The time value of money
Sponsored Links
This presentation is the property of its rightful owner.
1 / 53

The Time Value of Money PowerPoint PPT Presentation


  • 72 Views
  • Uploaded on
  • Presentation posted in: General

The Time Value of Money. Chapter 5. LEARNING OBJECTIVES. 1.   Explain the mechanics of compounding when invested. 2.  Present value and future value. 3.  Ordinary annuity and its future value. 4.  An ordinary annuity and an annuity due. 5.  Non-annual future or present value of a sum .

Download Presentation

The Time Value of Money

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


The Time Value of Money

Chapter 5


LEARNING OBJECTIVES

  • 1.  Explain the mechanics of compounding when invested.

  • 2.  Present value and future value.

  • 3.  Ordinary annuity and its future value.

  • 4.  An ordinary annuity and an annuity due.

  • 5.  Non-annual future or present value of a sum .

  • 6. Determine the present value of a perpetuity.


Power of time of value of money

  • History of Interest Rates

    $1000 ( 1 + .08)400 = ?


Power of time value of money

  • Money Angles: by Andrew Tobias.

    1.Chessboard with the King

    2.Manhattan


Terms

  • Compound Interest

  • Future value and Present Value

  • Annuities

  • Annuities Due

  • Amortized Loans

  • Compound Interest with Non-annual Periods

  • Present Value of an Uneven Stream·

  • Perpetuities


COMPOUND INTEREST

  • FV1=PV (1+i) (5-1)

  • Where FV1=the future value of the investment at the end of one year

  • i=the annual interest (or discount) rate

  • PV=the present value, or original amount invested at the beginning of the first year


Future value

1.Simple compounding

2.Complex compounding


Future value


  • FV1=PV (1+i)

  • =$100(1+0.06)

  • =$100(1.06)

  • =$106


Compound twice a year


Compound four times a year


Compound 12 times a year


Compound 360 times a year


Continuous compounding


Illustration of Compound Interest Calculations

Year Beginning Value Interest Earned Ending Value

1 $100.00 $6.00 $106.00

2 106.00 6.36 112.36

3 112.36 6.74 119.10

4 119.10 7.15 126.25

5 126.25 7.57 133.82

6 133.82 8.03 141.85

7 141.85 8.51 150.36

8 150.36 9.02 159.38

9 159.38 9.57 168.95

10 168.95 10.13 179.08


Future value and future value interest factor


FVn=PV(FVIFi,n)


Table 5-2

FVIFi,n or the Compound Sum of $1

N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100

2 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210

3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331

4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464

5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611

6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772

7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949

8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.815 1.993 2.144

9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358

10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594

11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853

12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138

13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452

14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797

15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177


PV=$300, Vn=$774; i=9 % N= ?


PV=$100; FVn=$179.10; n=10 years. I= ?


PRESENT VALUE


FV10=$500, n=10, i=6 % PV = ?


(PVIF i, n)

  • present-value interest factor for I and n (PVIF i, n),

    (PVIF i, n) = 1/(1+i)


Present value

  • FV10 =$1,500

  • N= 10 years

  • discount rate= 8 %

  • PV=$1500(0.463)

    =$694.50


Table 5-3

PVIFi,n or the Present Value of $1

N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909

2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826

3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751

4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683

5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621

6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564

7 0.933 0.871 0.813 0.760 0.711 0.655 0.623 0.583 0.547 0.513

8 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424

9 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386


ANNUITIES

  • Annuity: equal annual cash flows.

  • Ordinary annuity: at the end of each period.

  • Annuity due: at the beginning of each eriod.


  • Table 5-4

  • Illustration of a Five-Year $500 Annuity Compounded at 6 percent

  • YEAR 0 1 2 3 4 5

  • DOLLAR DEPOSITS AT END OF YEAR 500 500 500 500 500

  • $500.00

    • 530.00

    • 562.00

    • 595.50

    • 631.00

  • Future value of the annuity$2,818.50


  • Ordinary annuity

    FVIFAk,n = [(1/k) ( (1+ k)n – 1)]


    Present value of an Annuity


    Table 5-6

    Illustration of a Five-Year $500 Annuity Discounted to the Present at 6 percent

    YEAR 0 1 2 3 4 5

    Dollars received at the 500 500 500 500 500

    the end of year $471.50

    445.00

    420.00

    396.00

    373.50

    PV annuity $2,106.00


    PVIFAK,n = (1/k) [( 1 – 1/(1+k)n]


    Table 5-7

    PVIFi,n or the Present Value of an Annuity of $1

    N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

    1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909

    2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736

    3 2.941 2.884 2.829 2.775 2.723 2.673 2.642 2.577 2.531 2.487

    4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170

    5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.003 3.890 3.791

    6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355

    7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868

    8 7.652 7.326 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335

    9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759

    10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145


    n=10 years, I=5 percent, and current PMT=$1,000

    PV= $1,000(7.722)

    = $7,722


    PMT

    Annuity: $5,000, n =5 years, i=8 percent, PMT:?

    $5,000 = PMT (3.993)

    $1,252.19=PMT


    AMORTIZED LOANS


    Loan Amortization Schedule Involving a $6,000 Loan at 15 Percent to Be Repaid in Four Years

    Year Annuity Interest Portion Repayment of Outstanding

    Of The Annuity1 The Principal Loan Balance

    Portion Of The After The An-

    Annuity2 nuity Payment

    1 $2,101.58 $900.00 $1,201.58 $4,798.42

    22,101.58 719.76 1,381.82 3,416.60

    3 2,101.58 512.49 1,589.09 1,827.51

    4 2,101.58 274.07 1,827.51


    ANNUITIES DUE

    • FVn (annuity due)=PMT(FVIFA I,n)(1+I) (5-10)

      FV5=$500(FVIFA5%,5)(1+0.06)

      =$500(5.637)(1.06)

      =$2,987.61

       from $2,106 to $2,232.36,

      PV=$500(PVIFA6%,5)(1+0.06)

      =$500(4.212)(1.06)

      =$2,232.36


    End year

    Loan payment

    (1)

    Beginning principal

    (2)

    payments

    End of year principal(5)

    [(2)-(4)]

    Interest(3)

    [0.1 × (2)]

    Principal(4)

    [(1) - (3)]

    1

    $1892.74

    $6000.00

    $600.00

    $1292.74

    $4707.26

    2

    $1892.74

    $4707.26

    $470.73

    $1422.01

    $3285.25

    3

    $1892.74

    $3285.25

    $328.53

    $1564.21

    $1721.04

    4

    $1892.74

    $1721.04

    $172.10

    $1720.64


    The Value of $100 Compounded at Various IntervalsFOR 1 YEAR AT i PERCENT

    I = 2% 5% 10% 15%

    Compounded annually $102.00 $105.00 $110.00 $115.00

    Compounded semiannually 102.01 105.06 110.25 115.56

    Compounded quarterly 102.02 105.09 110.38 115.87

    Compounded monthly 102.02 105.12 110.47 116.08

    Compounded weekly (52) 102.02 105.12 110.51 116.16

    Compounded daily (365) 102.02 105.13 110.52 116.18


    PRESENT VALUE OF AN UNEVEN STREAM

    YEAR CASH FLOW YEAR CASH FLOW

    1 $500 6 500

    2 200 7 500

    3 -400 8 500

    4 500 9 500

    5 500 10 500


    • Present value of $500 received at the end of one year

    • = $500(0.943) = $471.50

    • 2. Present value of $200 received at the end of tree years

    • = $200(0.890) = 178.00

    • 3. Present value of a $400 outflow at the end of three years

    • = -400(0.840) = -336.00

    • 4. (a) Value at the end of year 3 and a $500 annuity, years 4 through 10

    • = $500 (5.582) = $2,791.00

    • (b) Present value of $2,791.00 received at the end of year 3

    • = 2,791(0.840) = 2,344.44

    • 5. Total present value = $2,657.94


    Quiz 1

    Warm up Quiz.

    Terms:

    : n = 5, m = 4, I =12 percent, and PV =$100 solve for fv


    Quiz 2

    What is the present value of an investment involving $200 received at the end of years 1 through 4, a $300 cash outflow at the end of year 5 to 8, and $500 received at the end of years 9 through 10, given a 5 percent discount rate?


    Quiz 3

    • A 25 year-old graduate has his $50,000 salary a year. How much will he get when he reaches to 60 (35 years later)year-old with a value rate of 8%(annual compounding).

    • The graduate will have his $80,000 salary at age of 30. How much will he get when he reaches to his age of 60(30 years later) with the value rate of 8%(semi-annual compounding).


    Quiz 4

    • The graduate will have his $100,000 salary at age of 40. How much will he get when he reaches to his age of 60(20 years later) with the value rate of 12%(quarterly-annual compounding).

    • Compute the future value from 25-30/30-40/40-60 year old with the same rate and the compounding rate.


    PERPETUITIES

    $500 perpetuity discounted back to the present at 8 percent?

    PV = $500/0.08 = $6,250


    Power of time of value of money

    • History of Interest Rates

      $1000 ( 1 + .08)400 = ?


    Power of time value of money

    • Money Angles: by Andrew Tobias.

      Chessboard with the King

      Manhattan


  • Login