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# Chapter 5 – Important Stuff - PowerPoint PPT Presentation

Chapter 5 – Important Stuff. Mechanics of compounding / discounting PV, FV, PMT – lump sums and annuities Relationships – time, interest rates, etc Calculations: PV’s, FV’s, loan payments, interest rates. Time Value of Money (TVM).

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• Mechanics of compounding / discounting

• PV, FV, PMT – lump sums and annuities

• Relationships – time, interest rates, etc

• Calculations: PV’s, FV’s, loan payments, interest rates

• 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 today’s value

• Problem types: monthly loan payments, growth of savings account; time to goal

• PV - Present value

• FV - Future value

• PMT - Amount of the payment

• N - Number of periods (years?)

• I/Y - Interest rate per period

• 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

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

YearBeginInterestFV

1 \$100.00 \$6.00 \$106.00

2 106.00 6.36 112.36

3 112.36 6.74 119.10

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

[email protected]%@6%@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

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 @ 6%

• From table: FV6%, 3 yr. = 500 *1.191 = 595.50

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

• 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%

Time to Double Your Money“Rule of 72”

• Enter 100 PV; 200 FV, 10 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

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

[ 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

@2%@5%@10%

Year 1 .980 .952 .909

Year 2 .961 .907 .826

Year 3 .942 .864 .751

Year 10 .820 .614 .386

Keystrokes\$100 @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

PV Decreases If

• Number of compounding periods (time) increases,

• The discount rate increases,

And/or

3. Compounding frequency increases

• 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.

End of

PMTFVIF \$

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

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

Amount we must put in bank today to

withdraw \$500 at end of next three years, earn 6% and have 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

• 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

• 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

CompoundingOne Year10 Years

Annually \$110.00 \$259.37

Semiannually 110.25 265.33

Quarterly 110.38 268.51

Monthly 110.47 270.70

• 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

TotalTo IntTo PrinEnd 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

• \$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 PMT=265.71

• 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

• 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

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

• Future value of a single payment

• Present value for the same

• Future value of an annuity

• Annuity’s present value

• Loans including monthly payments, effective rates and time to repay

• Present value of a perpetuity