Chapter 9 The Time Value of Money PDF

Chapter 9 The Time Value of Money Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1 Chapter 9- Learning Objectives  Identify various types of...

Chapter 9 The Time Value of Money Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1 Chapter 9- Learning Objectives  Identify various types of cash flow patterns (streams) that are observed in business.  Compute (a) the future values and (b) the present values of different cash flow streams, and explain the results.  Compute (a) the return (interest rate) on an investment (loan) and (b) how long it takes to reach a financial goal.  Explain the difference between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR), and explain when each is more appropriate to use.  Describe an amortized loan, and compute (a) amortized loan payments and (b) the balance (amount owed) on an amortized loan at a specific point during its life. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2 Time Value of Money  The principles and computations used to revalue cash payoffs at different times so they are stated in dollars of the same time period  The most important concept in finance used in nearly every financial decision Business decisions Personal finance decisions Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 3 Cash Flow Patterns Lump-sum amount – a single payment paid or received in the current period or some future period Annuity - A series of equal payments that occur at equal time intervals Uneven cash flow stream – multiple payments that are not equal and do not occur at equal intervals Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 4 Cash Flow Time Lines Graphical representations used to show timing of cash flows Time: 0 6% 1 Cash Flows: PV = 100 2 3 FV = ? Time 0 is today Time 1 is the end of Period 1 or the beginning of Period 2, and so forth. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 5 Future Value The amount to which a cash flow or series of cash flows will grow over a period of time when compounded at a given interest rate. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 6 Future Value How much would you have at the end of one year if you deposit $100 in a bank account that pays 5 percent interest each year? FVn = FV1 = PV + INT = PV + PV(r) = PV (1 + r) = $100(1 + 0.05) = $100(1.05) = $105 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 7 What’s the FV of an initial $700 after three years if r = 10%? 0 10% 1 2 700 3 FV = ? Finding FV is Compounding Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 8 Future Value After 1 year: FV1 = = = = PV + Interest1 = PV + PV (r) PV(1 + r) $700 (1.10) $770.00. After 2 years: FV2 = PV(1 + r)2 = $700 (1.10)2 = $847.00. After 3 years: FV3 = PV(1 + r)3 = $700 (1.10)3 = $931.70 In general, FVn = PV (1 + r)n Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 9 Three Ways to Solve Time Value of Money Problems Use Equations Use Financial Calculator Use Electronic Spreadsheet Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 10 Numerical (Equation) Solution FVn = PV(1+ r) n PV = $700, r = 10%, and n =3 3 FVn = $700(1.10) = $700(1.3310) = $931.70 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 11 Financial Calculator Solution FVn = PV(1+ r) n There are 4 variables. If 3 are known, the calculator will solve for the 4th. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 12 Financial Calculator Solution Here’s the setup to find FV: INPUTS 3 N 10 I/Y -700 PV 0 PMT OUTPUT ? FV =931.70 Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 13 Spreadsheet Solution According to the equation shown in cell C8, the input values must be entered in a specific order: I/Y, N, PMT, PV, and PMT type (not used for this problem). Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 14 If sales grow at 20% per year, how long before sales double? Solve for n: FVn = 1(1 + r)n 2 = 1(1.20)n The numerical solution is somewhat difficult. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 15 Graphical Illustration FV 2 3.8 1 0 1 2 3 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 4 Year 16 Financial Calculator Solution INPUTS OUTPUT ? 20 -1 0 N I/Y PV PMT 2 FV 3.8 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 17 Future Value of an Annuity  Annuity: A series of payments of equal amounts at equal intervals for a specified number of periods.  Ordinary (deferred) Annuity: An annuity whose payments occur at the end of each period.  Annuity Due: An annuity whose payments occur at the beginning of each period. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 18 Ordinary Annuity Versus Annuity Due Ordinary Annuity 0 r% 1 2 PMT PMT 1 2 PMT PMT 3 PMT Annuity Due 0 PMT 3 r% Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 19 FV of a 3-year Ordinary Annuity of $400 at 5% 0 5% 1 2 400 3 400 400 x (1.05)0 1 x (1.05) 2 x (1.05) Value of Each Deposit at the End of Year 3 400.00 420.00 441.00 FVA3 = 1,261.00 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 20 Numerical Solution n én-1 ù é (1 + r) -1ù t FVA n = PMTêå (1 + r) ú = PMTê ú r ë û ët= 0 û é (1.05)3 -1 ù FVA 3 = $400ê ú ë 0.05 û = $400(3.1525) = $1261.00 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 21 Financial Calculator Solution INPUTS 3 5 0 -400 ? N I/Y PV PMT FV OUTPUT Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. =1261.00 22 Spreadsheet Solution Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 23 FV of a 3-year Annuity Due of $400 at 5% 0 5% 400 1 2 3 400 x (1.05)0 x (1.05) 1 x (1.05) x (1.05) Value of Each Deposit at the End of Year 3 400 2 x (1.05) x (1.05) 420.00 441.00 463.05 FVA(DUE)3 = 1,324.05 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 24 Numerical Solution { n-1 é FVA(DUE)n = PMT ë(1+ r ) ´ (1+r)ùû + } 0 é + ë(1+ r ) ´ (1+r)ùû n = PMT å (1+ r) t 1 ìé (1+ r)n -1ù ü = PMT íê ú ´ (1+r)ý r û îë þ ìïé (1.05)3 -1ù üï FVA(DUE)3 = $400 íê ú ´ (1.05) ý ïîë 0.05 û ïþ = $400(3.31013) = $1,324.05 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 25 Financial Calculator Solution BGN INPUTS 3 5 0 -400 ? N I/Y PV PMT FV OUTPUT Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. =1,324.05 26 Spreadsheet Solution N= I/Y = PV = PMT = PMT type = FV = 3 5.00% $0.00 -$400.00 1 (0 = ordinary annuity; 1 = annuity due) ? FVA(DUE) = The equation used to solve for FV in cell B8 =FV(B2,B1,B4,B3,B5 $1,324.05 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Values that correspond to the cell reference in cell C8 =FV(0.05,3,-400,0,1) 27 Future Value of an Uneven Cash Flow 0 5% 1 2 400 3 300 250 x (1.05)0 1 x (1.05) 2 x (1.05) Value of Each Deposit at the End of Year 3 250.00 315.00 441.00 FVCF3 = 1,006.00 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 28 Numerical Solution ( ) FVCFn =CF1 1+r n-1 ( ) +CF2 1+r n-2 ( ) n-1 + +CFn 1+r = å CFt (1+r) t 0 t=0 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 29 Present Value  Present value is the value today of a future cash flow or series of cash flows.  Discounting is the process of finding the present value of a future cash flow or series of future cash flows; it is the reverse of compounding. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 30 What is the PV of $935 due in three years if r = 10%? 0 1 r = 10% 1 PV = 702.48 (1.10) ´ 2 1 772.73 (1.10) ´ 3 1 850.00 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (1.10) ´ 935.00 = FV3 31 Numerical Solution Solve FVn = PV (1 + r )n for PV: PV = FVn (1+r ) n æ 1 ö = FVn ç ÷ è1+r ø n 3 æ 1 ö PV = $935ç ÷ è 1.10 ø = $935 ( 0.7513) = $702.48 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 32 Financial Calculator Solution INPUTS OUTPUT 3 10 N I/Y ? 0 PV PMT 935 FV -702.48 Either PV or FV must be negative. Here PV = -702.48. Invest $702.48 today, take out $935 after 3 years. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 33 Spreadsheet Solution Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 34 Present Value of an Annuity  PVAn = the present value of an annuity with n payments  Each payment is discounted, and the sum of the discounted payments is the present value of the annuity Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 35 What is the PV of this Ordinary Annuity? Value of Each Deposit Today (Year 0) 380.95 362.81 0 5% 1 1 x 400 (1.05)1 345.54 1,089.30 = PVA3 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1 x (1.05)2 2 3 400 400 1 x (1.05)3 36 Numerical Solution 1 ù é 1 én ù 1 (1+r) n ú PVA n = PMTêå = PMTê tú êë r úû ët=1 (1 + r) û 1 é1- (1.05) ù 3 PVA 3 = $400ê ú ë 0.05 û = $400(2.72325) = $1089.30 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 37 Financial Calculator Solution INPUTS OUTPUT 3 5 ? 400 0 N I/Y PV PMT FV = -1,089.30 We know the payments but there is no lump sum FV, so enter 0 for future value. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 38 Spreadsheet Solution Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 39 Present Value of an Annuity Due 0 Value of Each Deposit Today (Year 0) 1 (1.05) x (1.05) x 2 400 400 05% 400 400.00 (1.05) x 380.95 362.81 1,143.76 = PVA (DUE)3 1 1 1 (1.05)2 3 x (1.05) x Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1 (1.05)3 x 40 Numerical Solution Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 41 Financial Calculator Solution Switch from “End” to “Begin”. Then enter variables to find PVA3 = $1,143.76 INPUTS OUTPUT BGN 3 5 ? -400 0 N I/Y PV PMT FV 42 -1,143.76 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 42 Spreadsheet Solution Insert a “1” for Type Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 43 Uneven Cash Flow Streams  A series of cash flows in which the amount varies from one period to the next: Payment (PMT) designates constant cash flows—that is, an annuity stream. Cash flow (CF) designates cash flows in general, both constant cash flows and uneven cash flows. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 44 Present Value of Uneven Cash Flow Stream Value of Each Deposit Today (Year 0) 380.95 272.11 0 5% 1 1 x 400 (1.05)1 1 x (1.05) 2 215.96 PV3 = 869.02 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2 3 300 250 1 x (1.05)3 45 Numerical Solution é ù é ù é ù n é ù ê 1 ú ê 1 ú ê 1 ú ê 1 ú PVCFn =CF1 ê +CF2 ê + +CFn ê = CFt ê 1ú 2ú nú å tú êë 1+r úû êë 1+r úû êë 1+r úû t=1 êë 1+r úû ( ) PVCFn = 400 + ( ) 300 + 250 (1.05) (1.05) (1.05) 1 3 3 ( ) ( ) =400(0.95238)+300(0.90703)+250(0.86384) =380.952+272.109+215.960=869.02 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 46 Financial Calculator Solution  Input in “CF” register:  CF0  CF1  CF2  CF3 =0 = 400 = 300 = 250  Enter I = 5%, then press NPV button to get NPV = 869.02. (Here NPV = PV) Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 47 Spreadsheet Solution Setup the spreadsheet so that the cash flows are ordered sequentially Use the NPV function to solve for the present value of the non-constant cash flow series. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 48 Semiannual and Other Compounding Periods  Annual compounding is the process of determining the future (present) value of a cash flow or series of cash flows when interest is added once a year.  Semiannual compounding is the process of determining the future (present) value of a cash flow or series of cash flows when interest is added twice a year. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 49 Compounding  Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated r constant?  If compounding is more frequent than once per year—for example, semi-annually, quarterly, or daily—interest is earned on interest. It is compounded more often and the future value will be larger. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 50 Comparison of Different Interest Rates rSIMPLE = Simple (Quoted) Rate Used to compute the interest paid per period APR = Annual Percentage Rate = rSIMPLE The rate reported to you by lenders when you borrow money APR is a non-compounded interest rate EAR = Effective Annual Rate = rEAR The rate that would produce the same future value if annual compounding had been used Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 51 EAR for a simple rate of 10%, compounded semi-annually EAR = rEAR rSIMPLE æ = ç1 + ç m è m ö ÷ -1 ÷ ø 2 0.10 ö æ = ç1 + ÷ - 1.0 2 ø è = (1.05) - 1.0 = 0.1025 = 10.25% 2 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 52 FV of $100 after 3 years if interest is 10% compounded semi-annually m´n æ ö rSIMPLE FVn = PVç1 + ÷ è m ø 0.10 ö æ FV3´2 = $100ç1 + ÷ 2 ø è 2´3 = $100(1.34010) = $134.01 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 53 FV of $100 after 3 years if interest is 10% compounded quarterly m´n æ ö rSIMPLE FVn = PVç1 + ÷ è m ø FV3´4 0.10 ö æ = $100ç1 + ÷ 4 ø è 4´3 = $100(1.34489) = $134.49 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 54 Fractional Time Periods Example: $100 deposited in a bank at EAR = 10% for 0.75 of the year 0 10% 0.25 0.50 - 100 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 0.75 1.00 FV = ? 55 Financial Calculator Solution Example: $100 deposited in a bank at EAR = 10% for 0.75 of the year INPUTS 0.75 N 10 I/Y -100 0 PV PMT OUTPUT Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ? FV 107.41 56 Spreadsheet Solution Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 57 Amortized Loans  Amortized Loan: A loan that is repaid in equal payments over its life; payment includes both principal repayment and interest  Amortization tables are widely used for home mortgages, auto loans, and so forth to determine how much of each payment represents principal repayment and how much represents interest.  Financial calculators (and spreadsheets) can be used to set up amortization tables. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 58 Amortization schedule for a $15,000, 8% loan that requires three equal annual payments Year: 0 1 2 3 PMT = ? PMT = ? PMT = ? r = 8% 15,000 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 59 Step 1: Determine the Required Payments INPUTS OUTPUT 3 8 15,000 N I/Y PV ? PMT 0 FV = -5,820.50 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 60 Step 2: Find Interest Charge for Year 1 INTt = Beginning balancet (r) INT1 = 15,000(0.08) = $1,200.00 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 61 Step 3: Find Repayment of Principal in Year 1 Repayment = PMT - INT = 5,820.50 - $1200.00 = $4,620.50 Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 62 Step 4: Find Ending Balance after Year 1 Ending bal. = Beginning bal. - Repayment = $15,000 - 4,620.50 = $10,379.50 Repeat these steps for the remainder of the payments (Years 2 and 3 in this case) to complete the amortization table. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 63 Loan Amortization Schedule $15,000 Loan at 8 Percent Interest Rate Year 1 2 3 a b c Beginning of Year Balance Payment Interest @ 8%a (1) (2) (3) = (1) x 0.08 $15,000.00 $5,820.50 $1,200.00 10,379.50 5,820.50 830.36 5,389.36 5,820.50 431.15 Repayment of Principalb (4) = (2) – (3) $4,620.50 4,990.14 5,389.35 Remaining Balancec (5) = (1) – (4) 10379.50 5,389.36 0.01 Interest is calculated by multiplying the loan balance in Column 1 by the interest rate (0.08). For example, the interest in Year 2 is $10,379.50 x 0.08 = $830.36. Repayment of principal is equal to the payment of $5,820.50 in Column 2 minus the interest charge for each year in Column 3. For example, the repayment of principal in Year 2 is $5,820.50 – $830.36 = $4,990.14. The $0.01 remaining balance at the end of Year 3 results from a rounding difference. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 64 Chapter Principles Key Time Value of Money Concepts  What are the three basic types of cash flow patterns?  Lump-sum amount – a single payment paid or received in the current period or some future period  Annuity - A series of equal payments that occur at equal time intervals  Uneven cash flow stream – multiple payments that are not equal and do not occur at equal intervals Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 65 Chapter Principles Key Time Value of Money Concepts  How are dollars from different time periods compared when making financial decisions?  Dollars from different time periods must be stated in the same “Time Value” before they can be compared.  Dollars can be translated into the same time period by computing either present value or future value. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 66 Chapter Principles Key Time Value of Money Concepts  How is the return on an investment determined?  The return is determined by the rate at which the investment grows over time.  Everything being equal, the current value of an investment is lower the higher the interest rate it earns in the future. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 67 Chapter Principles Key Time Value of Money Concepts  What is the difference between the Annual Percentage Rate (APR) and the Effective Annual rate (EAR)?  APR is a simple interest rate quoted on loans.  EAR is the actual interest rate or rate of return.  What is an amortized loan?  A loan paid off in equal payments over a specified period.  Payment includes principal and interest. Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 68 End of Chapter 9 The Time Value of Money Principles of Finance 5e, 9 The Time Value of Money © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 69