Title: Chapter 5 Important Stuff
1Chapter 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
2Time 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
3Financial Calculator Keys
- PV - Present value
- FV - Future value
- PMT - Amount of the payment
- N - Number of periods (years?)
- I/Y - Interest rate per period
4TI 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
5Calculator 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
6Compound 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
-
7Future 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
8Future 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
9Reading 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
10Future Value of 100
11FV 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
12FV 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
13Time 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
14Present 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
15Present 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
16Present 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
17Present Value of 100
18Keystrokes100 _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
19PV Decreases If
- Number of compounding periods (time) increases,
- The discount rate increases,
- And/or
- 3. Compounding frequency increases
20Annuities
- 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.
21FV 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
22Annuity 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
23Present 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
24PV of 5 Year 500 Annuity
25Nonannual 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
26Nonannual 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
27Compounding 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
28Amortizing 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
29600 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
30Calculate 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
31Perpetuities
- 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
32NPV 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
33Cash 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
34Present Value Irregular Flow
35Keystrokes 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