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TIME VALUE
1.
3.1 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Chapter 3 The Time Value of Money
2.
3.2 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. After studying Chapter 3, you should be able to: 1. Understand what is meant by "the time value of money." 2. Understand the relationship between present and future value. 3. Describe how the interest rate can be used to adjust the value of cash flows ā both forward and backward ā to a single point in time. 4. Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flows. 5. Distinguish between an āordinary annuityā and an āannuity due.ā 6. Use interest factor tables and understand how they provide a shortcut to calculating present and future values. 7. Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known. 8. Build an āamortization scheduleā for an installment-style loan.
3.
3.3 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Time Value of Money ā¢ The Interest Rate ā¢ Simple Interest ā¢ Compound Interest ā¢ Amortizing a Loan ā¢ Compounding More Than Once per Year
4.
3.4 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Obviously, $10,000 today. You already recognize that there is TIME VALUE TO MONEY!! The Interest Rate Which would you prefer ā $10,000 today or $10,000 in 5 years?
5.
3.5 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. TIME allows you the opportunity to postpone consumption and earn INTEREST. Why TIME? Why is TIME such an important element in your decision?
6.
3.6 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Types of Interest ā¢ Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). ā¢ Simple Interest Interest paid (earned) on only the original amount, or principal, borrowed (lent).
7.
3.7 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Simple Interest Formula Formula SI = P0(i)(n) SI: Simple Interest P0: Deposit today (t=0) i: Interest Rate per Period n: Number of Time Periods
8.
3.8 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. ā¢ SI = P0(i)(n) = $1,000(0.07)(2) = $140 Simple Interest Example ā¢ Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?
9.
3.9 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV = P0 + SI = $1,000 + $140 = $1,140 ā¢ Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. Simple Interest (FV) ā¢ What is the Future Value (FV) of the deposit?
10.
3.10 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Present Value is simply the $1,000 you originally deposited. That is the value today! ā¢ Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. Simple Interest (PV) ā¢ What is the Present Value (PV) of the previous problem?
11.
3.11 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 5000 10000 15000 20000 1st Year 10th Year 20th Year 30th Year Future Value of a Single $1,000 Deposit 10% Simple Interest 7% Compound Interest 10% Compound Interest Why Compound Interest? Future Value (U.S. Dollars)
12.
3.12 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years. Future Value Single Deposit (Graphic) 0 1 2 $1,000 FV2 7%
13.
3.13 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV1 = P0 (1 + i)1 = $1,000 (1.07) = $1,070 Compound Interest You earned $70 interest on your $1,000 deposit over the first year. This is the same amount of interest you would earn under simple interest. Future Value Single Deposit (Formula)
14.
3.14 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV1 = P0 (1 + i)1 = $1,000 (1.07) = $1,070 FV2 = FV1 (1 + i)1 = P0 (1 + i)(1 + i) = $1,000(1.07)(1.07) = P0 (1 + i)2 = $1,000(1.07)2 = $1,144.90 You earned an EXTRA $4.90 in Year 2 with compound over simple interest. Future Value Single Deposit (Formula)
15.
3.15 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV1 = P0(1 + i)1 FV2 = P0(1 + i)2 General Future Value Formula: FVn = P0 (1 + i)n or FVn = P0 (FVIFi,n) ā See Table I General Future Value Formula etc.
16.
3.16 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVIFi,n is found on Table I at the end of the book. Valuation Using Table I Period 6% 7% 8% 1 1.060 1.070 1.080 2 1.124 1.145 1.166 3 1.191 1.225 1.260 4 1.262 1.311 1.360 5 1.338 1.403 1.469
17.
3.17 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145 [Due to Rounding] Using Future Value Tables Period 6% 7% 8% 1 1.060 1.070 1.080 2 1.124 1.145 1.166 3 1.191 1.225 1.260 4 1.262 1.311 1.360 5 1.338 1.403 1.469
18.
3.18 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years. Story Problem Example 0 1 2 3 4 5 $10,000 FV5 10%
19.
3.19 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. ā¢ Calculation based on Table I: FV5 = $10,000 (FVIF10%, 5) = $10,000 (1.611) = $16,110 [Due to Rounding] Story Problem Solution ā¢ Calculation based on general formula: FVn = P0 (1 + i)n FV5 = $10,000 (1 + 0.10)5 = $16,105.10
20.
3.20 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Assume that you need $1,000 in 2 years. Letās examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually. 0 1 2 $1,000 7% PV1 PV0 Present Value Single Deposit (Graphic)
21.
3.21 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PV0 = FV2 / (1 + i)2 = $1,000 / (1.07)2 = FV2 / (1 + i)2 = $873.44 0 1 2 $1,000 7% PV0 Present Value Single Deposit (Formula)
22.
3.22 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PV0 = FV1 / (1 + i)1 PV0 = FV2 / (1 + i)2 General Present Value Formula: PV0 = FVn / (1 + i)n or PV0 = FVn (PVIFi,n) ā See Table II etc. General Present Value Formula
23.
3.23 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVIFi,n is found on Table II at the end of the book. Period 6% 7% 8% 1 0.943 0.935 0.926 2 0.890 0.873 0.857 3 0.840 0.816 0.794 4 0.792 0.763 0.735 5 0.747 0.713 0.681 Valuation Using Table II
24.
3.24 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873 [Due to Rounding] Period 6% 7% 8% 1 0.943 0.935 0.926 2 0.890 0.873 0.857 3 0.840 0.816 0.794 4 0.792 0.763 0.735 5 0.747 0.713 0.681 Using Present Value Tables
25.
3.25 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000 in 5 years at a discount rate of 10%. 0 1 2 3 4 5 $10,000 PV0 10% Story Problem Example
26.
3.26 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. ā¢ Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = $10,000 / (1 + 0.10)5 = $6,209.21 ā¢ Calculation based on Table I: PV0 = $10,000 (PVIF10%, 5) = $10,000 (0.621) = $6,210.00 [Due to Rounding] Story Problem Solution
27.
3.27 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. ā¢ Ordinary Annuity: Payments or receipts occur at the end of each period. ā¢ Annuity Due: Payments or receipts occur at the beginning of each period. ā¢ An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. Types of Annuities
28.
3.28 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. ā¢ Student Loan Payments ā¢ Car Loan Payments ā¢ Insurance Premiums ā¢ Mortgage Payments ā¢ Retirement Savings Examples of Annuities
29.
3.29 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 $100 $100 $100 (Ordinary Annuity) End of Period 1 End of Period 2 Today Equal Cash Flows Each 1 Period Apart End of Period 3 Parts of an Annuity
30.
3.30 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 $100 $100 $100 (Annuity Due) Beginning of Period 1 Beginning of Period 2 Today Equal Cash Flows Each 1 Period Apart Beginning of Period 3 Parts of an Annuity
31.
3.31 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVAn = R(1 + i)n-1 + R(1 + i)n-2 + ... + R(1 + i)1 + R(1 + i)0 R R R 0 1 2 n n+1 FVAn R = Periodic Cash Flow Cash flows occur at the end of the period i% . . . Overview of an Ordinary Annuity ā FVA
32.
3.32 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVA3 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0 = $1,145 + $1,070 + $1,000 = $3,215 $1,000 $1,000 $1,000 0 1 2 3 4 $3,215 = FVA3 7% $1,070 $1,145 Cash flows occur at the end of the period Example of an Ordinary Annuity ā FVA
33.
3.33 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The future value of an ordinary annuity can be viewed as occurring at the end of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the beginning of the last cash flow period. Hint on Annuity Valuation
34.
3.34 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVAn = R (FVIFAi%,n) FVA3 = $1,000 (FVIFA7%,3) = $1,000 (3.215) = $3,215 Period 6% 7% 8% 1 1.000 1.000 1.000 2 2.060 2.070 2.080 3 3.184 3.215 3.246 4 4.375 4.440 4.506 5 5.637 5.751 5.867 Valuation Using Table III
35.
3.35 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVADn = R(1 + i)n + R(1 + i)n-1 + ... + R(1 + i)2 + R(1 + i)1 = FVAn (1 + i) R R R R R 0 1 2 3 nā1 n FVADn i% . . . Overview View of an Annuity Due ā FVAD Cash flows occur at the beginning of the period
36.
3.36 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVAD3 = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1 = $1,225 + $1,145 + $1,070 = $3,440 $1,000 $1,000 $1,000 $1,070 0 1 2 3 4 $3,440 = FVAD3 7% $1,225 $1,145 Example of an Annuity Due ā FVAD Cash flows occur at the beginning of the period
37.
3.37 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FVADn = R (FVIFAi%,n)(1 + i) FVAD3 = $1,000 (FVIFA7%,3)(1.07) = $1,000 (3.215)(1.07) = $3,440 Period 6% 7% 8% 1 1.000 1.000 1.000 2 2.060 2.070 2.080 3 3.184 3.215 3.246 4 4.375 4.440 4.506 5 5.637 5.751 5.867 Valuation Using Table III
38.
3.38 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVAn = R/(1 + i)1 + R/(1 + i)2 + ... + R/(1 + i)n R R R 0 1 2 n n+1 PVAn R = Periodic Cash Flow i% . . . Overview of an Ordinary Annuity ā PVA Cash flows occur at the end of the period
39.
3.39 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVA3 = $1,000/(1.07)1 + $1,000/(1.07)2 + $1,000/(1.07)3 = $934.58 + $873.44 + $816.30 = $2,624.32 $1,000 $1,000 $1,000 0 1 2 3 4 $2,624.32 = PVA3 7% $934.58 $873.44 $816.30 Example of an Ordinary Annuity ā PVA Cash flows occur at the end of the period
40.
3.40 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The present value of an ordinary annuity can be viewed as occurring at the beginning of the first cash flow period, whereas the future value of an annuity due can be viewed as occurring at the end of the first cash flow period. Hint on Annuity Valuation
41.
3.41 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVAn = R (PVIFAi%,n) PVA3 = $1,000 (PVIFA7%,3) = $1,000 (2.624) = $2,624 Period 6% 7% 8% 1 0.943 0.935 0.926 2 1.833 1.808 1.783 3 2.673 2.624 2.577 4 3.465 3.387 3.312 5 4.212 4.100 3.993 Valuation Using Table IV
42.
3.42 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVADn = R/(1 + i)0 + R/(1 + i)1 + ... + R/(1 + i)nā1 = PVAn (1 + i) R R R R 0 1 2 nā1 n PVADn R: Periodic Cash Flow i% . . . Overview of an Annuity Due ā PVAD Cash flows occur at the beginning of the period
43.
3.43 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $2,808.02 $1,000.00 $1,000 $1,000 0 1 2 3 4 $2,808.02 = PVADn 7% $ 934.58 $ 873.44 Example of an Annuity Due ā PVAD Cash flows occur at the beginning of the period
44.
3.44 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVADn = R (PVIFAi%,n)(1 + i) PVAD3 = $1,000 (PVIFA7%,3)(1.07) = $1,000 (2.624)(1.07) = $2,808 Period 6% 7% 8% 1 0.943 0.935 0.926 2 1.833 1.808 1.783 3 2.673 2.624 2.577 4 3.465 3.387 3.312 5 4.212 4.100 3.993 Valuation Using Table IV
45.
3.45 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1. Read problem thoroughly 2. Create a time line 3. Put cash flows and arrows on time line 4. Determine if it is a PV or FV problem 5. Determine if solution involves a single ,annuity stream(s), or mixed flow 6. Solve the problem 7. Check with financial calculator (optional) Steps to Solve Time Value of Money Problems
46.
3.46 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller will receive the set of cash flows below. What is the Present Value at a discount rate of 10%. 0 1 2 3 4 5 $600 $600 $400 $400 $100 PV0 10% Mixed Flows Example
47.
3.47 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1. Solve a āpiece-at-a-timeā by discounting each piece back to t=0. 2. Solve a āgroup-at-a-timeā by first breaking problem into groups of annuity streams and any single cash flow groups. Then discount each group back to t=0. How to Solve?
48.
3.48 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $545.45 $495.87 $300.53 $273.21 $ 62.09 $1677.15 = PV0 of the Mixed Flow āPiece-At-A-Timeā
49.
3.49 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $1,041.60 $ 573.57 $ 62.10 $1,677.27 = PV0 of Mixed Flow [Using Tables] $600(PVIFA10%,2) = $600(1.736) = $1,041.60 $400(PVIFA10%,2)(PVIF10%,2) = $400(1.736)(0.826) = $573.57 $100 (PVIF10%,5) = $100 (0.621) = $62.10 āGroup-At-A-Timeā (#1)
50.
3.50 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 $400 $400 $400 $400 PV0 equals $1677.30. 0 1 2 $200 $200 0 1 2 3 4 5 $100 $1,268.00 $347.20 $62.10 Plus Plus āGroup-At-A-Timeā (#2)
51.
3.51 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. General Formula: FVn = PV0(1 + [i/m])mn n: Number of Years m: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n PV0: PV of the Cash Flow today Frequency of Compounding
52.
3.52 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller has $1,000 to invest for 2 Years at an annual interest rate of 12%. Annual FV2 = 1,000(1 + [0.12/1])(1)(2) = 1,254.40 Semi FV2 = 1,000(1 + [0.12/2])(2)(2) = 1,262.48 Impact of Frequency
53.
3.53 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Qrtly FV2 = 1,000(1 + [0.12/4])(4)(2) = 1,266.77 Monthly FV2 = 1,000(1 + [0.12/12])(12)(2) = 1,269.73 Daily FV2 = 1,000(1 + [0.12/365])(365)(2) = 1,271.20 Impact of Frequency
54.
3.54 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Effective Annual Interest Rate The actual rate of interest earned (paid) after adjusting the nominal rate for factors such as the number of compounding periods per year. (1 + [ i / m ] )m ā 1 Effective Annual Interest Rate
55.
3.55 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)? EAR = ( 1 + 0.06 / 4 )4 ā 1 = 1.0614 - 1 = 0.0614 or 6.14%! BWs Effective Annual Interest Rate
56.
3.56 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Amortization ļµAmortization is the paying off of debt with a Fixed repayments schedule in regular installments over a period of time. Consumers are most likely to encounter amortization with a mortgage or car loan.
57.
3.57 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1. Calculate the payment per period. 2. Determine the interest in Period t. (Loan Balance at t ā 1) x (i% / m) 3. Compute principal payment in Period t. (Payment - Interest from Step 2) 4. Determine ending balance in Period t. (Balance - principal payment from Step 3) 5. Start again at Step 2 and repeat. Steps to Amortizing a Loan
58.
3.58 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller is borrowing $10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years. Step 1: Payment PV0 = R (PVIFA i%,n) $10,000 = R (PVIFA 12%,5) $10,000 = R (3.605) R = $10,000 / 3.605 = $2,774 Amortizing a Loan Example
59.
3.59 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. End of Year Payment Interest Principal Ending Balance 0 ā ā ā $10,000 1 $2,774 $1,200 $1,574 8,426 2 2,774 1,011 1,763 6,663 3 2,774 800 1,974 4,689 4 2,774 563 2,211 2,478 5 2,775 297 2,478 0 $13,871 $3,871 $10,000 [Last Payment Slightly Higher Due to Rounding] Amortizing a Loan Example
60.
3.60 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. Ā© Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 2. Calculate Debt Outstanding ā The quantity of outstanding debt may be used in financing the day-to-day activities of the firm. 1. Determine Interest Expense ā Interest expenses may reduce taxable income of the firm. Usefulness of Amortization
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