...Discounting Compounding Translating today’s $1 into its equivalent FV FVn = PV ( 1 + i )n FV1= 100(1+.10)1=110 Discounting Translating tomorrow's $1 into its equivalent PV PVn = FV÷( 1 + i )n PV1= 110÷ (1+.10)1=100 4-3 Compounding and Discounting When making investment decisions, managers usually calculate PV. 4-4 2 FVIFi,n (FVIF Table) FVn = PV ( 1 + i )n 4-5 FV– Single Sum If you deposit $100 in an account earning 6%, how much would you have after 1 year? PV = 100 FV = 0 106 1 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .06, 1 ) = 100 (1.06)= $106 FV = PV (1 + i)n = 100 (1.06)1 = $106 4-6 3 FV– Single Sum If you deposit $100 in an account earning 6%, how much would you have after 5 years? PV = 100 FV = 0 133.82 5 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .06, 5 ) = 100 (1.3382)= $133.82 FV = PV (1 + i)n = 100 (1.06)5 = $133.82 4-7 FV– Single Sum If you deposit $100 in an account earning 6% with quarterly compounding, how much would you have after 5 years? PV = 100 0 FV = 134.68 5 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .015, 20 ) (can’t use FVIF table) FV = PV (1 + i/m)n×m = 100 (1.015)20 = $134.68 4-8 4 FV– Single Sum If you deposit $100 in an account earning 6% with monthly compounding, how much would you have after 5 years? PV = 100 FV...
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...a. Find the FV of $1,000 invested to earn 10% annually 5 years from now. Answer this question by using a math formula and also by using the Excel function wizard. Inputs: Formula: Wizard (FV): PV = I/YR = N = FV = PV(1+I)^N = 1000 10% 5 $ 1,610.51 $1,610.51 Note: When you use the wizard and fill in the menu items, the result is the formula you see on the formula line if you click on cell E12. Put the pointer on E12 and then click the function wizard (fx) to see the completed menu. Also, it is generally easiest to fill in the wizard menus by clicking on one of the menu slots to activate the cursor and then clicking on the cell where the item is given. Then, hit the tab key to move down to the next menu slot to continue filling out the dialog box. Experiment by changing the input values to see how quickly the output values change. b. Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results. Begin by typing in the row and column labels as shown below. We could fill in the table by inserting formulas in all the cells, but a better way is to use an Excel data table Note that the Row Input Cell is D9 and the Column Input Cell is D10, and we set Cell B32 equal to Cell E11. Then, we selected (highlighted) the range B32:E38, then clicked Data, Table, and filled in the menu items to complete the table. Years (D10): ...
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...Period Examples A. Future Value (FV) of a Single Current Lump Sum Received One Period Hence FV = PV(1+i) | PV: current (or present) value | | i: a given interest rate (or rate of return) | (If the tables are used, this is the related formula: FV = PV * FVIF Equation 2 in the Week 1 Lecture) Example: You place $100 today in a bank deposit account that pays 10% annual interest. In other words, interest on your $100 worth of principal is paid once a year and will be received one year from today. What will your deposit account be a year from today? Algebraically, the relationship is: FV = $100(1.1) = $110 Using Excel, try entering the following formula into a single spreadsheet cell (hit the "Enter" key on your keyboard after typing in the formula): =100*1.1 If you entered the formula correctly, the cell will display a value of 110. As an aside, while Excel contains numerous shortcuts for present- and future-value calculations, we will not consider these shortcuts for two reasons. First, they do not promote a thorough conceptual understanding of the algebraic processes that necessarily are involved; second, these shortcuts may not (under a variety of circumstances) accurately reflect the modeling required for the more complex cash flow processes that occur under real world conditions. B. Future Value (FV) of a Current Single Lump Sum Compounded Once Each Period for Multiple Periods FV = PV(1+i)n Note: Since FV = PV(1+i)1 = PV(1+i), the formula above also can...
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...CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) | | |Brief Exercises | | | |Topics |Questions | |Exercises |Problems | | 1. |Present value concepts. |1, 2, 3, 4, | | | | | | |5, 9, 17 | | | | | 2. |Use of tables. |13, 14 |8 |1 | | | 3. |Present and future value problems: | | | | | | |a. Unknown future amount. |7, 19 |1, 5, 13 |2, 3, 4, 7 | | | |b. Unknown payments. |10, 11, 12 |6, 12, |8, 16, 17 |2, 6 | | | | |15, 17 | | | | ...
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...timing, and risk as reflected in k © morevalue.com, 1997 Alex Tajirian Time Value of Money 6-3 2. TYPES OF VALUATION L Based on investors' preferences and attitudes towards consumption and risk. ! Demand & Supply analysis L Based on "cash flow (CF)", ! CF: stream of promised future income today = time of analysis | period s CF $100 200 -100 ... 0 | 1 | | 2 time 3 where periods can be hours, days, weeks, etc Note. 7 Positive CF means receiving $ (inflow), negative CF means paying $ (outflow) Thus, given the CFs and how good the promise is, its risk, everyone would agree on the value (price) of the income stream. © morevalue.com, 1997 Alex Tajirian Time Value of Money 6-4 3. FUTURE VALUE (FV) L Put $100 (CF) in a bank for one year at interest (i) = 10% What is value of $100 one year from today; (FV1) ? FV1 ' ' ' ' ' Future Value of a CF 1 period from today principal % interest payment principal % (interest rate) × (principal) $100 % (.1)($100) $100 × (1 % .1) ' $110 (1) where, subscript 1 denotes # of periods in the future Thus, the CF is compounded at rate "i". L What is value...
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...I: Financial Calculator Exercises (33 marks) The table on the next page contains practice examples as well as the questions for Assignment 1: Part I. (For a detailed description of each column in this table, see “How do I Read the Table?” below.) 1. Work through each example in Column B on your financial calculator. 2. Check your answer with the one provided (Column C). 3. Look to the right side of the yellow column-divider and work through the corresponding assignment question (Column E). · Note: Each numbered practice example corresponds to the same numbered assignment question (e.g., practice example 1: “Chain calculations – to the power of” with the calculation of (8 x 2)2 corresponds to the assignment Question 1 that asks you to calculate (1+0.25)8). · If you can do the practice example, you should be able to do the corresponding assignment question. 4. Pay careful attention when reading questions that include multiple sets of brackets (e.g., assignment question 6). These can be confusing, so work through them carefully. 5. To record your solutions, put your answer in Column F, on the same row as the assignment question. See example for Question 1: (1+0.25)8). 6. Don’t be alarmed by the number of questions! You will likely be able to complete the work more quickly than you think. 7. There are 33 questions in Part I. Each question is worth 1% of the total marks for Assignment 1. How Do I Read the Table? Start from the far left-hand column and read across...
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...CHAPTER 1 3. Assume that the inflation-free rate of interest is 3 percent and that the inflation rate is 10 percent with complete certainty and no taxes. Determine the nominal interest rate. i = nominal rate r = inflation-free rate i = r + p + rp p = inflation rate r = 3%; p = 10%; i = ? i = 0.03 + 0.1 + (0.03)(0.1) i = 0.133 = 13.3% 4. In a world of certainty with no taxes, the nominal interest rate is 10 percent and the inflation-free interest rate is 5 percent. What is the inflation rate? i = 10%; r = 5%; p = ? i = r + p + rp 0.1 = 0.05 + p + 0.05p 0.05 = 1.05p p = 0.0476 = 4.76% 5. Assume no taxes. Suppose the inflation-free interest rate is 5 percent. The market forecasts a deflation rate of 15 percent. What is the nominal interest rate? r = 5%; p = -15%; i = ? i = r + p + rp i = 0.05 + (-0.15) + 0.05(-0.15) i = -0.1075 = -10.75% *The nominal interest rate cannot be negative; no one will invest at a negative rate. CHAPTER 2 4. The Treasury announces an auction of $10 billion par value of 52-week Treasury bills. $2 billion of noncompetitive bids are received. The competitive bids are as follows: Price per $1 of par Par value 0.9200 $3 billion 0.9194 $3 billion 0.9188 $4 billion 0.9180 $2 billion 0.9180 $2 billion 0.9178 $6 billion Compute the price per dollar of par paid by noncompetitive...
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...computation of the time value of money is given for readers not familiar with this subject. Modern technology has made these calculations very easy. Many computer programs have built-in time-value functions, and a large assortment of handheld calculators will solve these problems using special keys. However, some people who use these methods do not understand the rationale for the answers and merely accept the results. At the other extreme, the calculations could be made using exponentials and/or logarithms. Such a procedure may provide a thorough learning experience, but it is tedious and time consuming. Compound interest tables have been developed to provide a relatively easy tool for solving time-value problems. They are found in Appendix A at the end of the textbook. Here we walk through four types of calculations, each representing one of the four tables. The Excel icons marked TVM refer to the Excel spreadsheets that can be found on the companion web site. T HE F UTURE VALUE OF A S INGLE S UM Module If you deposit $1,000 in a savings account that pays 7 percent interest annually, and 3A you do not withdraw this interest, the original amount will keep growing. (In real life, bank interest is usually compounded more frequently than once per year, but annual compounding is assumed here. In other words, the 7 percent will be credited to the account once per year, at the end of the year.) One year later, $70 of interest will be added to the account, making...
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...MT 217: Finance - Introduction Prof: Beverley Belgrove Unit 2: The Value of Money Name: Khazma Alsayed Date: 29-10-2012 SOLVING FOR r Suppose you can buy a security at a price of $78.35 that will pay you $100 after fi ve years. What annual rate of return will you earn if you purchase the security? Here you know PV, FV, and n, but you do not know r, the interest rate that you will earn on your investment. Using your financial calculator, enter the known values into the appropriate locations—that is, N _ 5, PV _ _78.35, PMT _ 0, and FV _ 100— and then solve for the unknown value. SOLVING FOR n Suppose you know that a security will provide a return of 10 percent per year, it will cost $68.30 to purchase, and you want to keep the investment until it grows to a value of $100. How long will it take the investment to grow to $100? In this case, we know PV, FV, and r, but we do not know n, the number of periods. Using your financial calculator, enter I/Y _ 10, PV _ –68.30, PMT _ 0, and FV _ 100; then solve for n _ 4. Compounding: To compute the future value of an amount invested today (a current amount), we “push forward” the current amount by adding interest for each period in which the money can earn interest in the future. This process is called compounding Amortization schedule: A schedule showing precisely how a loan will be repaid. It gives the payment required on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment...
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...Financial concepts are greatly important when determine which would be the best method to use for the firm or personal use. Some financial concepts are time value of money, risk and return, and interest rates. The activity of the assignment is to determine which options are best for the individual if the individual were given three alternatives of his or her inheritance; taking the $5,000 now, $1,000 for the next eight years, or taking a $12,000 at the end of the eight years. Assume that the individual can earn 11 percent interest annually. First, determine which what formulas will need to apply based on the way cash is being received. Perform the necessary calculations and determine which inheritance alternative would be best and why? Second, would he or she decision be different if he or she can earn interest at 12 percent? Without a proper calculation of the funds, decisions can be misconception. Receiving $5,000 cash now sound great and then invest for eight eights with 11 percent interest for the eight years. On the other hand, receiving $1,000 for the next eight years seems to be a little long and the amount is not that amazing but that $1,000 can be as large by the end of the eight years because the interest received increase each year—higher deposit at year two. For example, at year one, he or she invests $1,000 times that by the 11 percents interest rate will equal to $1,110 for the first year. For the second years, the interest will be calculate base...
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...Chapter 6 Time Value of Money LEARNING OBJECTIVES After reading this chapter, students should be able to: • Convert time value of money (TVM) problems from words to time lines. • Explain the relationship between compounding and discounting, between future and present value. • Calculate the future value of some beginning amount, and find the present value of a single payment to be received in the future. • Solve for time or interest rate, given the other three variables in the TVM equation. • Find the future value of a series of equal, periodic payments (an annuity) as well as the present value of such an annuity. • Explain the difference between an ordinary annuity and an annuity due, and calculate the difference in their values. • Calculate the value of a perpetuity. • Demonstrate how to find the present and future values of an uneven series of cash flows. • Distinguish among the following interest rates: Nominal (or Quoted) rate, Periodic rate, and Effective (or Equivalent) Annual Rate; and properly choose between securities with different compounding periods. • Solve time value of money problems that involve fractional time periods. • Construct loan amortization schedules for both fully-amortized and partially-amortized loans. LECTURE SUGGESTIONS We regard Chapter 6 as the most important chapter in the book, so we spend a good bit of time on it. We approach time value in...
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...present value concept is the value of future payments today – as money received today is more valuable than money received in the future, money received in the future has less value today. For example, say we decide that we are presented with an investment opportunity that earns 5% interest and we want this investment to be worth $10,000 in five years – how much do we invest? Using the formula PV=FV/〖(1+i)〗^n we would be able to figure the investment amount. PV=$10,000/〖(1+.05)〗^5 PV=$7,836.99 The present value of annuity is similar to present value but is used to calculate the current value an annuity or series of payments instead of a single payment. When finding the present value of an annuity we are discounting each future payment to reflect that payment’s current value and adding these discounted payments together to reach the present value of the annuity (Block, Hirt, & Danielsen, 2009). The formula to reach this value is: 〖PV〗_A=A× 〖PV〗_IFA; in addition to the formula we need to know the interest rate and period to use the present value of an annuity table. The future value is the measurement of “the value of an amount that is allowed to grow at a given...
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...John buys a house and pays it back in 5 years. The house is worth $150,000. The current rate is 6% and he expects rates to go up 1% every year. What does his amortization table look like? Year 1 payment Year 2 payment Year 3 payment Year 4 payment Year 5 payment N 5 N 4 N 3 N 2 N I 6.0% I 7.0% I 8.0% I 9.0% I PV -$150,000 PV -$123,391 PV -$95,600 PV -$66,152 PV FV $0 FV $0 FV $0 FV $0 FV PMT $35,609.46 PMT $36,428.36 PMT $37,095.82 PMT $37,605.16 PMT Loan Amortization Schedule, $100,000 with variable rates Amount borrowed: $150,000 The calculations for payment were done through excel calculations Beginning Amount (1) Payment (2) Interest (3) Repayment of Principal (4) Ending Balance (5) 150000 * 6% = 9000 interest on year 1 payment Year 35609.46 - 9000 = 26609.46 Repayment of principal for year 1 0 $150,000.00 150000 - 26609.46 = 123390.54 Ending balance for year 1 1 $150,000.00 $35,609.46 $9,000.00 $26,609.46 $123,390.54 123390.54 * 7% = 8637.34 interest on year 2 payment 2 $123,390.54 $36,428.36 $8,637.34 $27,791.02 $95,599.52 36428.36 - 8637.34 = 27791.02 Repayment of principal for year 2 3 $95,599.52 $37,095.82 $7,647.96 $29,447.86 $66,151.66 123390.54 - 27791.02 = 95599.52 Ending balance for year 2 4 $66,151.66 $37,605.16 $5,953.65 $31,651.51 $34,500.15 95599.52 * 8% = 7647.96 interest on...
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...Financial Management Lecture 1 Corporate Finance/Financial Decisions: Three important steps. * The Investment Decision: Expand, selling and so on. Decisions to spend or earn money. Capital budgeting. Capital budgeting is the planning and managing of a firms investment in non-current assets. The main thing is the cash flow. Evaluating; * Size of future cash flows * Timing of future cash flows * Risk to future cash flows. Cash flow timing is when a dollar today is worth more than a dollar at some future date. There is a trade-off between the size(amount) of an investements cash flow, and when the cash flow is recieved. So a dollar today, is more worth than a dollar a yeat from now. * The Finance Decision: How to found the fund to replace a machine for example. Capital structure decision. We are talking about firms that is listed. Capital structure is the specific mix of debt and equity maintained by the firm. Debt is loaned money and equity is the money in the firm, the own money. Decisions need to be made on both the financing mix, and how and where to raise the money. * The Dividend Decision: How to distribute the decision to expand for example. Involves the decision of wether to pay a dividend to shareholders or maintain the funds within the firm for internal growth. Factors important to this decision include growth opportunities, taxation and shareholders’ preferences. The top financial manager within a firm is usually the...
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...KEY CONCEPTS OF FINANCE A QUALITY E-LEARNING PROGRAM BY WWW.LEARNWITHFLIP.COM Understanding Money Money is a standardized unit of exchange. The physical form of money is currency. Different countries have different currencies. Interest is the amount earned or paid on money which is lent. Compound interest is the ‘interest earned on interest’. Compound Interest (C.I)= [P*(1+r/100)^t – P] P=Principal amount r=Rate of interest t=Time period in years Interest may be compounded annually, semi-annually, quarterly, monthly or even daily. This is known as the compounding frequency. Greater the frequency of compounding, the greater the effective return or yield. Always adjust the ‘r’ to map to the ‘t’. That is, if the compounding is quarterly, then take the quarterly interest rate, not the annual rate. Compounded Annual Growth Rate (CAGR) If we come across a projection of say, sales or profit 3 years from now, we need to arrive at a rate at which the sales was growing each year to arrive at that future number. That growth rate, which assumes compound growth each year, is called the CAGR. CAGR = (Final Value/Initial Value)1/n- 1 It’s defined as ‘the interest rate at which a given initial value will ‘grow’ to a final value in a given amount of time.’ Time Value Concept of Money Money earns interest with time. That means, INR 100 today is worth different amounts at different points in time. Hence, money has a ‘time value’. The fundamental concepts involved in understanding the...
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