TIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;


 Virgil McDowell
 6 years ago
 Views:
Transcription
1 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. One dollar today is worth more than one dollar tomorrow.
2 The reason why the value of money increases with time is because of the interest rate, which represents the cost of borrowing the money or the return obtainable by investing it. Because of the cost of money, interest must be considered by contractors when making decisions regarding their equipment. This requires a cash flow analysis, which recognizes that money has a different economic value depending on when it is received or paid.
3 In finance, we are often concerned with evaluating an investment (asset) that will pay out certain cash flows at given times in the future. In order to know what a reasonable price for such an investment (asset) is, we need to ask the question, How much are the cash flows we will receive in the future worth today?" At other times, we might be trying to save for some future event, such as retirement or college. In cases like these we may ask, "How much will my savings be worth when I need to use them?"
4 The answers we get to these questions will allow us to do things like save for our retirement, purchase cars and homes, invest in rare collectibles, and buy a business.
5 Objective 1: Compute how much a sum deposited today will grow to in the future. This is also referred to as the future value of a lump sum. What if your wealthy uncle had deposited $1,000 into an account when you were born and the account earned a return of 8% per year. How much would that account be worth on your 20 th birthday? This is the type of problem that future value of a lump sum techniques are designed to solve.
6 Objective 2: Compute the value today of a sum you will not receive until some future date. This is also referred to as the present value of a lump sum, since you are looking for the present value (the value today) of a sum of money that is promised to you at some point in the future. Say that as the beneficiary of a trust you were to receive a sum of $20,000 on your 25 th birthday. However, when you graduated from high school at age 18 you could not afford to go to college. Rather than delay your education until you turn 25. You might be able to sell the payment you will receive from the trust. How much would it be worth? This question is easily answered using the concepts of present value of a lump sum.
7 Objective 3: Compute how much a series of equal payments will grow to over time. This is also referred to as the future value of an annuity. The most common application of this concept is in retirement planning. Let s say that you deposited $2,000 per year into an individual retirement account, also called an IRA, and were able to earn 12% per year on your investment. If you continue your annual investing from the age of 25 until you retire at age 65, how large would your retirement nest egg be? It is easy to see the important implications of this type of calculation, and using the future value of annuity techniques will make problems like this easy to solve.
8 Objective 4: Compute the value today of a series of equal payments. This final time value of money concept is also called finding the present value of an annuity. Say you won a million dollars in the lottery. However, like most lotteries; this one pays out the money in twenty equal installments of $50,000 each. While the total dollar value received over the twentyyear period equals one million dollars, it is obviously not the same as having a million dollars in your hands today. Many lotteries now have started giving winners the choice of the traditional installment payments or a lump sum, which is paid out immediately. In effect, you are trading twenty annual payments of $50,000 for some dollar value received today. How much should you get if you make the trade? This is a question you can answer using present value of an annuity techniques.
9 Objective 5: Apply the time value of money methods to answer a variety of questions. The beauty of the techniques you will learn is that they can be applied to such a wide variety of problems and answer such a large number of important questions. Whether you are concerned with how much money you will have at retirement. Or whether you can afford the payments on a new sport utility vehicle, the concepts encompassed in this chapter will allow you to answer the question. If you learn these concepts well, you will be amazed at how often you will use them throughout the rest of your life.
10 Simple versus Compound Interest Simple Interest is money earned on an investment, which is not reinvested. It is easy to understand simple interest if you think of the interest payments as cash that is placed in a safe after it is received. Since the interest earned is sitting in a safe gathering dust, it cannot be reinvested. Hence, it "simply" accumulates over time, but does not grow in value once it is earned. Compound Interest is money (or interest) earned on an investment that is immediately reinvested, typically in the same investment. In contrast to simple interest, compound interest allows the investor to earn interest on interest. Over long periods of time, and this interest on interest can generate large amounts of money, and is often referred to as the power of compounding.
11 Assume that you invested $100 for 3 years at an interest rate of 10%. If the money was earning simple interest, at the end of the three years you would have a total of $130. This is found in the following manner: Year Interest Earned Cumulative 0  Value $ $100(.10)= $10.00 $ $100(.10)= $10.00 $ $100(.10)= $10.00 $130.00
12 Now assume, however, that the investment was set up to automatically reinvest the earnings at the same rate of return. In this case, you would be earning interest on interest, or compound interest. The total value of the investment at the end of three years is then found as follows: Year Interest Earned Cumulative 0  Value $ $100(.10)= $10.00 $ $110(.10)= $11.00 $ $121(.10)= $12.10 $ Notice that the compound interest approach results in a final investment value that is $2.10 larger than the simple interest approach. This "extra" money earned represents what was earned on the reinvested interest.
13 The Future Value of a Lump Sum We can use the example above to develop a formula that will allow us to find the future value of any lump sum investment under a compound interest scenario. In order to general this formula, all we need to do is examine how we arrived at the cumulative values in the table above. We found that the value of a $100 investment at the end of one year was $110. This can also be written as: $100(1+0.10)=$100(1+0.10) 1 = $110.00
14 Similarly, the value at the end of the second year, $121.00, can be written as: $100(1+.10)(1+.10)=$100(1+.10) 2 = $ Finally, the value at the end of the third year can be rewritten as: $100(1+.10)(1+.10)(1+.10)= $100(1+.10 )3 = $132.10
15 You can see the pattern. To find the future value of a lump sum, you only need to multiply the original investment times (1+i) n where i is the interest rate and n is the number of years for which the investment will be compounded. Now we can use this information to develop a generic equation that we can use for any lump sum amount and any number of periods. The formula is: FV = PV o (1+i) n Where FV n is the future value the lump sum will grow to n years from today, PV o is the present value of the investment at time zero (the lump sum you invested today), i is the interest rate and n is the number of years.
16 But what if your calculator doesn't have an exponent key? Without one, it can be impractical to find something like (1+.10) 25. Fortunately, these values have already been computed for you and put into an easy to use table. To use the tables, we convert preliminary equation into time value of money format. FV n =PV o (FVIF i,n ) We know (1+i) n = (FVIF i.n ). The values of FVIF Future Value Interest Factor you can find out in the tables or at
17 Example Assume we want to place $1,000 into an account today, could that the investment will earn an annual rate of return of 10% over the next five years. How much will we have at the end of the period?
18 NONANNUAL COMPOUNDING PERIODS In the previous examples, interest was paid once per year, which is also called annual compounding. Frequently, interest in accounts is paid more often than once per year. Many bank accounts, for example, pay interest monthly. Therefore, we must adjust our formula to allow for any interest payment schedule that may arise.
19 Equation shows how to adjust for any number of compounding periods per year: where FV n = PV(1 + i/m) mn FV n = the future value of a deposit at the end of the n th period PV = the initial deposit i = the annual interest rate n = the number of years the deposit is allowed to compound m = the number of times compouding occurs during the year
20 Similarly, we can adjust Equation to reflect nonannual compounding periods, with the result being: FV n =PV o (FVIF i/n,mxn ) and where all the variables are the same as defined above.
21 Now we can apply either of these new formulas to the following example Example: Assume we wanted to place $125 into a bank account earning 12% interest, compounded quarterly. If we left the investment in place for five years, what would be its value at the end of the period?
22 Effective Interest Rates If the bank increases the number of compounding periods, the amount earned on a deposit increases. This implies that a higher effective interest rate is being earned. The effective interest rate is the amount you would need to earn annually to be as well off as you are with multiple compounding periods per year. To determine the exact effective interest rate, we use the following equation: Effective Rate = (1+ i/m) m Where m is the number of compounding periods per year.
23 Accumulating a Future Balance Another application of future value is computing the initial deposit required to some future amount of money. Example: Suppose you are saving for your child's education, and want to have $10,000 available 10 years from now. If you can earn 8% annually on your investment, how much will you need to deposit today?
24 In other words, if you put $4, into an account earning 8% interest, it would grow to exactly $10,000 in ten years. This problem can also be solved in a similar manner using either the tables or a financial calculator.
25 Solving for Number of Periods and Interest Rates Up until now we have used the future value equation to find out either how much a deposit will grow to in the future, or how much we need to deposit today to have a given amount at some future time. But what if we want to determine the rate of return on an investment we have already made, or want to find out how long it will take for an investment to grow to a certain value? Solving for these different variables is not difficult; we just need to identity the future and present value amounts and at least one other variable and plug them into the previous equations.
26 Example: 1. Finding the interest rate i: Assume your uncle invested $1,000 m a trust fund for you 20years ago. Since then, the fund has grown in value to $6,727. What is the average annual compound rate of return earned on the account?
27 This problem can be solved easily using either financial factor tables or a financial calculator. The table solution starts by plugging the known variables into the future value equation. FV n = PV (FVIF i,n ) FV 20 = PV 0 (FVIF i,20 yrs. ) $6,727 = $1,000(FVIF i,20 yrs. ) = FVIF i,20 yrs. )
28 Now go to the FVIF table and on the row corresponding to 20 periods, find the value closest to and look at the top of that column to find the interest rate. In this case, the interest rate is 10%. If we wanted to use a financial calculator to solve the problem, we would enter the following inputs: FV = $6,727 PV = $1,000 N = 20 PMT = 0
29 Then compute the interest rate using the calculator key marked I. As with the tables, the answer you receive should be 10%. Note that the sign on the $1,000 initial deposit is negative. Some calculators require this because the PV is assumed to be an investment, and hence is really a cash outflow or negative cash flow. Some calculators do not follow this convention, however, and you will need to experiment to see which method gives you the correct answer.
30 2. Finding the Number of Periods n: Now suppose you have $5,000 to invest and your investment advisor tells you to expect a 12% rate of return. How long will it take you to double your money? Using the tables, and the FV formula, we have:
31 FV = PV (FVIF i,n ) FV n = PV o (FVIF 12%,n ) $10,000 = $5,000(FVIFi 12%,n ) =FVIF 12%,n The next step is to consult the FVIF table. Run down the 12% interest rate column until you come as close as possible to the value The closest value you will find is 1.974, which corresponds to 6 years. In other words, it will take slightly more than 6 years to double your money if you can earn a 12% rate of return.
32 Future Value of an Annuity An annuity is a stream of equal cash flows. The two basic types of annuities are the ordinary annuity and the annuity due. With an ordinary annuity, payments occur at the end of each period. In contrast, an annuity due's payments occur at the beginning of each period. The future value of an annuity can be found by summing the future values of each year's cash flows. It is important to remember that with an ordinary annuity, payment is made at the end of the period, so in the last period no interest will be received.
33 To simplify the future value of an ordinary annuity calculation, a precalculated future value interest factor for an annuity is provided. When interest is compounded annually at "i" percent for "n" periods, this factor is multiplied by the amount to be deposited annually at the end of each year, resulting in the future value of an annuity. Where: FV annuity = PMT (FVIFA i,n ) PMT FVIFA i,n = the equal payment made at equal intervals, and = the future value interest factor of an annuity from table
34 The payments for an annuity due are received at the beginning of each period. Because of this, the equation for finding the future value of an annuity must be converted to work for the future value of an annuity due. Previous equation can be converted for use with an annuity due simply by multiplying the righthand side of the equation by 1+i. This results in the following: FV annuity due = PMT (FVIFA i,n )(1 + i) This new equation recognizes the fact that the payments of an annuity due are received one period sooner, and they therefore are compounded for one additional period as well
35 Suppose you planned to invest $2,000 per year into an Individual Retirement Account (IRA) for the next 20 years. What would be the value of your account if you could receive a 12% annual rate of return on your investment? Assume first that you are dealing with an ordinary annuity, and then solve assuming you have an annuity due.
36 To solve the problem as an ordinary annuity, we apply following: FV annuity = PMT (FVIFA i,n ) FV annuity = $2,000(FVIFA 12%,20yrs. ) FV annuity = $2,000(72.052) FV annuity = $144,104
37 To solve the problem as an annuity due, we simply apply the annuity due formula. FV annuity due = PMT (FVIFA i,n )(1 + i) FV annuity due = $2,000(FVIFA i,n12%,20yrs. )( ) FV annuity due = $2,000(72.052)(1.12) FV annuity due = $161,396 Note that depositing the annual payment at the beginning of the year instead of the end of the year results in more man $17,000 in additional retirement funds at the end of 20 years. This provides a good illustration of the power of compounding.
38 Present Value of a Lump Sum We previously derived equation, which establishes the future value of a deposit. Take another look at this equation: FV n = PV 0 (1 + i) n To convert this equation to a present value equation, all that we need is a little algebra. Rearrange the terms in the equation so that PV is all by itself on the righthand side, and we have the following: PV 0 = FV n / (1 + i) n And when the PV interest factors from the tables in the book are used, the equation becomes: PV 0 = FV(PVIF i,n )
39 The present value of a single amount is found by discounting the cash flow back to time zero. The process of discounting is simply the inverse of compounding interest. The application of discounting is concerned with answering the question: "If l am earning i percent on my money, what will I be willing to pay today (at time zero) for the opportunity to receive the designated cash flow n periods from now?"
40 To illustrate, let s work through the following example. Assume you have the chance to buy a rare baseball card as on investment. You believe that you could sell this card in 8 years for $12,000 to help pay part of your daughter's college expenses as a freshman at an exclusive private school. If you require a 10% rate of return on your investments, how much should you be willing to pay for the card today?
41 PV = FV n / (1 + i) n PV = $12,000 / ( ) 8 PV = $12,000 / PV = $5, In other words, if you paid $5, for the card today, and sold it 8 years later for $12,000, you would have earned a 10% annual rate of return on your investment. If you paid more than $5,597.01, you would not be able to earn the required 10%. Of course, if you paid less than $5,597.01, you would earn more than 10%.
42 The Present Value of Mixed Streams Say you want to find the present value of an investment that pays a series of unequal cash flows over a period of years. To solve problems like this the technique is simply to find the individual PV of each cash flow and sum the PV's together.
43 Example: Assume you were considering buying part ownership in a hot dog stand. You expect business to grow over time, and you have estimated the following annual cash flows from / your portion of the stand s ownership. Assuming an 8% required rate of return, how much should you pay for your ownership share?
44
45 PV = $500(PVIF 8%,1 ) + $600(PVIF 8%,2 ) + $800(PVIF 8%,3 ) + $950(PVIF 8%,4 ) PV = $500(0.926) + $600(0.857) + $800(0.794) + $950(0.735) PV=$ $ $ $ PV= $2, The calculator solution is $2,310.71, which is slightly larger due to rounding.
46 Increasing the Compounding Period As with future value, nonannual compounding periods require a bit of adjustment before the PV can be found. The PV equation for multiple compounding periods is: PV=FV n / (1 + i/m) mn where m = number of compounding periods per year n = number of years i = annual interest rate We can also write this in TVM notation as follows: PV=FV n (PVIP i/m,mn )
47 Example: Find the present value of $1,500 to be received 5 years from now, if the appropriate rate of return is 12% compounded quarterly.
48 PV= $1,500 PVIF 12%/4,4(5) ) PV=$1,500(PVIF 3%,20periods ) PV=$1,500(0.554) PV=$ The calculator solution for this problem is $
49 Present Value of an Annuity If we want to find the PV of a stream of equal cash flows, we use a concept called the present value of an annuity. The formula is: where PV annuity = PMT (PVIFA i,n ) PMT = the $ amount of the equal payments.
50 Example: Assume you just won the Illinois lottery, and the prize was $50,000 per year for the next 20 years. Lottery officials claim you won a "one million dollar" prize because the payments sum to $1,000,000. However, what if you decided you needed all the cash today, and wanted to sell your stream of payments? If the going rate of interest in the market was 10%, how much would your lottery winnings really be worth?
51 Using the annuity formula: PV annuity = PJMT (PVIFA i,n ) PV annuity = 50,000 (PVIFA 10%,20 ) PV annuity = 50,000 (8.514) PV annuity = 50,000 ($425,700.00) The calculator solution is $425,678. So winning the "one million dollar" lottery is worth only $425,700 in today's dollars, or less than half what tottery officials claimed it was worth.
52 Perpetuities Annuities whose payments go on for infinity are called perpetuities. On the surface, it would seem impossible to value such an asset, since the payments we need to value never end. Fortunately, valuing perpetuities is actually very simple. The formula for the value of perpetuity is: PV 0 = PMT / i
53 Examples: Suppose you were able to buy on investment that makes $500 annual payments that never end. If you require a 12% rate of return on your investment, how much would you be willing to pay for the perpetuity?
54 PV 0 = PMT / i PV 0 = $500 / 0.12 PV 0 = $4,166.67
55 Another way to look at this problem is to ask yourself the following question: "If I could place $4, into a bank account earning 12% interest, and if l wanted to spend only the interest each year, how large would my annual payments be?" By simply multiplying $4, by the interest rate (0.12), you come up with the annual interest earned on your investment, or $500. If you leave the money in the account forever, you have just created a perpetuity that pays $500 each year. The cost to create such perpetuity is $4,166.67, which therefore also must be its present value.
56 Uneven Streams When an annuity is mixed with other irregular payments we have what is called an imbedded annuity. To solve for the present value of mixedcash flow streams we find the present value of the annuity, and then add the present value of any other cash flows.
57 Assume you are evaluating cm investment that pays $50 at the end of year 1, $75 at the end of year 2, $90 at the end of year 3, and $100 at the end of years 4 through 6. If you require a 10% rate of return on your investments, what is the most you should be willing to pay for this investment? In order to solve this problem, first draw a timeline like the one below. The irregular payments in years 1 through 3 require us to find their associated present values individually and then add them up. The embedded annuity in years 4 through 6 allows us to use the annuity formula. However, the present value of an annuity formula is designed to find the PV of an annuity where the payments begin at the end of the first year. In this case, the annuity payments begin at the end of the fourth year. Therefore, the formula has to be modified somewhat.
58
59 The solution is: PV = $50(PVIF 10%,1 )+ $75(PVIF 10%,2 )+ $90(PVIF 10%,3 )+ $100(PVIFA 10%,3 )(PVIF 10%,3 ) PV=$50(0.909)+$75(0.826)+$90(.751)+$100(2.487)(0.751) PV=$45.45+$61.95+$67.59+$ PV=$361.76
60 Note that the annuity formula finds the value of the annuity one period before the first payment is made. This is because the formula is designed to find the present value of an ordinary annuity (where the first payment is received at the end of year 1). Hence, multiplying the $100 payment by FVIFA 10%,3 yields a value of $248.70, but that is really the value of the annuity at the end of year 3, one period before the 1 st $100 payment is made. In order to obtain the proper result, we must discount $ back to time zero. This was accomplished using PVIF 10%,3 in the solution above. The timeline shows how each of the original cash flows is discounted back to time zero and then added to the others. The final result is that the investment would be worth $
Chapter 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 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 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 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 informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationChapter 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 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 informationReal estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions
Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 31 a) Future Value = $12,000 (FVIF, 9%, 7 years) = $12,000 (1.82804) = $21,936 (annual compounding) b) Future Value
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 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 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 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 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 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 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 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 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 informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationCHAPTER 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 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 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 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 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 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 informationTime Value of Money. Background
Time Value of Money (Text reference: Chapter 4) Topics Background One period case  single cash flow Multiperiod case  single cash flow Multiperiod case  compounding periods Multiperiod case  multiple
More 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 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 informationImportant Financial Concepts
Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More informationChapter 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 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 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 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 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 informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationCHAPTER 4 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 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 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 informationSolutions to Problems: Chapter 5
Solutions to Problems: Chapter 5 P51. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
More informationChapter 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 informationTime Value of Money Dallas Brozik, Marshall University
Time Value of Money Dallas Brozik, Marshall University There are few times in any discipline when one topic is so important that it is absolutely fundamental in the understanding of the discipline. The
More informationCompounding Quarterly, Monthly, and Daily
126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,
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 information3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
More informationCHAPTER 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 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 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 informationHow To Value Cash Flow
Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value
More 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 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 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 informationP42, page 204: Future value calculation. FVIFi,n = (1+i) n. P43, page 204: Number of periods estimation
P42, page 204: Future value calculation Use the basic formula for future value along with the given interest rate, i, nad the number of periods, n, to calculate the future value interest factor, FVIF,
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 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 informationTT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007
TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how
More 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 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 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 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 informationFinancial Management
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
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 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 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 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 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More 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 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 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 informationKey Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 11. Chapter 4
Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More 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 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 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 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 informationTime Value of Money PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA
Time Value of Money 1 PAPER 3A: COST ACCOUNTING CHAPTER 2 BY: CA KAPILESHWAR BHALLA Learning objectives 2 Understand the Concept of time value of money. Understand the relationship between present and
More informationChapter 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 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 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 information5 More on Annuities and Loans
5 More on Annuities and Loans 5.1 Introduction This section introduces Annuities. Much of the mathematics of annuities is similar to that of loans. Indeed, we will see that a loan and an annuity are just
More 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 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 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 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 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 Concept of Present Value
The Concept of Present Value If you could have $100 today or $100 next week which would you choose? Of course you would choose the $100 today. Why? Hopefully you said because you could invest it and make
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 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 informationIn Section 5.3, we ll modify the worksheet shown above. This will allow us to use Excel to calculate the different amounts in the annuity formula,
Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout
More informationAnnuities and Sinking Funds
Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded
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 informationKENT FAMILY FINANCES
FACTS KENT FAMILY FINANCES Ken and Kendra Kent have been married twelve years and have twin 4yearold sons. Kendra earns $78,000 as a Walmart assistant manager and Ken is a stayathome dad. They give
More information1 Interest rates, and riskfree investments
Interest rates, and riskfree investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 ($) in an account that offers a fixed (never to change over time)
More 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 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 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 informationThe Time Value of Money
CHAPTER 7 The Time Value of Money After studying this chapter, you should be able to: 1. Explain the concept of the time value of money. 2. Calculate the present value and future value of a stream of cash
More information