Chapter 5 Important Stuff

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Chapter 5 Important Stuff

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Financial Calculator Keys. PV - Present value. FV - Future value. PMT ... 8,000 car loan payable monthly over three years at 12%. What is your payment? ... – PowerPoint PPT presentation

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Title: Chapter 5 Important Stuff


1
Chapter 5 Important Stuff
  • Mechanics of compounding / discounting
  • PV, FV, PMT lump sums and annuities
  • Relationships time, interest rates, etc
  • Calculations PVs, FVs, loan payments, interest
    rates

2
Time Value of Money (TVM)
  • Time Value of Money relationship between value
    at two points in time
  • Today versus tomorrow today versus yesterday
  • Because an invested dollar can earn interest, its
    future value is greater than todays value
  • Problem types monthly loan payments, growth of
    savings account time to goal

3
Financial Calculator Keys
  • PV - Present value
  • FV - Future value
  • PMT - Amount of the payment
  • N - Number of periods (years?)
  • I/Y - Interest rate per period

4
TI Calculator ManualStrongly Suggested Readings
  • Getting Started page 6 and 7
  • Overview page 1-4, 1-10 and 1-20
  • Worksheets pages 2-14 and 2-15
  • TVM 3-1 to 3-9
  • Cash Flow - All

5
Calculator Tips
  • Decimals and Compounding Periods
  • 2nd (gray), Format (bottom row), 4, enter, CE/C
    (lower left) - hit twice
  • Compounding 2nd , I/Y, 1, enter, CE/C
    extremely important !!
  • Right arrow key fixes misteaks
  • One cash flow must be negative or error

6
Compound Interest _at_ 6
  • Year Begin Interest FV
  • 1 100.00 6.00 106.00
  • 2 106.00 6.36 112.36
  • 3 112.36 6.74 119.10

7
Future Value (FV)
  • Algebraically FVn PV (1 i)n
  • Underlies all TVM calculations
  • Keystrokes 100 /- PV 3 N 0 PMT
  • 6 I/Y CPT FV 119.10
  • One cash flow must be negative
  • Error 5 means you forgot a negative sign

8
Future Value Interest Factor
  • Year _at_2 _at_6 _at_10
  • 1.020 1.060 1.100
  • 1.040 1.124 1.210
  • 3 1.104 1.191 1.611
  • 10 1.219 1.791 2.594

9
Reading the Formulas and TablesFVn PV (1 i)n
  • Plain English The future value in period n is
    the present value (PV) times the quantity (i plus
    the interest rate) raised to the nth power where
    n equals the number of compounding periods.
  • Future value of 500 invested 3 yrs _at_ 6
  • From table FV6, 3 yr. 500 1.191 595.50

10
Future Value of 100
11
FV Can Be Increased By
  • 1. Increasing the length of time it is compounded
  • 2. Compounding at a higher rate
  • And/or
  • 3. Compounding more frequently

12
FV Other Keystrokes
  • How long for an investment to grow from 15,444
    to 20,000 if earn 9 when compounded annually?
    Must solve for N.
  • 15444 /- PV 20000 FV 0 PMT I/Y 9
  • CPT N 3 years
  • What rate earned if start at 15,444 and reach
    20,000 in 3 years? Solve for I/Y.
  • 15444 /- PV 20000 FV 0 PMT 3 N
  • CPT I/Y 9

13
Time to Double Your MoneyRule of 72
  • Enter 100 PV 200 FV, I/Y, solve for N or
  • Use Rule of 72 says number of years to double
    is approximately equal to 72 divided by the
    interest rate.
  • Doubling time 72
  • Interest Rate

14
Present Value (PV)
  • If I earn 10, how much must I deposit
  • today to have 100 in three years? 75.10
  • This is inverse compounding
  • Discount rate interest rate used to bring
    (discount) future money back to present
  • For lump sums (only) PV and FV are reciprocals

15
Present Value Formula
  • 1
  • PV FVn (1 i) n
  • PVIF and FVIF for lump sums only are reciprocals.
    For 5 over ten years
  • FVIF 1.629 1 / .614
  • PVIF .614 1 / 1.629

16
Present Value Interest Factor
  • _at_2 _at_5 _at_10
  • Year 1 .980 .952 .909
  • Year 2 .961 .907 .826
  • Year 3 .942 .864 .751
  • Year 10 .820 .614 .386

17
Present Value of 100
18
Keystrokes100 _at_5 for ten years
  • For PV /-100 FV 0 PMT 5 I/Y 10 N
  • CPT PV 61.39
  • For I/Y 100 FV 0 PMT /-61.39 PV
  • 10 N CPT I/Y 5
  • For N 100 FV /-61.39 PV 0 PMT
  • 5 I/Y CPT N 10 years

19
PV Decreases If
  • Number of compounding periods (time) increases,
  • The discount rate increases,
  • And/or
  • 3. Compounding frequency increases

20
Annuities
  • Series of equal dollar payments
  • Usually at the end of the year/period
  • If I deposit 100 in the bank each year starting
    a year from now, how much will I have at the end
    of three years if I earn 6? 318.36
  • We are solving for the FV of the series by
    summing FV of each payment.

21
FV of 100 Annuity _at_ 6
  • End of
  • PMT FVIF
  • Year 3 100 1.0000 100.00
  • Year 2 100 1.0600 106.00
  • Year 1 100 1.1236 112.36
  • 318.36
  • The payment at end Year 3 earns nothing

22
Annuity Keystrokes
  • What will I have if deposit 100 per year
    starting at the end of the year for three years
    and earn 6?
  • 0 PV 100/- PMT 3 N 6 I/Y
  • CPT FV 318.36
  • PV is zero - nothing in the bank today

23
Present Value of an Annuity
  • Amount we must put in bank today to
  • withdraw 500 at end of next three years
  • with nothing left at the end?
  • Present valuing each of three payments
  • Keystrokes 500/- PMT 0 FV 3 N
  • 6 I/Y CPT PV 1,336.51

24
PV of 5 Year 500 Annuity
25
Nonannual Compounding
  • Invest for ten years at 12 compounded quarterly.
    What are we really doing?
  • Investing for 40 periods (10 4) at 3 (12/4)
  • Make sure 2nd I/Y is set to 1.
  • Need to adjust rate per period downward which is
    offset by increase in N

26
Nonannual Compounding
  • FVn PV ( 1 i/m) m n
  • m number of compounding periods per year so per
    period rate is i/m
  • And m n is the number of years times the
    compounding frequency which adjusts to the rate
    per period

27
Compounding 100 _at_10
  • Compounding One Year 10 Years
  • Annually 110.00 259.37
  • Semiannually 110.25 265.33
  • Quarterly 110.38 268.51
  • Monthly 110.47 270.70

28
Amortizing Loans
  • Paid off in equal installments
  • Makes it an annuity
  • Payment pays interest first, remainder goes to
    principal (which declines)
  • 600 loan at 15 over four years with equal
    annual payments of 210.16

29
600 Loan Amortization
  • Total To Int To Prin End Bal
  • Year 1 210.16 90.00 120.16 479.84
  • Year 2 210.16 71.98 138.18 341.66
  • Year 3 210.16 51.25 158.91 182.75
  • Year 4 210.16 27.41 182.75 0

30
Calculate a Loan Payment
  • 8,000 car loan payable monthly over three years
    at 12. What is your payment?
  • How many monthly periods in 3 yrs? 36 N
  • Monthly rate? 12/12 1/mo I/Y
  • What is FV? Zero because loan paid out
  • 8000/- PV 0 FV 1.0 I/Y 36 N
  • CPT PMT265.71

31
Perpetuities
  • Equal payments that continue forever
  • Like Energizer Bunny and preferred stock
  • Present Value Payment Amount
  • Interest Rate
  • Preferred stock pays 8/yr, int rate- 10
  • Payment fixed at 8/ .10 80 market price

32
NPV IRR Uneven Cash Flows
  • Occur frequently in business problems
  • All we are doing is present valuing each cash
    flow, positive or negative
  • Need to switch to CF mode in calculator
  • Keystrokes in handout and on web page
  • Question on final but not FinCoach
  • Be sure to read 4-12 to 4-14 in manual and/or
    Table X in Appendix A of text

33
Cash Flow Time Line
  • Understanding time big problem
  • Remember number line from algebra
  • Visualize in picture form when each cash flow
    occurs by time period, amount and sign.
  • Time 0____1____2____3____4____5___?
  • Flows 200 300 50 ?
  • -100 0 0

34
Present Value Irregular Flow
35
Keystrokes You Should Know
  • Future value of a single payment
  • Present value for the same
  • Future value of an annuity
  • Annuitys present value
  • Loans including monthly payments, effective rates
    and time to repay
  • Present value of a perpetuity
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