財(cái)務(wù)管理英文課件：C3-The Time Value of Money

1、3.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 3.2 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1.Understand

2、 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 amou

3、nt 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 f

4、actor 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 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education L

5、imited 2009. Created by Gregory Kuhlemeyer. The Interest Rate Simple Interest Compound Interest Amortizing a Loan Compounding More Than Once per Year 3.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Obviou

6、sly, . You already recognize that there is ! Which would you prefer or ? 3.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. allows you the opportunity to postpone consumption and earn . Why is such an import

7、ant element in your decision? 3.6 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Interest paid (earned) on

8、 only the original amount, or principal, borrowed (lent). 3.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. SI = P0(i)(n) SI:Simple Interest P0:Deposit today (t=0) i:Interest Rate per Period n:Number of Tim

9、e Periods 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) = Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated int

10、erest at the end of the 2nd year? 3.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = P0 + SI = $1,000 + $140 = is the value at some future time of a present amount of money, or a series of payments, evalua

11、ted at a given interest rate. What is the () of the deposit? 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! is t

12、he current value of a future amount of money, or a series of payments, evaluated at a given interest rate. What is the () of the previous problem? 3.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 5000 1

13、0000 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 Future Value (U.S. Dollars) 3.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009.

14、 Created by Gregory Kuhlemeyer. Assume that you deposit at a compound interest rate of 7% for . 0 1 7% 3.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = (1 + i)1 = (1.07) = Compound Interest You earned $

15、70 interest on your $1,000 deposit over the first year. This is the same amount of interest you would earn under simple interest. 3.14 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = (1 + i)1 = (1.07) = = F

16、V1 (1 + i)1 = (1 + i)(1 + i) = (1.07)(1.07) = (1 + i)2 = (1.07)2 = You earned an EXTRA in Year 2 with compound over simple interest. 3.15 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = P0(1 + i)1 = P0(1 +

17、i)2 General Formula: = P0 (1 + i)n or = P0 ( i,n復(fù)利終值系數(shù)) etc. 3.16 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. i,n is found on Table I at the end of the book. Period6%7%8% 11.0601.0701.080 21.1241.1451.166

18、 31.1911.2251.260 41.2621.3111.360 51.3381.4031.469 3.17 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = $1,000 ( 7%,2) = $1,000 (1.145) = Due to Rounding Period6%7%8% 11.0601.0701.080 21.1241.1451.166 31.1

19、911.2251.260 41.2621.3111.360 51.3381.4031.469 3.18 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 today will become at a compound annual interest rate of

20、10% for . 0 1 2 3 4 10% 3.19 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Calculation based on Table I: = $10,000 ( 10%, 5) = $10,000 (1.611) = Due to Rounding Calculation based on general formula: = P0 (1

21、 + i)n = $10,000 (1 + 0.10)5 = Please look at case on p46 question. 3.20 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. We will use the Quick! How long does it take to double $5,000 at a compound rate of 12%

22、 per year (approx.)? 3.21 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Approx. Years to Double = / i% / 12% = Actual Time is 6.12 Years Quick! How long does it take to double $5,000 at a compound rate of 1

23、2% per year (approx.)? 3.22 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Assume that you need in Lets examine the process to determine how much you need to deposit today at a discount rate of 7% compounded

24、 annually. 0 1 7% PV1 3.23 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = / (1 + i)2 = / (1.07)2 = / (1 + i)2 = 0 1 7% 3.24 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pear

25、son Education Limited 2009. Created by Gregory Kuhlemeyer. = / (1 + i)1 = / (1 + i)2 General Formula: = / (1 + i)n or = ( i,n) etc. 3.25 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. i,n is found on Table I

26、I 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 3.26 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = (PVIF7%,2)

27、= (.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 3.27 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller

28、 wants to know how large of a deposit to make so that the money will grow to in at a discount rate of 10%. 0 1 2 3 4 10% 3.28 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Calculation based on general formu

29、la: = / (1 + i)n = / (1 + 0.10)5 = Calculation based on Table I: = ( 10%, 5) = (0.621) = Due to Rounding 3.29 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. How to calculate the unknown interest? P49 How to

30、calculate the unknown number of compounding periods? P50 3.30 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. : Payments or receipts occur at the end of each period. : Payments or receipts occur at the beginn

31、ing of each period. Perpetual represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. 3.31 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Student Loan Pa

32、yments Car Loan Payments Insurance Premiums Mortgage Payments Retirement Savings 3.32 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) of Period 1 of Period 2 Today Ca

33、sh Flows Each 1 Period Apart of Period 3 3.33 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) of Period 1 of Period 2 Today Cash Flows Each 1 Period Apart of Period 3 3.34

34、 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = 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+1 R = Periodic Cash Flow Cash flows occur at the end of the period i% . . . 3.35 Van Horn

35、e and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. uFVA=A+A(1+i)+A(1+i)2+A(1+i)3 + -+ A(1+i)n-2 + A(1+i)n-1 then： i i AFVA n 1)1 ( 年金終值系數(shù)年金終值系數(shù) FVIFA(i,n) 3.36 Van Horne and Wachowicz, Fundamentals of Financial Manageme

36、nt, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0 = $1,145 + $1,070 + $1,000 = $1,000 $1,000 $1,000 0 1 2 4 7% $1,070 $1,145 Cash flows occur at the end of the period 3.37 Van Horne and Wachowicz, Fundamentals of Financia

37、l 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 of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the of the last cash flow period

38、. 3.38 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R (FVIFAi%,n) = $1,000 (FVIFA7%,3) = $1,000 (3.215) = Period6%7%8% 11.0001.0001.000 22.0602.0702.080 33.1843.2153.246 44.3754.4404.506 55.6375.7515.867

39、 3.39 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R(1 + i)n + R(1 + i)n-1 + . + R(1 + i)2 + R(1 + i)1 = (1 + i) R R R R R 0 1 2 3 n i% . . . Cash flows occur at the beginning of the period 3.40 Van Horn

40、e and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1 = $1,225 + $1,145 + $1,070 = $1,000 $1,000 $1,000 $1,070 0 1 2 4 7% $1,225 $1,145 Cash flows occur at the beginning of t

41、he period 3.41 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R (FVIFAi%,n)(1 + i) = $1,000 (FVIFA7%,3)(1.07) = $1,000 (3.215)(1.07) = Period6%7%8% 11.0001.0001.000 22.0602.0702.080 33.1843.2153.246 44.375

42、4.4404.506 55.6375.7515.867 3.42 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R/(1 + i)1 + R/(1 + i)2 + . + R/(1 + i)n R R R 0 1 2 n+1 R = Periodic Cash Flow i% . . . Cash flows occur at the end of the p

43、eriod 3.43 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. nn i A i A i A i APVA )1 ( 1 )1 ( 1 )1 ( 1 )1 ( 1 12 i i APVA n )1/(11 即： 年金現(xiàn)值系數(shù)年金現(xiàn)值系數(shù) ,PVIFA(i,n) 3.44 Van Horne and Wachowicz, Fundamentals of Fina

44、ncial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = $1,000/(1.07)1 + $1,000/(1.07)2 + $1,000/(1.07)3 = $934.58 + $873.44 + $816.30 = $1,000 $1,000 $1,000 0 1 2 4 7% $934.58 $873.44 $816.30 Cash flows occur at the end of the period 3.45 Van Horne and Wacho

45、wicz, 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 of the first cash flow period, whereas the future value of an annuity due can be viewed as occurring at

46、the of the first cash flow period. 3.46 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R (PVIFAi%,n) = $1,000 (PVIFA7%,3) = $1,000 (2.624) = Period6%7%8% 10.9430.9350.926 21.8331.8081.783 32.6732.6242.577

47、43.4653.3873.312 54.2124.1003.993 3.47 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. How about the FV & PV OF the Perpetuity? Fv: NONE PV: P= A i 3.48 Van Horne and Wachowicz, Fundamentals of Financial Mana

48、gement, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R/(1 + i)0 + R/(1 + i)1 + . + R/(1 + i)n1 = (1 + i) R R R R 0 1 2 n R: Periodic Cash Flow i% . . . Cash flows occur at the beginning of the period 3.49 Van Horne and Wachowicz, Fundamentals of Financial Management

49、, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $1,000.00 $1,000 $1,000 0 1 2 4 = 7% $ 934.58 $ 873.44 Cash flows occur at the beginning of the period 3.50 Van Horne and Wachowicz, Fundamentals of Financial Managemen

50、t, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. = R (PVIFAi%,n)(1 + i) = $1,000 (PVIFA7%,3)(1.07) = $1,000 (2.624)(1.07) = Period6%7%8% 10.9430.9350.926 21.8331.8081.783 32.6732.6242.577 43.4653.3873.312 54.2124.1003.993 3.51 Van Horne and Wachowicz, Fundamentals of F

51、inancial 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 m

52、ixed flow 6. Solve the problem 7. Check with financial calculator (optional) 3.52 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 at a discou

53、nt rate of . 0 1 2 3 4 3.53 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1. Solve a “” by discounting each back to t=0. 2. Solve a “” by first breaking problem into groups of annuity streams and any single

54、 cash flow groups. Then discount each back to t=0. 3.54 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 10% 3.55 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson

55、Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 10% $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 3.56 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearso

56、n Education Limited 2009. Created by Gregory Kuhlemeyer. 0 1 2 3 4 equals 0 1 2 0 1 2 3 4 5 3.57 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. General Formula: FVn= (1 + i/m)mn n: Number of Years m: Compoun

57、ding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n : PV of the Cash Flow today 3.58 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Julie Miller has to invest for 2 Years at an annua

58、l interest rate of 12%. Annual FV2 = (1 + 0.12/1)(1)(2) = Semi FV2 = (1 + 0.12/2)(2)(2) = 3.59 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Qrtly FV2= (1 + 0.12/4)(4)(2) = Monthly FV2= (1 + 0.12/12)(12)(2) = Daily FV2= (1 + 0.12/365)(365)(2) = 3.60 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Effe