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ch 3.ppt
1.
3.1 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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. © 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 – both forward and backward – 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 “ordinary annuity” and an “annuity due.” 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 “amortization schedule” for an installment-style loan.
3.
3.3 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Time Value of Money • The Interest Rate • Simple Interest • Compound Interest • Amortizing a Loan • Compounding More Than Once per Year
4.
3.4 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – $10,000 today or $10,000 in 5 years?
5.
3.5 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Types of Interest • Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). • 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. © 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. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • SI = P0(i)(n) = $1,000(0.07)(2) = $140 Simple Interest Example • 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. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. FV = P0 + SI = $1,000 + $140 = $1,140 • 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) • What is the Future Value (FV) of the deposit?
10.
3.10 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Present Value is simply the $1,000 you originally deposited. That is the value today! • 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) • What is the Present Value (PV) of the previous problem?
11.
3.11 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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. © 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. © 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. © 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. © 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) – See Table I General Future Value Formula etc.
16.
3.16 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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. © 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. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. TVM on the Calculator • Use the highlighted row of keys for solving any of the FV, PV, FVA, PVA, FVAD, and PVAD problems N: Number of periods I/Y:Interest rate per period PV: Present value PMT: Payment per period FV: Future value CLR TVM: Clears all of the inputs into the above TVM keys Source: Courtesy of Texas Instruments
19.
3.19 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Using The TI BAII+ Calculator N I/Y PV PMT FV Inputs Compute Focus on 3rd Row of keys (will be displayed in slides as shown above)
20.
3.20 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Entering the FV Problem Press: 2nd CLR TVM 2 N 7 I/Y –1000 PV 0 PMT CPT FV Source: Courtesy of Texas Instruments
21.
3.21 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N: 2 Periods (enter as 2) I/Y: 7% interest rate per period (enter as 7 NOT 0.07) PV: $1,000 (enter as negative as you have “less”) PMT: Not relevant in this situation (enter as 0) FV: Compute (Resulting answer is positive) Solving the FV Problem N I/Y PV PMT FV Inputs Compute 2 7 –1,000 0 1,144.90
22.
3.22 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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%
23.
3.23 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • Calculation based on Table I: FV5 = $10,000 (FVIF10%, 5) = $10,000 (1.611) = $16,110 [Due to Rounding] Story Problem Solution • Calculation based on general formula: FVn = P0 (1 + i)n FV5 = $10,000 (1 + 0.10)5 = $16,105.10
24.
3.24 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Entering the FV Problem Press: 2nd CLR TVM 5 N 10 I/Y –10000 PV 0 PMT CPT FV Source: Courtesy of Texas Instruments
25.
3.25 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The result indicates that a $10,000 investment that earns 10% annually for 5 years will result in a future value of $16,105.10. Solving the FV Problem N I/Y PV PMT FV Inputs Compute 5 10 –10,000 0 16,105.10
26.
3.26 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. We will use the “Rule-of-72”. Double Your Money!!! Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
27.
3.27 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Approx. Years to Double = 72 / i% 72 / 12% = 6 Years [Actual Time is 6.12 Years] The “Rule-of-72” Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
28.
3.28 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The result indicates that a $1,000 investment that earns 12% annually will double to $2,000 in 6.12 years. Note: 72/12% = approx. 6 years Solving the Period Problem N I/Y PV PMT FV Inputs Compute 12 –1,000 0 +2,000 6.12 years
29.
3.29 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Assume that you need $1,000 in 2 years. Let’s 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)
30.
3.30 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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)
31.
3.31 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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) – See Table II etc. General Present Value Formula
32.
3.32 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
33.
3.33 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
34.
3.34 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N: 2 Periods (enter as 2) I/Y: 7% interest rate per period (enter as 7 NOT 0.07) PV: Compute (Resulting answer is negative “deposit”) PMT: Not relevant in this situation (enter as 0) FV: $1,000 (enter as positive as you “receive $”) N I/Y PV PMT FV Inputs Compute 2 7 0 +1,000 –873.44 Solving the PV Problem
35.
3.35 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
36.
3.36 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = $10,000 / (1 + 0.10)5 = $6,209.21 • Calculation based on Table I: PV0 = $10,000 (PVIF10%, 5) = $10,000 (0.621) = $6,210.00 [Due to Rounding] Story Problem Solution
37.
3.37 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N I/Y PV PMT FV Inputs Compute 5 10 0 +10,000 –6,209.21 The result indicates that a $10,000 future value that will earn 10% annually for 5 years requires a $6,209.21 deposit today (present value). Solving the PV Problem
38.
3.38 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • Ordinary Annuity: Payments or receipts occur at the end of each period. • Annuity Due: Payments or receipts occur at the beginning of each period. • An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. Types of Annuities
39.
3.39 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • Student Loan Payments • Car Loan Payments • Insurance Premiums • Mortgage Payments • Retirement Savings Examples of Annuities
40.
3.40 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
41.
3.41 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
42.
3.42 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – FVA
43.
3.43 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – FVA
44.
3.44 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
45.
3.45 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
46.
3.46 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N: 3 Periods (enter as 3 year-end deposits) I/Y: 7% interest rate per period (enter as 7 NOT 0.07) PV: Not relevant in this situation (no beg value) PMT: $1,000 (negative as you deposit annually) FV: Compute (Resulting answer is positive) N I/Y PV PMT FV Inputs Compute 3 7 0 –1,000 3,214.90 Solving the FVA Problem
47.
3.47 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 n–1 n FVADn i% . . . Overview View of an Annuity Due – FVAD Cash flows occur at the beginning of the period
48.
3.48 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – FVAD Cash flows occur at the beginning of the period
49.
3.49 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
50.
3.50 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N I/Y PV PMT FV Inputs Compute 3 7 0 –1,000 3,439.94 Complete the problem the same as an “ordinary annuity” problem, except you must change the calculator setting to “BGN” first. Don’t forget to change back! Step 1: Press 2nd BGN keys Step 2: Press 2nd SET keys Step 3: Press 2nd QUIT keys Solving the FVAD Problem
51.
3.51 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – PVA Cash flows occur at the end of the period
52.
3.52 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – PVA Cash flows occur at the end of the period
53.
3.53 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
54.
3.54 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
55.
3.55 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N: 3 Periods (enter as 3 year-end deposits) I/Y: 7% interest rate per period (enter as 7 NOT .07) PV: Compute (Resulting answer is positive) PMT: $1,000 (negative as you deposit annually) FV: Not relevant in this situation (no ending value) N I/Y PV PMT FV Inputs Compute 3 7 –1,000 0 2,624.32 Solving the PVA Problem
56.
3.56 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. PVADn = R/(1 + i)0 + R/(1 + i)1 + ... + R/(1 + i)n–1 = PVAn (1 + i) R R R R 0 1 2 n–1 n PVADn R: Periodic Cash Flow i% . . . Overview of an Annuity Due – PVAD Cash flows occur at the beginning of the period
57.
3.57 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – PVAD Cash flows occur at the beginning of the period
58.
3.58 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
59.
3.59 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. N I/Y PV PMT FV Inputs Compute 3 7 –1,000 0 2,808.02 Complete the problem the same as an “ordinary annuity” problem, except you must change the calculator setting to “BGN” first. Don’t forget to change back! Step 1: Press 2nd BGN keys Step 2: Press 2nd SET keys Step 3: Press 2nd QUIT keys Solving the PVAD Problem
60.
3.60 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 CF, annuity stream(s), or mixed flow 6. Solve the problem 7. Check with financial calculator (optional) Steps to Solve Time Value of Money Problems
61.
3.61 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
62.
3.62 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1. Solve a “piece-at-a-time” by discounting each piece back to t=0. 2. Solve a “group-at-a-time” 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?
63.
3.63 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 “Piece-At-A-Time”
64.
3.64 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 “Group-At-A-Time” (#1)
65.
3.65 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 “Group-At-A-Time” (#2)
66.
3.66 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. • Use the highlighted key for starting the process of solving a mixed cash flow problem • Press the CF key and down arrow key through a few of the keys as you look at the definitions on the next slide Solving the Mixed Flows Problem using CF Registry Source: Courtesy of Texas Instruments
67.
3.67 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining the calculator variables: For CF0: This is ALWAYS the cash flow occurring at time t=0 (usually 0 for these problems) For Cnn:* This is the cash flow SIZE of the nth group of cash flows. Note that a “group” may only contain a single cash flow (e.g., $351.76). For Fnn:* This is the cash flow FREQUENCY of the nth group of cash flows. Note that this is always a positive whole number (e.g., 1, 2, 20, etc.). * nn represents the nth cash flow or frequency. Thus, the first cash flow is C01, while the tenth cash flow is C10. Solving the Mixed Flows Problem using CF Registry
68.
3.68 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Steps in the Process Step 1: Press CF key Step 2: Press 2nd CLR Work keys Step 3: For CF0 Press 0 Enter ↓ keys Step 4: For C01 Press 600 Enter ↓ keys Step 5: For F01 Press 2 Enter ↓ keys Step 6: For C02 Press 400 Enter ↓ keys Step 7: For F02 Press 2 Enter ↓ keys Solving the Mixed Flows Problem using CF Registry
69.
3.69 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Steps in the Process Step 8: For C03 Press 100 Enter ↓ keys Step 9: For F03 Press 1 Enter ↓ keys Step 10: Press ↓ ↓ keys Step 11: Press NPV key Step 12: For I =, Enter 10 Enter ↓ keys Step 13: Press CPT key Result: Present Value = $1,677.15 Solving the Mixed Flows Problem using CF Registry
70.
3.70 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
71.
3.71 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
72.
3.72 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
73.
3.73 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The result indicates that a $1,000 investment that earns a 12% annual rate compounded quarterly for 2 years will earn a future value of $1,266.77. N I/Y PV PMT FV Inputs Compute 2(4) 12/4 –1,000 0 1266.77 Solving the Frequency Problem (Quarterly)
74.
3.74 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd P/Y 4 ENTER 2nd QUIT 12 I/Y –1000 PV 0 PMT 2 2nd xP/Y N CPT FV Solving the Frequency Problem (Quarterly Altern.) Source: Courtesy of Texas Instruments
75.
3.75 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The result indicates that a $1,000 investment that earns a 12% annual rate compounded daily for 2 years will earn a future value of $1,271.20. N I/Y PV PMT FV Inputs Compute 2(365) 12/365 –1,000 0 1271.20 Solving the Frequency Problem (Daily)
76.
3.76 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd P/Y 365 ENTER 2nd QUIT 12 I/Y –1000 PV 0 PMT 2 2nd xP/Y N CPT FV Solving the Frequency Problem (Daily Alternative) Source: Courtesy of Texas Instruments
77.
3.77 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – 1 Effective Annual Interest Rate
78.
3.78 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – 1 = 1.0614 - 1 = 0.0614 or 6.14%! BWs Effective Annual Interest Rate
79.
3.79 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd I Conv 6 ENTER ↓ ↓ 4 ENTER ↑ CPT 2nd QUIT Converting to an EAR Source: Courtesy of Texas Instruments
80.
3.80 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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 – 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
81.
3.81 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © 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
82.
3.82 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. End of Year Payment Interest Principal Ending Balance 0 — — — $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
83.
3.83 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The result indicates that a $10,000 loan that costs 12% annually for 5 years and will be completely paid off at that time will require $2,774.10 annual payments. N I/Y PV PMT FV Inputs Compute 5 12 10,000 0 –2774.10 Solving for the Payment
84.
3.84 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd Amort 1 ENTER 1 ENTER Results: BAL = 8,425.90* ↓ PRN = –1,574.10* ↓ INT = –1,200.00* ↓ Year 1 information only *Note: Compare to 3-82 Using the Amortization Functions of the Calculator Source: Courtesy of Texas Instruments
85.
3.85 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd Amort 2 ENTER 2 ENTER Results: BAL = 6,662.91* ↓ PRN = –1,763.99* ↓ INT = –1,011.11* ↓ Year 2 information only *Note: Compare to 3-82 Using the Amortization Functions of the Calculator Source: Courtesy of Texas Instruments
86.
3.86 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Press: 2nd Amort 1 ENTER 5 ENTER Results: BAL = 0.00 ↓ PRN = – 10,000.00 ↓ INT = –3,870.49 ↓ Entire 5 Years of loan information (see the total line of 3-82) Using the Amortization Functions of the Calculator Source: Courtesy of Texas Instruments
87.
3.87 Van Horne
and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the day-to-day activities of the firm. 1. Determine Interest Expense – Interest expenses may reduce taxable income of the firm. Usefulness of Amortization
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