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

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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

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Future Value of 100
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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

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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

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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

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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

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Present Value of 100
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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

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PV Decreases If

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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Present Value Irregular Flow
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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