Financial Management


 Berniece Cross
 6 years ago
 Views:
Transcription
1 Just Published! 206 Financial Management Principles & Practice 7e By Timothy Gallagher Colorado State University Changes to the new Seventh Edition: Updating of all time sensitive material and some new chapter openers that refer to recent major financial events Many fictional company and people names in endofchapter material changes to appeal to today s college age students Brandnew test item file and test disk Improved PowerPoint Lecture Slidesall new design All new problems in Chapter 8 Time Value of Money plus many new problems in other chapters. Benefit corporations including those chartered by those states that allow corporate charters that permit the firm to consider the interests of society and nonowners along with those of the owners and those corporations certified by B Lab as having similarly broad goals Aftermath of the 2008 Financial Crisis including updates on regulatory changes inspired by this crisis and the implementation of the Dodd Frank law and its Volker Rule Activist investors how they influence companies and how they pressure companies into certain actions that might not otherwise be undertaken Spreadsheet solutions and descriptions, including Excel screen shots for time value of money and capital budgeting material Textbook Media Press Replacing Oligarch Textbooks since 2004 The Quality Instructors Expect At Prices Students Can Afford
2 7th Edition Student Options & Prices For Instructors Instructor s Manual Solutions Manual Computerized Test Bank PowerPoint Lecture Slides To Review Online Textbook To Request Paperback I just had to let you know what a big fan I am of Gallagher's textbook. Gallagher has a knack for presenting difficult concepts in a clear and straightforward manner without compromising the rigorous standards I have for my students. And all this in your lowcost format? Amazing! I just can't say enough. You've got to get the word out about this book! Susan C. Myrick; Professor of Business; Allegheny College.
3 3 More about 7e The Gallagher text is a great choice at any price, and compares favorably with its market leading (and much more expensive) competitors. Jack Trifts, Ph.D., Professor of Finance, Bryant University Table of Contents Here s a partial list of colleges/universities that used the previous editions of Gallagher: Finance and the Firm 2 Financial Markets and Interest Rates 3 Financial Institutions 4 Review of Accounting 5 Analysis of Financial Statements 6 Forecasting for Financial Planning 7 Risk and Return 8 The Time Value of Money 9 The Cost of Capital 0 Capital Budgeting Decision Methods Estimating Incremental Cash Flows 2 Business Valuation 3 Capital Structures Basics 4 Corporate Bonds, Preferred Stock & Leasing 5 Common Stock 6 Dividend Policy 7 Working Capital Policy 8 Managing Cash 9 Accounts Receivable and Inventory 20 ShortTerm Financing 2 International Finance 3
4 For your students: a popular spreadsheet supplement! 7e Spreadsheet TutorPak Tutorial, Stepthru Applications, and Topic JumpCharts Created by the textbook author, Tim Gallagher, PhD., and his colleague at Colorado State University, Hong Miao, PhD, 7e Spreadsheet TutorPak features four handy tools to help students understand Microsoft Excel spreadsheets, and then both practice and apply their spreadsheet skills to meet the objectives of this course. Spreadsheets 0 An Introduction to Using Microsoft Excel By Tim Gallagher Ph Colorado State University and Hong Miao Ph Colorado State University e Spreadsheet TutorPak Tutorial, Stepthru Applications, and Topic Jump Charts for Microsoft Excel Spreadsheets 0: An Introduction to Using Microsoft Excel : this 25page booklet helps students learn how to create and manipulate Microsoft Excel spreadsheets so they can apply these skills to solve financial problems on their own. The tutorial starts with simple concepts such as inserting and deleting rows and columns, copying and pasting with absolute and relative addresses, and then tackles more complex applications like looking up financial functions, graphing, and how to use macros. (Format: PDF) Spreadsheet Stepthru Applications: Tied to specific problems in 7e, these Microsoft Excel spreadsheets feature builtin macros that allow students to see the spreadsheet being built, step by step, up to the point where the problem being addressed is solved. Correlated to chapters where a new concept is introduced, the spreadsheets are set up with macros that allow the student to hit a key to move from step to step n, so the student simply opens the downloaded spreadsheet and follows the directions. Students test their mastery by entering data into the spreadsheet. A macro causes the spreadsheet to "reply," and the student responds with the next indicated step, and so on until the problem is solved. While useful for testing mastery for all concepts, this application is a great tool for helping students grasp the future value of a single amount, present value of a single amount, future value of an annuity, and internal rate of return. In all problems solved in the main body of each chapter, where algebraic, table, and financial calculator solutions are shown, the Excel approach to solving these problems is now offered. (Format Microsoft Excel ) Return to Topic JumpStart
5 Spreadsheet Supplements (contd ) 7e Spreadsheet TutorPak Tutorial, Stepthru Applications, and Topic JumpCharts Features (contd.): Enhanced Microsoft Excel Spreadsheets: Designed to provide dynamic illustration of important financial concepts presented in the textbook. For example, an amortization table is provided that allows students to vary the loan amount, interest rate, and maturity of an amortized loan and see the resulting changes to the monthbymonth figures. Mean, standard deviation, and correlation coefficient input values can be changed by the student (includes the generation of twoasset portfolio values, with a graph). Price, variable cost, and fixed cost figures can be varied by the students with the resulting breakeven information, including a graph, provided by the spreadsheet. These are just a few examples of how important finance concepts are presented in a dynamic way to facilitate learning, rather than relying on only a static two dimensional page. (Format Microsoft Excel ) Return to Topic JumpStart Topic JumpCharts: Lists and describes in detail the Stepthru Applications by chapter, with handy bookmarks, so students can jump right to the Stepthru Application they want to work on. (Format: PDF) BUN LE PRICE: $5 00 7e Spreadsheet TutorPak Tutorial, Stepthru Applications, and Topic JumpCharts when bundled with 6e purchased at Textbook Media web site STAN ALONE PRICE: $9 90
6 The Time Value of Money The importance of money flows from it being a link between the present and the future. John Maynard Keynes 8 CHAPTER Get a Free $,000 Bond with Every Car Bought This Week! There is a car dealer who appears on television regularly. He does his own commercials. He is quite loud and is also very aggressive. According to him you will pay way too much if you buy your car from anyone else in town. You might have a car dealer like this in your hometown. The author of this book used to watch and listen to the television commercials for a particular car dealer. One promotion struck him as being particularly interesting. The automobile manufacturers had been offering cash rebates to buyers of particular cars but this promotion had recently ended. This local car dealer seemed to be picking up where the manufacturers had left off. He was offering a free $,000 bond with every new car purchased during a particular week. This sounded pretty good. The fine print of this deal was not revealed until the buyer was signing the final sales papers. Even then you had to look close since the print was small. It turns out the $,000 bond offered to each car buyer was what is known as a zero coupon bond. This means that there are no periodic interest payments. The buyer of the bond pays a price less than the face value of $,000 and then at maturity the issuer pays $,000 to the holder of the bond. The investor s return is entirely equal to the difference between the lower price paid for the bond and the $,000 received at maturity. How much less than $,000 did the dealer have to pay to get this bond he was giving away? The amount paid by the dealer is what the bond would be worth (less after paying commissions) if the car buyer wanted to sell this bond now. It turns out that this bond had a maturity of 30 years. This is how long the car buyer would have to wait to receive the $,000. The value of the bond at the time the car was purchased was about $57. This is what the car dealer paid for each of these bonds and is the amount the car buyer would get from selling the bond. It s a pretty shrewd marketing gimmick when a car dealer can buy something for $57 and get the customers to believe they are receiving something worth $,000. Learning Objectives After reading this chapter, you should be able to:. Explain the time value of money and its importance in the business world. 2. Calculate the future value and present value of a single amount. 3. Find the future and present values of an annuity. 4. Solve time value of money problems with uneven cash flows. 5. Solve for the interest rate, number or amount of payments, or the number of periods in a future or present value problem. 63
7 In this chapter you will become armed against such deceptions. It s all in the time value of money. Source: This is inspired by an actual marketing promotion. Some of the details have been changed, and all identities have been hidden, so the author does not get sued. Chapter Overview 64 Part 2 Essential Concepts in Finance A dollar in hand today is worth more than a promise of a dollar tomorrow. This is one of the basic principles of financial decision making. Time value analysis is a crucial part of financial decisions. It helps answer questions about how much money an investment will make over time and how much a firm must invest now to earn an expected payoff later. In this chapter we will investigate why money has time value, as well as learn how to calculate the future value of cash invested today and the present value of cash to be received in the future. We will also discuss the present and future values of an annuity a series of equal cash payments at regular time intervals. Finally, we will examine special time value of money problems, such as how to find the rate of return on an investment and how to deal with a series of uneven cash payments. Why Money Has Time Value The time value of money means that money you hold in your hand today is worth more than the same amount of money you expect to receive in the future. Similarly, a given amount of money you must pay out today is a greater burden than the same amount paid in the future. In Chapter 2 we learned that interest rates are positive in part because people prefer to consume now rather than later. Positive interest rates indicate, then, that money has time value. When one person lets another borrow money, the first person requires compensation in exchange for reducing current consumption. The person who borrows the money is willing to pay to increase current consumption. The cost paid by the borrower to the lender for reducing consumption, known as an opportunity cost, is the real rate of interest. The real rate of interest reflects compensation for the pure time value of money. The real rate of interest does not include interest charged for expected inflation or the other risk factors discussed in Chapter 2. Recall from the interest rate discussion in Chapter 2 that many factors including the pure time value of money, inflation risk, default risk, illiquidity risk, and maturity risk determine market interest rates. The required rate of return on an investment reflects the pure time value of money, an adjustment for expected inflation, and any other risk premiums present. Measuring the Time Value of Money Financial managers adjust for the time value of money by calculating the future value and the present value. Future value and present value are mirror images of each other. Future value is the value of a starting amount at a future point in time, given the rate of growth per period and the number of periods until that future time. How much will $,000 invested today at a 0 percent interest rate grow to in 5 years? Present value is the value of a future amount today, assuming a specific required interest rate for a number of periods until that future amount is realized. How much should we pay today to obtain a promised payment of $,000 in 5 years if investing money today would yield a 0 percent rate of return per year? The Future Value of a Single Amount To calculate the future value of a single amount, we must first understand how money grows over time. Once money is invested, it earns an interest rate that compensates for the time value of money and, as we learned in Chapter 2, for default risk, inflation, and other
8 factors. Often, the interest earned on investments is compound interest interest earned on interest and on the original principal. In contrast, simple interest is interest earned only on the original principal. To illustrate compound interest, assume the financial manager of SaveCom decided to invest $00 of the firm s excess cash in an account that earns an annual interest rate of 5 percent. In one year, SaveCom will earn $5 in interest, calculated as follows: Balance at the end of year = Principal + Interest = $00 + (00.05) = $00 ( +.05) = $00.05 = $05 The total amount in the account at the end of year, then, is $05. But look what happens in years 2 and 3. In year 2, SaveCom will earn 5 percent of 05. The $05 is the original principal of $00 plus the first year s interest so the interest earned in year 2 is $5.25, rather than $5.00. The end of year 2 balance is $0.25 $00 in original principal and $0.25 in interest. In year 3, SaveCom will earn 5 percent of $0.25, or $5.5, for an ending balance of $5.76, shown as follows: Beginning = Ending Balance ( + Interest Rate) Balance Interest Year $ = $05.00 $5.00 Year 2 $ = $0.25 $5.25 Year 3 $ = $5.76 $5.5 In our example, SaveCom earned $5 in interest in year, $5.25 in interest in year 2 ($0.25 $05.00), and $5.5 in year 3 ($5.76 $0.25) because of the compounding effect. If the SaveCom deposit earned interest only on the original principal, rather than on the principal and interest, the balance in the account at the end of year 3 would be $5 ($00 + ($5 3) = $5). In our case the compounding effect accounts for an extra $.76 ($5.76 $5.00 =.76). The simplest way to find the balance at the end of year 3 is to multiply the original principal by plus the interest rate per period (expressed as a decimal), + k, raised to the power of the number of compounding periods, n. Here s the formula for finding the future value or ending balance given the original principal, interest rate per period, and number of compounding periods: Future Value for a Single Amount Algebraic Method FV = PV ( + k) n (8a) where: FV = Future Value, the ending amount PV = Present Value, the starting amount, or original principal k = Rate of interest per period (expressed as a decimal) n = Number of time periods. The compounding periods are usually years but not always. As you will see later in the chapter, compounding periods can be months, weeks, days, or any specified period of time. Chapter 8 The Time Value of Money 65
9 In our SaveCom example, PV is the original deposit of $00, k is 5 percent, and n is 3. To solve for the ending balance, or FV, we apply Equation 8a as follows: FV = PV ( + k) n = $00 (.05) 3 = $ = $5.76 We may also solve for future value using a financial table. Financial tables are a compilation of values, known as interest factors, that represent a term, ( + k) n in this case, in time value of money formulas. Table I in the Appendix at the end of the book is developed by calculating ( + k) n for many combinations of k and n. Table I in the Appendix at the end of the book is the future value interest factor (FVIF) table. The formula for future value using the FVIF table follows: Future Value for a Single Amount Table Method FV = PV ( FVIF k, n ) (8b) where: FV = Future Value, the ending amount PV = Present Value, the starting amount FVIF k,n = Future Value Interest Factor given interest rate, k, and number of periods, n, from Table I In our SaveCom example, in which $00 is deposited in an account at 5 percent interest for three years, the ending balance, or FV, according to Equation 8b, is as follows: FV = PV ( FVIF k, n ) = $00 ( FVIF 5%, 3 ) = $ (from the FVIF table) = $5.76 To solve for FV using a financial calculator, we enter the numbers for PV, n, and k (k is depicted as I/Y on the TI BAII PLUS calculator; on other calculators it may be symbolized by i or I), and ask the calculator to compute FV. The keystrokes follow. Take Note Because future value interest factors are rounded to four decimal places in Table I, you may get a slightly different solution Step : First press TI BAII PLUS Financial Calculator Solution. This clears all the time value of money keys of all compared to a problem previously calculated or entered values. solved by the algebraic method. Step 2: Press,. This sets the calculator to the mode where one payment per year is expected, which is the assumption for the problems in this chapter. Older TI BAII PLUS financial calculators were set at the factory to a default value of 2 for P/Y. Change this default value to as shown here if you have Older TI BAII PLUS financial calculators were set at the factory to a default value one of these older calculators. For the past several years TI has made the default of 2 for P/Y. Change this default value to as shown here if you have one of these value for P/Y. If after pressing you see the value in the display older calculators. For the past several years TI has made the default value for P/Y. If window you may press twice to back out of this. No changes to the P/Y after pressing you see the value in the display window you may press twice to back out of this. value No changes are needed to the if your P/Y calculator value are is needed already if set your to the calculator default value is already of. set to You may similarly skip this adjustment throughout this chapter where the financial calculator solutions are shown if your calculator already has its P/Y 66 Part 2 Essential Concepts in Finance value set to. If your calculator is an older one that requires you to change the default value of P/Y from 2 to, you do not need to make that change again. The default value of P/Y will stay set to unless you specifically
10 value for P/Y. If after pressing you see the value in the display window you may press twice to back out of this. No changes to the P/Y value are needed if your calculator is already set to the default value of. the default You value may of similarly. You may skip similarly this adjustment skip this throughout adjustment this chapter throughout where this the chapter where the financial calculator solutions are are shown shown if your if your calculator calculator already already has its has P/Y its P/Y value set to value. If set your to calculator. If your calculator is an older is an one older that one requires that requires you to you change to change the default value of P/Y the from default 2 to value, you of P/Y do not from need 2 to to, make you do that not change need to again. make that The change default value of P/Y will again. stay set The to default unless value you of specifically P/Y will stay change set to it. unless you specifically change it. Step 3: Input values for principal (PV), interest rate (k or I/Y on the calculator), and number of periods (n) Answer: 5.76 In the SaveCom example, we input 00 for the present value (PV), 3 for number of periods (N), and 5 for the interest rate per year (I/Y). Then we ask the calculator to compute the future value, FV. The result is $5.76. Our TI BAII PLUS is set to display two decimal places. You may choose a greater or lesser number if you wish. This future value problem can also be solved using the FV function in the spreadsheet below. E0 $5.76 We have learned four ways to calculate the future value of a single amount: the algebraic method, the financial table method, the financial calculator method, and the spreadsheet method. In the next section, we see how future values are related to changes in the interest rate, k, and the number of time periods, n. We also input 00 for the pv value in the spreadsheet. The Sensitivity of Future Values to Changes in Interest Rates or the Number of Compounding Periods Future value has a positive relationship with the interest rate, k, and with the number of periods, n. That is, as the interest rate increases, future value increases. Similarly, as the number of periods increases, so does future value. In contrast, future value decreases with decreases in k and n values. It is important to understand the sensitivity of future value to k and n because increases are exponential, as shown by the ( + k) n term in the future value formula. Consider this: A business that invests $0,000 in a savings account at 5 percent for 20 years will have a future value of $26, If the interest rate is 8 percent for the same 20 years, the future value of the investment is $46, We see that the future value of the investment increases as k increases. Figure 8a shows this graphically. Now let s say that the business deposits $0,000 for 0 years at a 5 percent annual interest rate. The future value of that sum is $6, Another business deposits $0,000 for 20 years at the same 5 percent annual interest rate. The future value of that $0,000 investment Chapter 8 The Time Value of Money 67
11 FIGURE 8a Future Value at Different Interest Rates Figure 8a shows the future value of $0,000 after 20 years at interest rates of 5 percent and 8 percent. $50,000 $45,000 $40,000 $35,000 Future Value of $0,000 After 20 Years at 5% and 8% Future Value at 5% Future Value at 8% Future Value, FV $30,000 $25,000 $20,000 $5,000 $0,000 $5,000 $ Number of Years, n FIGURE 8b Future Value at Different Times Figure 8b shows the future value of $0,000 after 0 years and 20 years at an interest rate of 5 percent. $30,000 $25,000 $20,000 Future Value of $0,000 after 0 Years and 20 Years at 5% Future Value after 0 years Future Value after 20 years Future Value, FV $5,000 $0,000 $5,000 $ Number of Years, n is $26, Just as with the interest rate, the higher the number of periods, the higher the future value. Figure 8b shows this graphically. The Present Value of a Single Amount Present value is today s dollar value of a specific future amount. With a bond, for instance, the issuer promises the investor future cash payments at specified points in time. With 68 Part 2 Essential Concepts in Finance
12 an investment in new plant or equipment, certain cash receipts are expected. When we calculate the present value of a future promised or expected cash payment, we discount it (mark it down in value) because it is worth less if it is to be received later rather than now. Similarly, future cash outflows are less burdensome than present cash outflows of the same amount. Future cash outflows are similarly discounted (made less negative). In present value analysis, then, the interest rate used in this discounting process is known as the discount rate. The discount rate is the required rate of return on an investment. It reflects the lost opportunity to spend or invest now (the opportunity cost) and the various risks assumed because we must wait for the funds. Discounting is the inverse of compounding. Compound interest causes the value of a beginning amount to increase at an increasing rate. Discounting causes the present value of a future amount to decrease at a decreasing rate. To demonstrate, imagine the SaveCom financial manager needed to know how much to invest now to generate $5.76 in three years, given an interest rate of 5 percent. Given what we know so far, the calculation would look like this: FV = PV ( + k) $5.76 = PV.05 $5.76 = PV PV = $ n To simplify solving present value problems, we modify the future value for a single amount equation by multiplying both sides by /( + k) n to isolate PV on one side of the equal sign. The present value formula for a single amount follows: The Present Value of a Single Amount Formula Algebraic Method PV = FV ( + k) n (82a) where: PV = Present Value, the starting amount FV = Future Value, the ending amount k = Discount rate of interest per period (expressed as a decimal) n = Number of time periods Applying this formula to the SaveCom example, in which its financial manager wanted to know how much the firm should pay today to receive $5.76 at the end of three years, assuming a 5 percent discount rate starting today, the following is the present value of the investment: PV = FV n ( + k) = $5.76 ( +.05) 3 = $ = $00.00 Chapter 8 The Time Value of Money 69
13 SaveCom should be willing to pay $00 today to receive $5.76 three years from now at a 5 percent discount rate. To solve for PV, we may also use the Present Value Interest Factor Table in Table II in the Appendix at the end of the book. A present value interest factor, or PVIF, is calculated and shown in Table II. It equals /( + k) n for given combinations of k and n. The table method formula, Equation 82b, follows: The Present Value of a Single Amount Formula Table Method PV = FV (PVIF k, n ) (82b) where: PV = Present Value FV = Future Value PVIF k,n = Present Value Interest Factor given discount rate, k, and number of periods, n, from Table II In our example, SaveCom s financial manager wanted to solve for the amount that must be invested today at a 5 percent interest rate to accumulate $5.76 within three years. Applying the present value table formula, we find the following solution: ( ) PV = FV PVIF k, n = $5.76 ( PVIF 5%, 3 ) = $ (from the PVIF table) = $99.99 (slightly lower than $00 due to the rounding to four places in the table) The present value of $5.76, discounted back three years at a 5 percent discount rate, is $00. To solve for present value using a financial calculator, enter the numbers for future value, FV, the number of periods, n, and the interest rate, k symbolized as I/Y on the calculator then hit the CPT (compute) and PV (present value) keys. The sequence follows: Step : Press TI BAII PLUS Financial Calculator Solution to clear previous values. Step 2: Press, to ensure the calculator is in the mode for annual interest payments. Step 3: Input the values for future value, the interest rate, and number of periods, and compute PV Answer: The financial calculator result is displayed as a negative number to show that the present value sum is a cash outflow that is, that sum will have to be invested to earn $5.76 in three years at a 5 percent annual interest rate. This present value problem can also be solved using the PV function in the spreadsheet that follows. 70 Part 2 Essential Concepts in Finance
14 E0 This Excel spreadsheet shows you how to compute the present value of $5.76 discounted back 3 years with a 5% annual discount rate. Note that the computed PV has a negative value indicating that you should be willing to pay that amount now for the right to receive $5.76 in three years with a 5% discount rate. $00.00 We have examined how to find present value using the algebraic, table, financial calculator, and spreadsheet methods. Next, we see how present value analysis is affected by the discount rate, k, and the number of compounding periods, n. The Sensitivity of Present Values to Changes in the Interest Rate or the Number of Compounding Periods In contrast with future value, present value is inversely related to k and n values. In other words, present value moves in the opposite direction of k and n. If k increases, present value decreases; if k decreases, present value increases. If n increases, present value decreases; if n decreases, present value increases. Consider this: A business that expects a 5 percent annual return on its investment (k = 5%) should be willing to pay $3, today (the present value) for $0,000 to be received 20 years from now. If the expected annual return is 8 percent for the same 20 years, the present value of the investment is only $2, We see that the present value of the investment decreases as the value of k increases. The way the present value of the $0,000 varies with changes in the required rate of return is shown graphically in Figure 82a. Now let s say that a business expects to receive $0,000 ten years from now. If its required rate of return for the investment is 5 percent annually, then it should be willing to pay $6,39 for the investment today (the present value is $6,39). If another business expects to receive $0,000 twenty years from now and it has the same 5 percent annual required rate of return, then it should be willing to pay $3,769 for the investment (the present value is $3,769). Just as with the interest rate, the greater the number of periods, the lower the present value. Figure 82b shows how it works. In this section we have learned how to find the future value and the present value of a single amount. Next, we will examine how to find the future value and present value of several amounts. Working with Annuities Financial managers often need to assess a series of cash flows rather than just one. One common type of cash flow series is the annuity a series of equal cash flows, spaced evenly over time. Professional athletes often sign contracts that provide annuities for them after they retire, in addition to the signing bonus and regular salary they may receive during their playing years. Consumers can purchase annuities from insurance companies as a means of providing Chapter 8 The Time Value of Money 7
15 FIGURE 82a Present Value at Different Interest Rates Figure 82a shows the present value of $0,000 to be received in 20 years at interest rates of 5 percent and 8 percent. Present Value, PV $2,000 $0,000 $8,000 $6,000 $4,000 Present Value of $0,000 Expected in 20 Years at 5% and 8% Present Value at 5% Present Value at 8% $2,000 $ Number of Years, n FIGURE 82b Present Value at Different Times Figure 82b shows the present value of $0,000 to be received in 0 years and 20 years at an interest rate of 5 percent. Present Value, PV $2,000 $0,000 $8,000 $6,000 $4,000 Present Value of $0,000 to Be Received in 0 Years and 20 Years at 5% Present Value for 0Year Deal Present Value for 20Year Deal $2,000 $ Number of Years, n 72 Part 2 Essential Concepts in Finance retirement income. The investor pays the insurance company a lump sum now in order to receive future payments of equal size at regularly spaced time intervals (usually monthly). Another example of an annuity is the interest on a bond. The interest payments are usually equal dollar amounts paid either annually or semiannually during the life of the bond. Annuities are a significant part of many financial problems. You should learn to recognize annuities and determine their value, future or present. In this section we will explain how to
16 calculate the future value and present value of annuities in which cash flows occur at the end of the specified time periods. Annuities in which the cash flows occur at the end of each of the specified time periods are known as ordinary annuities. Annuities in which the cash flows occur at the beginning of each of the specified time periods are known as annuities due. Future Value of an Ordinary Annuity Financial managers often plan for the future. When they do, they often need to know how much money to save on a regular basis to accumulate a given amount of cash at a specified future time. The future value of an annuity is the amount that a given number of annuity payments, n, will grow to at a future date, for a given periodic interest rate, k. For instance, suppose the SaveCom Company plans to invest $500 in a money market account at the end of each year for the next four years, beginning one year from today. The business expects to earn a 5 percent annual rate of return on its investment. How much money will SaveCom have in the account at the end of four years? The problem is illustrated in the timeline in Figure 83. The t values in the timeline represent the end of each time period. Thus, t is the end of the first year, t 2 is the end of the second year, and so on. The symbol t 0 is now, the present point in time. Because the $500 payments are each single amounts, we can solve this problem one step at a time. Looking at Figure 84, we see that the first step is to calculate the future value of the cash flows that occur at t, t 2, t 3, and t 4 using the future value formula for a single amount. The next step is to add the four values together. The sum of those values is the annuity s future value. As shown in Figure 84, the sum of the future values of the four single amounts is the annuity s future value, $2, However, the stepbystep process illustrated in Figure 84 is timeconsuming even in this simple example. Calculating the future value of a 20 or 30year annuity, such as would be the case with many bonds, would take an enormous amount of time. Instead, we can calculate the future value of an annuity easily by using the following formula: Future Value of an Annuity Algebraic Method FVA = PMT n ( + k) k (83a) where: FVA = Future Value of an Annuity PMT = Amount of each annuity payment k = Interest rate per time period expressed as a decimal n = Number of annuity payments t 0 (Today) t t 2 t 3 t 4 FIGURE 83 SaveCom Annuity Timeline $500 $500 $500 $500 FV at 5% interest for 3 years FV at 5% interest for 2 years FV at 5% interest for year Σ = FVA =? Chapter 8 The Time Value of Money 73
17 FIGURE 84 Future Value of the SaveCom Annuity t 0 (Today) t t 2 t 3 t 4 $500 $500 $500 $500 FVA FV = 500 ( +.05) 3 FV = 500 ( +.05) = = FV = 500 = = 525 FV = 500 ( +.05) = = Σ = FVA = $2,55.05 Using Equation 83a in our SaveCom example, we solve for the future value of the annuity at 5 percent interest (k = 5%) with four $500 endofyear payments (n = 4 and PMT = $500), as follows: FVA = 500 ( +.05) 4.05 = = $2,55.05 For a $500 annuity with a 5 percent interest rate and four annuity payments, we see that the future value of the SaveCom annuity is $2, To find the future value of an annuity with the table method, we must find the future value interest factor for an annuity (FVIFA), found in Table III in the Appendix at the end of the book. The FVIFA k, n is the value of [( + k) n ] k for different combinations of k and n. Future Value of an Annuity Formula Table Method FVA = PMT FVIFA k, n (83b) where: FVA = Future Value of an Annuity PMT = Amount of each annuity payment FVIFA k, n = Future Value Interest Factor for an Annuity from Table III k = Interest rate per period n = Number of annuity payments In our SaveCom example, then, we need to find the FVIFA for a discount rate of 5 percent with four annuity payments. Table III in the Appendix shows that the FVIFA k = 5%, n = 4 is Using the table method, we find the following future value of the SaveCom annuity: FVA = 500 FVIFA 5%, 4 = (from the FVIFA table) = $2, Part 2 Essential Concepts in Finance
18 To find the future value of an annuity using a financial calculator, key in the values for the annuity payment (PMT), n, and k (remember that the notation for the interest rate on the TI BAII PLUS calculator is I/Y, not k). Then compute the future value of the annuity (FV on the calculator). For a series of four $500 endofyear (ordinary annuity) payments where n = 4 and k = 5 percent, the computation is as follows: Step : Step 2: Step 3: Press TI BAII PLUS Financial Calculator Solution to clear previous values. Press,. Repeat until END shows in the display to set the annual interest rate mode and to set the annuity payment to end of period mode. Input the values and compute Answer: 2,55.06 Take Note Note that slight differences occur between the table solution and the algebraic, financial calculator, and spreadsheet solutions. This is because our financial tables round interest factors to four decimal places, whereas the other methods generally use many more significant figures for greater accuracy. The spreadsheet that follows solves this same future value problem using the FV function. E9 $2,55.06 In the financial calculator and spreadsheet inputs, note that the payment is keyed in as a negative number to indicate that the payments are cash outflows the payments flow out from the company into an investment. The Present Value of an Ordinary Annuity Because annuity payments are often promised (as with interest on a bond investment) or expected (as with cash inflows from an investment in new plant or equipment), it is important to know how much these investments are worth to us today. For example, assume that the financial manager of Buy4Later, Inc. learns of an annuity that promises to make four annual payments of $500, beginning one year from today. How much should the company be willing to pay to obtain that annuity? The answer is the present value of the annuity. Because an annuity is nothing more than a series of equal single amounts, we could calculate the present value of an annuity with the present value formula for a single amount and sum the totals, but that would be a cumbersome process. Imagine calculating the present value of a 50year annuity! We would have to find the present value for each of the 50 annuity payments and total them. Chapter 8 The Time Value of Money 75
19 Fortunately, we can calculate the present value of an annuity in one step with the following formula: The Present Value of an Annuity Formula Algebraic Method PVA = PMT ( + k) n k (84a) where: PVA = Present Value of an Annuity PMT = Amount of each annuity payment k = Discount rate per period expressed as a decimal n = Number of annuity payments Using our example of a fouryear ordinary annuity with payments of $500 per year and a 5 percent discount rate, we solve for the present value of the annuity as follows: PVA = 500 ( +.05) 4.05 = = $, The present value of the fouryear ordinary annuity with equal yearly payments of $500 at a 5 percent discount rate is $, We can also use the financial table for the present value interest factor for an annuity (PVIFA) to solve present value of annuity problems. The PVIFA table is found in Table IV in the Appendix at the end of the book. The formula for the table method follows: The Present Value of an Annuity Formula Table Method PVA = PMT PVIFA k, n (84b) where: PVA = Present Value of an Annuity PMT = Amount of each annuity payment PVIFA k, n = Present Value Interest Factor for an Annuity from Table IV k = Discount rate per period n = Number of annuity payments Applying Equation 84b, we find that the present value of the fouryear annuity with $500 equal payments and a 5 percent discount rate is as follows: 2 PVA = 500 PVIFA 5%, 4 = = $, Part 2 Essential Concepts in Finance 2. The $.03 difference between the algebraic result and the table formula solution is due to differences in rounding.
20 We may also solve for the present value of an annuity with a financial calculator or spreadsheet. For the financial calculator, simply key in the values for the payment, PMT, number of payment periods, n, and the interest rate, k symbolized by I/Y on the TI BAII PLUS calculator and ask the calculator to compute PVA (PV on the calculator). For the series of four $500 payments where n = 4 and k = 5 percent, the computation follows: TI BAII PLUS Financial Calculator Solution Step : Step 2: Step 3: Press to clear previous values. Press,. Repeat until END shows in the display to set the annual interest rate mode and to set the annuity payment to end of period mode. Input the values and compute Answer:, The PV function in the spreadsheet below also solves this present value of an ordinary annuity problem. E0 $, The financial calculator and spreadsheet present value results are displayed as negative numbers. An investment (a cash outflow) of $, would earn a 5 percent annual rate of return if $500 is received at the end of each year for the next four years. Future and Present Values of Annuities Due Sometimes we must deal with annuities in which the annuity payments occur at the beginning of each period. These are known as annuities due, in contrast to ordinary annuities in which the payments occurred at the end of each period, as described in the preceding section. Annuities due are more likely to occur when doing future value of annuity (FVA) problems than when doing present value of annuity (PVA) problems. Today, for instance, you may start a retirement program, investing regular equal amounts each month or year. Calculating the amount you would accumulate when you reach retirement age would Chapter 8 The Time Value of Money 77
21 be a future value of an annuity due problem. Evaluating the present value of a promised or expected series of annuity payments that began today would be a present value of an annuity due problem. This is less common because car and mortgage payments almost always start at the end of the first period making them ordinary annuities. Whenever you run into an FVA or a PVA of an annuity due problem, the adjustment needed is the same in both cases. Use the FVA or PVA of an ordinary annuity formula shown earlier, then multiply your answer by ( + k). We multiply the FVA or PVA formula by ( + k) because annuities due have annuity payments earning interest one period sooner. So, higher FVA and PVA values result with an annuity due. The first payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due problems, each annuity payment occurs one period sooner, so the payments are discounted less severely. In our SaveCom example, the future value of a $500 ordinary annuity, with k = 5% and n = 4, was $2, If the $500 payments occurred at the beginning of each period instead of at the end, we would multiply $2,55.06 by.05 ( + k = +.05). The product, $2,262.8, is the future value of the annuity due. In our earlier Buy4Later, Inc., example, we found that the present value of a $500 ordinary annuity, with k = 5% and n = 4, was $, If the $500 payments occurred at the beginning of each period instead of at the end, we would multiply $, by.05 ( + k = +.05) and find that the present value of Buy4Later s annuity due is $, The financial calculator solutions for these annuity due problems are shown next. Future Value of a FourYear, $500 Annuity Due, k = 5% TI BAII PLUS Financial Calculator Solution Step : Step 2: Step 3: Press to clear previous values. Press,. Repeat command until the display shows BGN, to set to the annual interest rate mode and to set the annuity payment to beginning of period mode. Input the values for the annuity due and compute Answer: 2, Here is the spreadsheet solution. Note how the [type] value is set to to indicate that this is an annuity due problem. E0 Step : Step 2: Step 3: Press Present Value of a FourYear, $500 Annuity Due, k = 5% TI BAII PLUS Financial Calculator Solution to clear previous values. Press,. Repeat command until the display shows BGN, to set to the annual interest rate mode and to set the annuity payment to beginning of period mode. This Excel spreadsheet computes the future value of a 4 year annual annuity due of $500 using a 5% annual discount rate. Note that the FV function inputs the $500 annuity payment Inpuas t the negative values because for theyou annuity would pay dueout andthat compute. amount at the beginning of each year to have $2, in 5 years Answer:,86.62 $2, Part 2 Essential Concepts in Finance
22 Present Value of a FourYear, $500 Annuity Due, k = 5% TI BAII PLUS Financial Calculator Solution Step : Step 2: Step 3: Press to clear previous values. Press,. Repeat command until the display shows BGN, to set to the annual interest rate mode and to set the annuity payment to beginning of period mode. Input the values for the annuity due and compute Answer:,86.62 Here is the spreadsheet solution. Note how the [type] value is again set to to indicate that this is an annuity due problem. E0 This Excel spreadsheet computes the present value of a 4 year annual annuity due of $500 using a 5% annual discount rate. Note that the PV function displays $,86.62 as a negative value because you would be willing to pay out that amount now to receive $500 at the beginning of each year for 4 years with a 5% annual discount rate. $,86.62 In this section we discussed ordinary annuities and annuities due and learned how to compute the present and future values of the annuities. Next, we will learn what a perpetuity is and how to solve for its present value. Perpetuities An annuity that goes on forever is called a perpetual annuity or a perpetuity. Perpetuities contain an infinite number of annuity payments. An example of a perpetuity is the dividends typically paid on a preferred stock issue. The future value of perpetuities cannot be calculated, but the present value can be. We start with the present value of an annuity formula, Equation 83a. PVA = PMT ( + k) n k Now imagine what happens in the equation as the number of payments (n) gets larger and larger. The ( + k) n term will get larger and larger, and as it does, it will cause the /( + k) n fraction to become smaller and smaller. As n approaches infinity, the ( + k) n Chapter 8 The Time Value of Money 79
23 term becomes infinitely large, and the /( + k) n term approaches zero. The entire formula reduces to the following equation: Present Value of Perpetuity PVP = PMT 0 k or PVP = PMT k (85) where: PVP = Present Value of a Perpetuity k = Discount rate expressed as a decimal Neither the table method nor the financial calculator can solve for the present value of a perpetuity. This is because the PVIFA table does not contain values for infinity and the financial calculator does not have an infinity key. Suppose you had the opportunity to buy a share of preferred stock that pays $70 per year forever. If your required rate of return is 8 percent, what is the present value of the promised dividends to you? In other words, given your required rate of return, how much should you be willing to pay for the preferred stock? The answer, found by applying Equation 85, follows: PVP = PMT = $70 k.08 = $875 The present value of the preferred stock dividends, with a k of 8 percent and a payment of $70 per year forever, is $875. Present Value of an Investment with Uneven Cash Flows Unlike annuities that have equal payments over time, many investments have payments that are unequal over time. That is, some investments have payments that vary over time. When the periodic payments vary, we say that the cash flow streams are uneven. For instance, a professional athlete may sign a contract that provides for an immediate $7 million signing bonus, followed by a salary of $2 million in year, $4 million in year 2, then $6 million in years 3 and 4. What is the present value of the promised payments that total $25 million? Assume a discount rate of 8 percent. The present value calculations are shown in Table 8. As we see from Table 8, we calculate the present value of an uneven series of cash flows by finding the present value of a single amount for each series and summing the totals. We can also use a financial calculator to find the present value of this uneven series of cash flows. The worksheet mode of the TI BAII PLUS calculator is especially helpful in solving problems with uneven cash flows. The C display shows each cash payment following CF 0, the initial cash flow. The F display key indicates the frequency of that payment. The keystrokes follow. 80 Part 2 Essential Concepts in Finance
24 TI BAII PLUS Financial Calculator PV Solution Uneven Series of Cash Flows Keystrokes Display CF 0 = old contents CF 0 = ,000, C0 = 2,000, F0 = C02 = 4,000, F02 = C03 = 6,000, F03 = 2.00 I = I = 8.00 NPV = 2,454, Take Note We used the NPV (net present value) key on our calculator to solve this problem. NPV will be discussed in Chapter 0. We see from the calculator keystrokes that we are solving for the present value of a single amount for each payment in the series except for the last two payments, which are the same. The value of F03, the frequency of the third cash flow after the initial cash flow, was 2 instead of because the $6 million payment occurred twice in the series (in years 3 and 4). We have seen how to calculate the future value and present value of annuities, the present value of a perpetuity, and the present value of an investment with uneven cash flows. Now we turn to time value of money problems in which we solve for k, n, or the annuity payment. TABLE 8 The Present Value of an Uneven Stream of Cash Flows Time Cash Flow PV of Cash Flow t 0 $7,000,000 $7,000,000 = 0.08 t $2,000,000 $2,000,000 =.08 t 2 $4,000,000 $4,000,000 = 2.08 t 3 $6,000,000 $6,000,000 = 3.08 t 4 $6,000,000 $6,000,000 = 4.08 $7,000,000 $,85,852 $3,429,355 $4,762,993 $4,40,79 Sum of the PVs = $2,454,380 Chapter 8 The Time Value of Money 8
25 Special Time Value of Money Problems Financial managers often face time value of money problems even when they know both the present value and the future value of an investment. In those cases, financial managers may be asked to find out what return an investment made that is, what the interest rate is on the investment. Still other times financial managers must find either the number of payment periods or the amount of an annuity payment. In the next section, we will learn how to solve for k and n. We will also learn how to find the annuity payment (PMT). Finding the Interest Rate Financial managers frequently have to solve for the interest rate, k, when firms make a longterm investment. The method of solving for k depends on whether the investment is a single amount or an annuity. Finding k for a SingleAmount Investment Financial managers may need to determine how much periodic return an investment generated over time. For example, imagine that you are head of the finance department of GrabLand, Inc. Say that GrabLand purchased a house on prime land 20 years ago for $40,000. Recently, GrabLand sold the property for $06,3. What average annual rate of return did the firm earn on its 20year investment? First, the future value or ending amount of the property is $06,3. The present value the starting amount is $40,000. The number of periods, n, is 20. Armed with those facts, you could solve this problem using the table version of the future value of a single amount formula, Equation 8b, as follows: FV = PV FVIF $06,3 = $40,000 FVIF $06,3 $40,000 = FVIF = FVIF ( k, n ) k =?, n = 20 k =?, n = 20 ( k =?, n = 20 ) Now find the FVIF value in Table I, shown in part below. The whole table is in the Appendix at the end of the book. You know n = 20, so find the n = 20 row on the lefthand side of the table. You also know that the FVIF value is , so move across the n = 20 row until you find (or come close to) the value You find the value in the k = 5% column. You discover, then, that GrabLand s property investment had an interest rate of 5 percent. Future Value Interest Factors, Compounded at k percent for n Periods, Part of Table I Number of Periods, Interest Rate, k n 0% % 2% 3% 4% 5% 6% 7% 8% 9% 0% Part 2 Essential Concepts in Finance
Important 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 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 informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More 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 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 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 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 informationTexas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More 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 informationHow To Read The Book \"Financial Planning\"
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More 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 informationPrinciples of Managerial Finance INTEREST RATE FACTOR SUPPLEMENT
Principles of Managerial Finance INTEREST RATE FACTOR SUPPLEMENT 1 5 Time Value of Money FINANCIAL TABLES Financial tables include various future and present value interest factors that simplify time value
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More 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 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 informationBasic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i)
Chapter 28 Basic Financial Tools: A Review The building blocks of finance include the time value of money, risk and its relationship with rates of return, and stock and bond valuation models. These topics
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 informationCompounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.
Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has builtin preset assumptions
More 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 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 informationCHAPTER 5 HOW TO VALUE STOCKS AND BONDS
CHAPTER 5 HOW TO VALUE STOCKS AND BONDS Answers to Concepts Review and Critical Thinking Questions 1. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used
More 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 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 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 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 informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationCHAPTER 4 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 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 informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Longterm Treasury securities have substantial
More informationIntroduction. Turning the Calculator On and Off
Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction
More 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 4. Time Value of Money
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More 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 informationSolutions to Problems
Solutions to Problems P41. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,
More 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
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 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 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 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 informationHewlettPackard 10BII Tutorial
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
More informationHow To Calculate The Value Of A Project
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
More 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 informationOklahoma State University Spears School of Business. Time Value of Money
Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a signin bonus for your new job? 1. $15,000 cash upon signing the
More 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 informationChris Leung, Ph.D., CFA, FRM
FNE 215 Financial Planning Chris Leung, Ph.D., CFA, FRM Email: chleung@chuhai.edu.hk Chapter 2 Planning with Personal Financial Statements Chapter Objectives Explain how to create your personal cash flow
More informationFinancial Math on Spreadsheet and Calculator Version 4.0
Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationappendix B COMPOUND SUM OF AN ANNUITY OF $1 appendix C PRESENT VALUE OF $1 appendix D PRESENT VALUE OF AN ANNUITY OF $1
appendices appendix A COMPOUND SUM OF $1 appendix B COMPOUND SUM OF AN ANNUITY OF $1 appendix C PRESENT VALUE OF $1 appendix D PRESENT VALUE OF AN ANNUITY OF $1 appendix E TIME VALUE OF MONEY AND INVESTMENT
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 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 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 informationTexas Instruments BAII PLUS Tutorial
Omar M. Al Nasser, Ph.D., MBA. Visiting Assistant Professor of Finance School of Business Administration University of HoustonVictoria Email: alnassero@uhv.edu Texas Instruments BAII PLUS Tutorial To
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More 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 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 informationSolutions Manual. Corporate Finance. Ross, Westerfield, and Jaffe 9 th edition
Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders
More 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 information1.21.3 Time Value of Money and Discounted Cash Flows
1.1.3 ime Value of Money and Discounted ash Flows ime Value of Money (VM)  the Intuition A cash flow today is worth more than a cash flow in the future since: Individuals prefer present consumption to
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 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 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 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 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 informationContinue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
More 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 informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL738 Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationTexas Instruments BAII PLUS Tutorial
To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in
More 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 informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are
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 information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
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 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 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 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 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 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 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 informationChapter 3 Present Value and Securities Valuation
Chapter 3 Present Value and Securities Valuation The objectives of this chapter are to enable you to:! Value cash flows to be paid in the future! Value series of cash flows, including annuities and perpetuities!
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 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 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 informationPV Tutorial Using Calculator (Sharp EL738)
EYK 152 PV Tutorial Using Calculator (Sharp EL738) TABLE OF CONTENTS Calculator Configuration and Abbreviations Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise
More informationIn this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.
Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.
More informationEXAM 2 OVERVIEW. Binay Adhikari
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
More 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 informationChapter 3 Present Value
Chapter 3 Present Value MULTIPLE CHOICE 1. Which of the following cannot be calculated? a. Present value of an annuity. b. Future value of an annuity. c. Present value of a perpetuity. d. Future value
More 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 informationHANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR
HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL733A Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationIMPORTANT FINANCIAL CONCEPTS
PART2 IMPORTANT FINANCIAL CONCEPTS CHAPTERS IN THIS PART 4 Time Value of Money 5 Risk and Return 6 Interest Rates and Bond Valuation 7 Stock Valuation Integrative Case 2: Encore International 147 CHAPTER
More information10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans
10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation
More information