Integrated Case First National Bank Time Value of Money Analysis


 Oswin Johnson
 2 years ago
 Views:
Transcription
1 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 analysis covering the following questions. A. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an ordinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of $50, $100, $75, and $50 at the end of Years 0 through 3. ANSWER: [Show S51 through S54 here.] A time line is a graphical representation that is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; Time 1 is the end of the first year, or 1 year from today; and so on Year I/YR% Lump sum 100 Cash flow I/YR% Annuity I/YR% Uneven cash flow stream A lump sum is a single flow; for example, a $100 inflow in Year 2, as shown in the top time line. Chapter 5: Time Value of Money Integrated Case 1
2 An annuity is a series of equal cash flows occurring over equal intervals, as illustrated in the middle time line. An uneven cash flow stream is an irregular series of cash flows that do not constitute an annuity, as in the lower time line. 50 represents a cash outflow rather than a receipt or inflow. B. (1) What s the future value of $100 after 3 years if it earns 10%, annual compounding? ANSWER: [Show S55 through S57 here.] Show dollars corresponding to question mark, calculated as follows: % 100 FV =? After 1 year: FV 1 = PV + I 1 = PV + PV(I) = PV(1 + I) = $100(1.10) = $ Similarly: FV 2 = FV 1 + I 2 = FV 1 + FV 1 (I) = FV 1 (1 + I) = $110(1.10) = $ = PV(1 + I)(1 + I) = PV(1 + I) 2. FV 3 = FV 2 + I 3 = FV 2 + FV 2 (I) = FV 2 (1 + I) = $121(1.10) = $ = PV(1 + I) 2 (1 + I) = PV(1 + I) 3. In general, we see that: FV N = PV(1 + I) N, So FV 3 = $100(1.10) 3 = $100(1.3310) = $ Integrated Case Chapter 5: Time Value of Money
3 Note that this equation has 4 variables: FV N, PV, I/YR, and N. Here, we know all except FV N, so we solve for FV N. We will, however, often solve for one of the other three variables. By far, the easiest way to work all time value problems is with a financial calculator. Just plug in any three of the four values and find the fourth. Finding future values (moving to the right along the time line) is called compounding. Note that there are 3 ways of finding FV 3 : Regular calculator: 1. $100(1.10)(1.10)(1.10) = $ $100(1.10) 3 = $ Financial calculator: This is especially efficient for more complex problems, including exam problems. Input the following values: N = 3, I/YR = 10, PV = 100, PMT = 0, and solve for FV = $ Spreadsheet: Spreadsheet programs are ideally suited for solving time value of money problems. The spreadsheet can be set up using the specific FV spreadsheet function or by entering a FV formula/equation. B. (2) What s the present value of $100 to be received in 3 years if the interest rate is 10%, annual compounding? Answer: [Show S58 through S510 here.] Finding present values, or discounting (moving to the left along the time line), is the reverse of compounding, and the basic present value equation is the reciprocal of the compounding equation: Chapter 5: Time Value of Money Integrated Case 3
4 % PV =? 100 FV N = PV(1 + I) N transforms to: FVN PV = (1 + I) N =FV N I N =FV N (1 + I ) N Thus: PV = $ = $100(0.7513) = $ The same methods (regular calculator, financial calculator, and spreadsheet program) used for finding future values are also used to find present values, which is called discounting. Using a financial calculator input: N = 3, I/YR = 10, PMT = 0, FV = 100, and then solve for PV = $ C. What annual interest rate would cause $100 to grow to $ in 3 years? ANSWER: [Show S511 here.] $100(1 + I) $100(1 + I) 2 $100(1 + I) 3 FV = $100(1 + I) 3 = $ Using a financial calculator; enter N = 3, PV = 100, PMT = 0, FV = , then press the I/YR button to find I/YR = 8%. Calculators can find interest rates quite easily, even when periods and/or interest rates are not whole numbers, and when 4 Integrated Case Chapter 5: Time Value of Money
5 uneven cash flow streams are involved. (With uneven cash flows, we must use the CFLO function, and the interest rate is called the IRR, or internal rate of return; we will use this feature in capital budgeting.) D. If a company s sales are growing at a rate of 20% annually, how long will it take sales to double? ANSWER: [Show S512 here.] We have this situation in time line format: % 1 2 Say we want to find out how long it will take us to double our money at an interest rate of 20%. We can use any numbers, say $1 and $2, with this equation: FV N = $2 = $1(1 + I) N = $1(1.20) N. We would plug I/YR = 20, PV = 1, PMT = 0, and FV = 2 into our calculator, and then press the N button to find the number of years it would take 1 (or any other beginning amount) to double when growth occurs FV Year at a 20% rate. The answer is 3.8 years, but some calculators will round this value up to the next highest whole number. The graph also shows what is happening. 4 Chapter 5: Time Value of Money Integrated Case 5
6 Optional Question A farmer can spend $60/acre to plant pine trees on some marginal land. The expected real rate of return is 4%, and the expected inflation rate is 6%. What is the expected value of the timber after 20 years? ANSWER: FV 20 = $60( ) 20 = $60(1.10) 20 = $ per acre. We could have asked: How long would it take $60 to grow to $403.65, given the real rate of return of 4% and an inflation rate of 6%? Of course, the answer would be 20 years. E. What s the difference between an ordinary annuity and an annuity due? What type of annuity is shown here? How would you change it to the other type of annuity? ANSWER: [Show S513 here.] This is an ordinary annuity it has its payments at the end of each period; that is, the first payment is made 1 period from today. Conversely, an annuity due has its first payment today. In other words, an ordinary annuity has endofperiod payments, while an annuity due has beginningofperiod payments. The annuity shown above is an ordinary annuity. To convert it to an annuity due, shift each payment to the left, so you end up with a payment under the 0 but none under the 3. F. (1) What is the future value of a 3year, $100 ordinary annuity if the annual interest rate is 10%? 6 Integrated Case Chapter 5: Time Value of Money
7 ANSWER: [Show S514 here.] % $331 Go through the following discussion. One approach would be to treat each annuity flow as a lump sum. Here we have FVA N = $100(1) + $100(1.10) + $100(1.10) 2 = $100[1 + (1.10) + (1.10) 2 ] = $100(3.3100) = $ Future values of annuities may be calculated in 3 ways: (1) Treat the payments as lump sums. (2) Use a financial calculator. (3) Use a spreadsheet. F. (2) What is its present value? ANSWER: [Show S515 here.] % The present value of the annuity is $ Here we used the lump sum approach, but the same result could be obtained by using a calculator. Input N = 3, I/YR = 10, PMT = 100, FV = 0, and press the PV button. Chapter 5: Time Value of Money Integrated Case 7
8 F. (3) What would the future and present values be if it was an annuity due? ANSWER: [Show S516 and S517 here.] If the annuity were an annuity due, each payment would be shifted to the left, so each payment is compounded over an additional period or discounted back over one less period. In our situation, the future value of the annuity due is $364.10: FVA 3 Due = $331.00(1.10) 1 = $ This same result could be obtained by using the time line: $ $ $ = $ The best way to work annuity due problems is to switch your calculator to beg or beginning or due mode, and go through the normal process. Note that it s critical to remember to change back to end mode after working an annuity due problem with your calculator. In our situation, the present value of the annuity due is $273.55: PVA 3 Due = $248.68(1.10) 1 = $ This same result could be obtained by using the time line: $100 + $ $82.64 = $ G. A 5year $100 ordinary annuity has an annual interest rate of 10%. (1) What is its present value? 8 Integrated Case Chapter 5: Time Value of Money
9 ANSWER: [Show S518 here.] % The present value of the annuity is $ Here we used the lump sum approach, but the same result could be obtained by using a calculator. Input N = 5, I/YR = 10, PMT = 100, FV = 0, and press the PV button. G. (2) What would the present value be if it was a 10year annuity? ANSWER: [Show S519 here.] The present value of the 10year annuity is $ To solve with a financial calculator, input N = 10, I/YR = 10, PMT = 100, FV = 0, and press the PV button. G. (3) What would the present value be if it was a 25year annuity? ANSWER: The present value of the 25year annuity is $ To solve with a financial calculator, input N = 25, I/YR = 10, PMT = 100, FV = 0, and press the PV button. G. (4) What would the present value be if this was a perpetuity? ANSWER: The present value of the $100 perpetuity is $1,000. The PV is solved by dividing the annual payment by the interest rate: $100/0.10 = $1,000. Chapter 5: Time Value of Money Integrated Case 9
10 H. A 20yearold student wants to save $3 a day for her retirement. Every day she places $3 in a drawer. At the end of each year, she invests the accumulated savings ($1,095) in a brokerage account with an expected annual return of 12%. (1) If she keeps saving in this manner, how much will she have accumulated at age 65? ANSWER: [Show S520 and S521 here.] If she begins saving today, and sticks to her plan, she will have saved $1,487, by the time she reaches 65. With a financial calculator, enter the following inputs: N = 45, I/YR = 12, PV = 0, PMT = 1095, then press the FV button to solve for $1,487, H. (2) If a 40yearold investor began saving in this manner, how much would he have at age 65? ANSWER: [Show S522 here.] This question demonstrates the power of compound interest and the importance of getting started on a regular savings program at an early age. The 40year old investor will have saved only $146, by the time he reaches 65. With a financial calculator, enter the following inputs: N = 25, I/YR = 12, PV = 0, PMT = 1095, then press the FV button to solve for $146, H. (3) How much would the 40yearold investor have to save each year to accumulate the same amount at 65 as the 20yearold investor? ANSWER: [Show S523 here.] Again, this question demonstrates the power of compound interest and the importance of getting started on a regular savings program at an early age. The 40year old investor will have to save $11, every year, or $30.56 per day, in order 10 Integrated Case Chapter 5: Time Value of Money
11 to have as much saved as the 20year old investor by the time he reaches 65. With a financial calculator, enter the following inputs: N = 25, I/YR = 12, PV = 0, FV = , then press the PMT button to solve for $11, I. What is the present value of the following uneven cash flow stream? The annual interest rate is 10% Years ANSWER: [Show S524 and S525 here.] Here we have an uneven cash flow stream. The most straightforward approach is to find the PVs of each cash flow and then sum them as shown below: Years 10% (34.15) Note that the $50 Year 4 outflow remains an outflow even when discounted. There are numerous ways of finding the present value of an uneven cash flow stream. But by far the easiest way to deal with uneven cash flow streams is with a financial calculator. Calculators have a function that on the HP17B is called CFLO, for cash flow. Other calculators could use other designations such as CF 0 and CF j, but they explain how to use them in the manual. Anyway, you would input the cash flows, so they are in the Chapter 5: Time Value of Money Integrated Case 11
12 calculator s memory, then input the interest rate, I/YR, and then press the NPV or PV button to find the present value. J. (1) Will the future value be larger or smaller if we compound an initial amount more often than annually (e.g., semiannually, holding the stated (nominal) rate constant)? Why? ANSWER: [Show S526 here.] Accounts that pay interest more frequently than once a year, for example, semiannually, quarterly, or daily, have future values that are higher because interest is earned on interest more often. Virtually all banks now pay interest daily on passbook and money fund accounts, so they use daily compounding. J. (2) Define (a) the stated (or quoted or nominal) rate, (b) the periodic rate, and (c) the effective annual rate (EAR or EFF%). ANSWER: [Show S527 and S528 here.] The quoted, or nominal, rate is merely the quoted percentage rate of return, the periodic rate is the rate charged by a lender or paid by a borrower each period (periodic rate = I NOM /M), and the effective annual rate (EAR) is the rate of interest that would provide an identical future dollar value under annual compounding. J. (3) What is the EAR corresponding to a nominal rate of 10% compounded semiannually? Compounded quarterly? Compounded daily? ANSWER: [Show S529 through S531 here.] The effective annual rate for 10% semiannual compounding, is 10.25%: EAR = Effective annual rate = 1 + I NOM M M Integrated Case Chapter 5: Time Value of Money
13 If I NOM = 10% and interest is compounded semiannually, then: EAR = = (1.05) = = = 10.25%. For quarterly compounding, the effective annual rate is 10.38%: (1.025) = = = 10.38%. Daily compounding would produce an effective annual rate of 10.52%. J. (4) What is the future value of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? ANSWER: [Show S532 here.] Under semiannual compounding, the $100 is compounded over 6 semiannual periods at a 5.0% periodic rate: I NOM = 10%. FV N = MN INOM 1 + M 0.10 = $ = $100(1.05) 6 = $ Quarterly: FV N = $100(1.025) 12 = $ The return when using quarterly compounding is clearly higher. Another approach here would be to use the effective annual rate and compound over annual periods: Semiannually: $100(1.1025) 3 = $ Quarterly: $100(1.1038) 3 = $ (3) Chapter 5: Time Value of Money Integrated Case 13
14 K. When will the EAR equal the nominal (quoted) rate? ANSWER: [Show S533 here.] If annual compounding is used, then the nominal rate will be equal to the effective annual rate. If more frequent compounding is used, the effective annual rate will be above the nominal rate. L. (1) What is the value at the end of Year 3 of the following cash flow stream if interest is 10%, compounded semiannually? (Hint: You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.) Periods ANSWER: [Show S534 through S536 here.] Periods 5% = $100(1.05) = $100(1.05) 4 $ Here we have a different situation. The payments occur annually, but compounding occurs each 6 months. Thus, we cannot use normal annuity valuation techniques. 14 Integrated Case Chapter 5: Time Value of Money
15 L. (2) What is the PV? ANSWER: [Show S537 here.] Periods 5% $ PV = 100(1.05) $ To use a financial calculator, input N = 3, I/YR = 10.25, PMT = 100, FV = 0, and then press the PV key to find PV = $ L. (3) What would be wrong with your answer to Parts L(1) and L(2) if you used the nominal rate, 10%, rather than the EAR or the periodic rate, I NOM /2 = 10%/2 = 5% to solve the problems? ANSWER: I NOM can be used in the calculations only when annual compounding occurs. If the nominal rate of 10% were used to discount the payment stream, the present value would be overstated by $ $ = $ M. (1) Construct an amortization schedule for a $1,000, 10% annual interest loan with 3 equal installments. (2) What is the annual interest expense for the borrower and the annual interest income for the lender during Year 2? ANSWER: [Show S538 through S544 here.] To begin, note that the face amount of the loan, $1,000, is the present value of a 3year annuity at a 10% rate: Chapter 5: Time Value of Money Integrated Case 15
16 % 1,000 PMT PMT PMT PVA 3 = PMT + PMT + PMT 1 + I 1 + I 1 + I $1,000 = PMT(1 + I) 1 + PMT(1 + I) 2 + PMT(1 + I) 3. We have an equation with only one unknown, so we can solve it to find PMT. The easy way is with a financial calculator. Input N = 3, I/YR = 10, PV = 1000, FV = 0, and then press the PMT button to get PMT = , rounded to $ Amortization Schedule: Beginning Payment of Ending Period Balance Payment Interest Principal Balance 1 $1, $ $ $ $ * *Due to rounding, the third payment was increased by $0.02 to cause the ending balance after the third year to equal $0. Now make the following points regarding the amortization schedule: The $ annual payment includes both interest and principal. Interest in the first year is calculated as follows: 1st year interest = I Beginning balance = 0.1 $1,000 = $100. The repayment of principal is the difference between the $ annual payment and the interest payment: 1st year principal repayment = $ $100 = $ Integrated Case Chapter 5: Time Value of Money
17 The loan balance at the end of the first year is: 1st year ending balance = Beginning balance Principal repayment = $1,000 $ = $ We would continue these steps in the following years. Notice that the interest each year declines because the beginning loan balance is declining. Since the payment is constant, but the interest component is declining, the principal repayment portion is increasing each year. The interest component is an expense that is deductible to a business or a homeowner, and it is taxable income to the lender. If you buy a house, you will get a schedule constructed like ours, but longer, with = 360 monthly payments if you get a 30 year, fixedrate mortgage. The payment may have to be increased by a few cents in the final year to take care of rounding errors and make the final payment produce a zero ending balance. The lender received a 10% rate of interest on the average amount of money that was invested each year, and the $1,000 loan was paid off. This is what amortization schedules are designed to do. Most financial calculators have amortization functions built in. Chapter 5: Time Value of Money Integrated Case 17
Chapter 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 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 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 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 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 informationEhrhardt Chapter 8 Page 1
Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More 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 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 information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationTime Value of Money. 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 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. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 6. Discounted Cash Flow Valuation. 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 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 4. Time lines show timing of cash flows. Time Value Topics. Future value Present value Rates of return Amortization
Time Value Topics Chapter 4 Time Value of Money Future value Present value Rates of return Amortization 1 2 Determinants of Intrinsic Value: The Present Value Equation Net operating Required investments
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 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 informationCalculator (HewlettPackard 10BII) Tutorial
UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT Calculator (HewlettPackard 10BII) Tutorial To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key s primary function
More informationMHSA 8630  Healthcare Financial Management Time Value of Money Analysis
MHSA 8630  Healthcare Financial Management Time Value of Money Analysis ** One of the most fundamental tenets of financial management relates to the time value of money. The old adage that a dollar in
More 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 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 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 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 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 information3. Time value of money
1 Simple interest 2 3. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More 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 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 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 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 1: Time Value of Money
1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting
More 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 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 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 informationCh. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,
Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flowseither payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash
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 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 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 28 Time Value of Money
Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit $100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:
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 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 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 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 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 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 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 informationFinance 331 Corporate Financial Management Week 1 Week 3 Note: For formulas, a Texas Instruments BAII Plus calculator was used.
Chapter 1 Finance 331 What is finance?  Finance has to do with decisions about money and/or cash flows. These decisions have to do with money being raised or used. General parts of finance include: 
More 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 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 informationBUSI 121 Foundations of Real Estate Mathematics
Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia Outline Introduction Cash Flow Problems Cash Flow
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 Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More 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 4 Time Value of Money
Chapter 4 Time Value of Money Solutions to Problems P41. LG 1: Using a Time Line Basic (a), (b), and (c) Compounding Future Value $25,000 $3,000 $6,000 $6,000 $10,000 $8,000 $7,000 > 0 1 2 3 4 5 6 End
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 informationPrepared by: Dalia A. Marafi Version 2.0
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
More informationTime Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationThe Interest Rate: A loan, expressed as a percentage of the amount loaned per year.
Interest Rates Time Value of Money The Interest Rate Simple Interest Amortizing a Loan The Interest Rate: A loan, expressed as a percentage of the amount loaned per year. Interest rate is the "price" of
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 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 informationUNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis
This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, endofchapter problems, and endofchapter
More informationNPV calculation. Academic Resource Center
NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year
More informationHewlettPackard 10B Tutorial
To begin, look at the face of the calculator. Every key (except one, the gold shift key) on the 10B has two functions: each key's primary function is noted in white on the key itself, while each key's
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 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 informationUsing Financial Calculators
Chapter 4 Discounted Cash Flow Valuation 4B1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your HewlettPackard or Texas Instruments BA II Plus financial calculator
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 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 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 informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationChapter 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 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 informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More 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 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 informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More 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 informationFINANCIAL CALCULATIONS
FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N
More information2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?
CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equalsized
More 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 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 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 informationUSING FINANCIAL CALCULATORS
lwww.wiley.com/col APPEDIX C USIG FIACIAL CALCULATORS OBJECTIVE 1 Use a financial calculator to solve time value of money problems. Illustration C1 Financial Calculator Keys Business professionals, once
More informationChapter 5 Time Value of Money
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 of Cash Flows 7. Other Compounding
More informationFIN 3000. Chapter 6. Annuities. Liuren Wu
FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate
More informationChapter. Discounted Cash Flow Valuation. CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG.
Chapter 6 Discounted Cash Flow Valuation CORPRATE FINANCE FUNDAMENTALS by Ross, Westerfield & Jordan CIG. Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute
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 informationSharp EL733A Tutorial
To begin, look at the face of the calculator. Almost every key on the EL733A has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in
More informationTHE TIME VALUE OF MONEY
QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost
More informationChapter 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 2 Present Value
Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of riskadjusted
More informationLearning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:
Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value
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 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 informationFIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1
FIN 5413: Chapter 03  Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems  Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 31 a) Future Value = FV(n,i,PV,PMT)
More 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 informationKey Concepts and Skills
Chapters 5 and 6 Calculators Time Value of Money and Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2013 by The McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able
More information