annuities and Loans 4.1 Introduction In previous section, we discussed different methods for crediting interest, and we claimed that compound interest is the correct way to credit interest. This section
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 informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
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 informationFoundation review. Introduction. Learning objectives
Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation
More information