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Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less...

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Time Value of Money Introduction
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Page 1: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Time Value of MoneyIntroduction

Page 2: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

TVM Preferences

• More vs. Less

• Sooner vs. Later

• More Now vs. Less Later

• Less Now vs. More Later ????

Page 3: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

TVM Questions

• What will my investment grow to?

• How much do I need today?

• How fast must my investment grow?

• How long will it take?

Page 4: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compare and Contrast

1970 2011

Cost of a first-class stamp:  $ 0.06 $ 0.44

Cost of a gallon of gas:  $ 0.36 $ 2.98

Cost of a dozen eggs:  $ 0.62 $ 2.20

Cost of a gallon of Milk:  $ 1.15 $ 3.69

TVM

4.98%

5.29%

3.14%

2.88%

Page 5: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

TVM Basic Concepts

• Simple vs. Compound Interest

Simple Interest = interest earned only on principal (amount loaned)

Compound Interest = interest earned on principal and any unpaid interest earned in an earlier time period

Page 6: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Simple Interest Calculation

PVn*i*PV FV

Principal

Periods x Rate Interest x Principal ValueFuture

Page 7: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Interest Example

• Principal $1,000• Interest Rate 10%• Term 5 years

Page 8: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Interest Example

FV = (1,000 x .10 x 5) + 1,000

FV = 500 +1,000

FV = 1,500

Page 9: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Simple Interest Example

• Principal $1,000• Total Interest 500• Ending Balance $1,500

Page 10: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compound Interest Calculation

n

1-n

1 Periodsi

n

1Periods

i) (1 *PV FV

Principal

Rate Interest * Interest

Rate Interest * Principal ValueFuture

Page 11: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compound Interest Example

611,1

1.611 x 1,000 FV

(1.10) x 1000 FV

.10) (1 x 1,000 FV

5

5

FV

Page 12: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compound Interest Example

• Principal $1,000• Total Interest Rate 611• Ending Balance $1,611

Page 13: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Time Value of Money

Page 14: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Calculator Tips• Set Calculator to 4 decimal points• Set P/Yr to 1 and do not change• Clear calculator before calculation• Use recommended format• Learn to use special features• Read carefully• Know the concepts of TVM

Page 15: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

TVM Concepts• Use a time line• Use + or - to indicate cash flow• Periodic Cash flows can be at

Beginning or End of Period• Calculators use Percentages• Excel uses decimals

Page 16: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Lump Sum vs. Periodic Pmts• Lump Sum

–Single Payment–At time zero–Present ValueOR–Single Payment–At end of time–Future Value

• Periodic Payment–Ordinary Annuity

• Pmt at end of periods• For life of investment

–Annuity Due• Pmt at beg. of periods• For life of investment

–PMT

Page 17: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuities

• Must be–Equal Amounts–Occurring in every compounding

period–Ordinary Annuity – End of Period–Annuity Due – Beginning of Period

Page 18: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuity?

01 1002 1003 1004 1005 100

Page 19: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuity?

0 1001 1002 1003 1004 1005

Page 20: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuity?

0 10012 10034 1005

Page 21: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuity?

01 1002 2003 3004 4005 500

Page 22: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Lump Sum & Periodic Payment

• Combination–Single Payment–With periodic payments for life of

investment–PV & PMT

Page 23: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Recommended StructureFuture ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 24: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

If you invest $1,000 in a savings account earning 10% compounded annually, how much will you have after 5 years?

Page 25: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value ?Present Value (1,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 26: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value 1,610.51 Present Value (1,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 27: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

If you invest $10,000 in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 50 years?

Page 28: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 29: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value ?Present Value (10,000.00) PaymentAnnual Rate 12.00%Years 50Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 30: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value

Future Value 2,890,021.90 Present Value (10,000.00) PaymentAnnual Rate 12.00%Years 50Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 31: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

If you invest $10,000 at the end of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

Page 32: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 33: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value ?Present ValuePayment (10,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 34: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value 63,528.47 Present ValuePayment (10,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 35: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

If you invest $10,000 at the beginning of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

Page 36: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 37: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value ?Present ValuePayment (10,000.00) Annual Rate 12.00%Years 5Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 38: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value 71,151.89 Present ValuePayment (10,000.00) Annual Rate 12.00%Years 5Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 39: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Ordinary Annuity

Time Payment Return FV

0

1 10,000 12% / 4 yrs 15,735.19

2 10,000 12% / 3 yrs 14,049.28

3 10,000 12% / 2 yrs 12,544.00

4 10,000 12% / 1 yr 11,200.00

5 10,000 12% / 0 yrs 10,000.00

Total 63,528.47

Page 40: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annuity Due

Time Payment Return FV

0 10,000 12% / 5 yrs 17623.42

1 10,000 12% / 4 yrs 15,735.19

2 10,000 12% / 3 yrs 14,049.28

3 10,000 12% / 2 yrs 12,544.00

4 10,000 12% / 1 yr 11,200.00

5

Total 71,151.89

Page 41: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of a Combination

If you invest $10,000 today and $1,000 at the end of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?

Page 42: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of a Combination

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 43: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value

Future Value ?Present Value (10,000.00) Payment (1,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 44: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value

Future Value 23,976.26 Present Value (10,000.00) Payment (1,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 45: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Combination Investment

Time Payment Return FV

0 10,000 12% / 5 yrs 17,623.42

1 1,000 12% / 4 yrs 1,573.52

2 1,000 12% / 3 yrs 1,404.93

3 1,000 12% / 2 yrs 1,254.40

4 1,000 12% / 1 yr 1,120.00

5 1,000 12% / 0 yrs 1,000.00

Total 23,976.26

Page 46: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

TVM can also solve for the rate of return required for a PV to reach a FV in n years.

Page 47: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

What rate of return is required for $10,000 to grow to $16,000 in 5 years?

Page 48: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 49: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 16,000.00 Present Value (10,000.00) PaymentAnnual Rate ?Years 5Beg / EndCompounding PeriodsRate / Period

Page 50: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 16,000.00 Present Value (10,000.00) PaymentAnnual Rate 9.86%Years 5Beg / EndCompounding PeriodsRate / Period

Page 51: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

If you invest $2,000 at the end of each year for 5 years, what rate of return must your investment earn for you to have $16,000 at the end of that period?

Page 52: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 53: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 16,000.00 Present ValuePayment (2,000.00) Annual Rate ?Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 54: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 16,000.00 Present ValuePayment (2,000.00) Annual Rate 23.69%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 55: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

If you invest $10,000 today and $500 at the end of each year for the next 5 years, what rate of return must you earn to have $16,000 at the end of that period?

Page 56: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 57: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 16,000.00 Present Value (10,000.00) Payment (500.00) Annual Rate ?Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 58: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 16,000.00 Present Value (10,000.00) Payment (500.00) Annual Rate 5.71%Years 5Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 59: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

TVM can also solve for the holding period required for a PV, a series of Payments or a combination of PV and Payments to reach a FV given a specific rate of return

Page 60: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

How long will it take for a $10,000 investment to grow to $24,000 if it earns 11.25% compounded annually?

Page 61: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 62: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

Future Value 24,000.00 Present Value (10,000.00) PaymentAnnual Rate 11.25%Years ?Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 63: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

Future Value 24,000.00 Present Value (10,000.00) PaymentAnnual RateYears 8.21Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 64: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

If you deposit $3,000 at the beginning of each year in a savings account earning 9.75%, how long will it take for you to save for a $20,000 down payment for a house?

Page 65: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 66: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of PeriodsFuture Value 20,000.00 Present ValuePayment (3,000.00) Annual Rate 9.75%Years ?Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 67: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

Future Value 20,000.00 Present ValuePayment (3,000.00) Annual Rate 9.75%Years 5Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 68: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value

TVM can also solve for the price you would pay for a FV, a series of Payments, or a combination of a series of Payments and a FV given a specific rate of return and holding period.

Page 69: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Future Amount

What would you pay for the right to collect $8,000 in 7 years, if your required return is 8.75%?

Page 70: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 71: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Future Amount

Future Value 8,000.00 Present Value ?PaymentAnnual Rate 8.75%Years 7Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 72: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Future Amount

Future Value 8,000.00 Present Value (4,447.18) PaymentAnnual Rate 8.75%Years 7Beg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 73: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Stop

Page 74: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of Periodic Payments

What would you pay for the right to collect $8,000 at the beginning of each year for 7 years, if your required return is 8.75%?

Page 75: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 76: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of Periodic Payment

Future ValuePresent Value ?Payment 8,000.00 Annual Rate 8.75%Years 7Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 77: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of Periodic Payment

Future ValuePresent Value (44,156.42) Payment 8,000.00 Annual Rate 8.75%Years 7Beg / End BegCompounding PeriodsRate / PeriodYears * Periods

Page 78: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Combination

What would you pay for the right to collect $800 at the end of each year for 7 years and an additional $10,000 at the end of the period, if your required return is 7.25%?

Page 79: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 80: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Combination

Future Value 10,000.00 Present Value ?Payment 800.00 Annual Rate 7.25%Years 7Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 81: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Present Value of a Combination

Future Value 10,000.00 Present Value (10,400.70) Payment 800.00 Annual Rate 7.25%Years 7Beg / End EndCompounding PeriodsRate / PeriodYears * Periods

Page 82: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Time Value of Money

Compounding Periods Shorter than One Year

Page 83: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compounding Periods• Cash Flows are often more

frequent than annually–Monthly, quarterly, semi-annually

• If Compound periods < annual–Effective Interest Rate is higher–FV is higher and PV is lower

Page 84: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Compound Interest Formula with Compounding Periods less

than 1 Year

mn*

m

i1*PVFV

Where m = the number of compounding periods within the year.

Page 85: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Adjustments for Compounding Periods < Annual

• Compounding Periods = m• Divide Annual rate by m

i/m• Multiply Years by m

n x m• Input i/m for I/Y• Input (n x m) for N

Page 86: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

If you invest $6,000 in a savings account earning 10% compounded quarterly, how much will you have after 5 years?

Page 87: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 88: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value ?Present Value (6,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding Periods 4Rate / Period 2.50%Years * Periods 20

Page 89: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value $9,831.70Present Value (6,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding Periods 4Rate / Period 2.50%Years * Periods 20

Page 90: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

If you invest $1,000 in a savings account earning 10% compounded daily, how much will you have after 5 years?

Page 91: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 92: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value ?Present Value (1,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding Periods 365Rate / Period 0.0274%Years * Periods 1,825

Page 93: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of Lump Sum

Future Value $1,648.61Present Value (1,000.00) PaymentAnnual Rate 10.00%Years 5Beg / EndCompounding Periods 365Rate / Period 0.0274%Years * Periods 1,825

Page 94: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

If you invest $1,000 at the end of each month in a mutual fund that is expected to earn a 12% after-tax return, how much will you have at the end of 5 years?

Page 95: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 96: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value ?Present ValuePayment (1,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding Periods 12Rate / Period 1.00%Years * Periods 60

Page 97: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value $81,669.67Present ValuePayment (1,000.00) Annual Rate 12.00%Years 5Beg / End EndCompounding Periods 12Rate / Period 1.00%Years * Periods 60

Page 98: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

If you invest $1,000 at the beginning of each month in a mutual fund that is expected to earn a 12% after-tax return, how much will you have at the end of 5 years?

Page 99: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 100: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value ?Present ValuePayment (1,000.00) Annual Rate 12.00%Years 5Beg / End BegCompounding Periods 12Rate / Period 1.00%Years * Periods 60

Page 101: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future Value of an Annuity

Future Value $82,486.37Present ValuePayment (1,000.00) Annual Rate 12.00%Years 5Beg / End BegCompounding Periods 12Rate / Period 1.00%Years * Periods 60

Page 102: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

If you invest $2,000 at the end of each quarter for 5 years, what rate of return must your investment earn for you to have $60,000 at the end of that period?

Page 103: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 104: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 60,000.00 Present ValuePayment (2,000.00) Annual Rate ?Years 5Beg / End EndCompounding Periods 4Rate / Period ?Years * Periods 20

Page 105: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 60,000.00 Present ValuePayment (2,000.00) Annual Rate ?Years 5Beg / End EndCompounding Periods 4Rate / Period 4.07%Years * Periods 20

Page 106: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

Future Value 60,000.00 Present ValuePayment (2,000.00) Annual Rate 16.29%Years 5Beg / End EndCompounding Periods 4Rate / Period 4.07%Years * Periods 20

Page 107: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of Return

If you invest $10,000 today and $500 at the end of each month for the next 5 years, what rate of return must you earn to have $60,000 at the end of that period?

Page 108: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 109: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 60,000.00 Present Value (10,000.00) Payment (500.00) Annual Rate ?Years 5Beg / End EndCompounding Periods 12Rate / PeriodYears * Periods 60

Page 110: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 60,000.00 Present Value (10,000.00) Payment (500.00) Annual Rate ?Years 5Beg / End EndCompounding Periods 12Rate / Period 1.04%Years * Periods 60

Page 111: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Annual Rate of ReturnFuture Value 60,000.00 Present Value (10,000.00) Payment (500.00) Annual Rate 12.50%Years 5Beg / End EndCompounding Periods 12Rate / Period 1.04%Years * Periods 60

Page 112: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of Periods

If you deposit $300 at the beginning of each month in a savings account earning 9.75%, how long will it take for you to save for a $20,000 down payment for a house?

Page 113: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Future ValuePresent ValuePaymentAnnual RateYearsBeg / EndCompounding PeriodsRate / PeriodYears * Periods

Page 114: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of PeriodsFuture Value 20,000.00 Present ValuePayment (300.00) Annual Rate 9.75%Years ?Beg / End BegCompounding Periods 12Rate / Period 0.81%Years * Periods ?

Page 115: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of PeriodsFuture Value 20,000.00 Present ValuePayment (300.00) Annual Rate 9.75%Years ?Beg / End BegCompounding Periods 12Rate / Period 0.81%Years * Periods 53

Page 116: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Number of PeriodsFuture Value 20,000.00 Present ValuePayment (300.00) Annual Rate 9.75%Years 4.43Beg / End BegCompounding Periods 12Rate / Period 0.81%Years * Periods 53

Page 117: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

• How do you calculate Present Value when your required return is 9.0% and you expect to receive the following cash flows:

Year 1 2,000 Year 2 3,000 Year 5 1,000

Page 118: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

• Alternative One – The Hard Way

1. Draw a Time Line

2. Calculate the PV of each cash flow

3. Total the Present Values

Page 119: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

CF 1FV 2,000I/Y 9.00%N 1PV (1,834.86)

Page 120: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

CF 1 CF 2FV 2,000 3,000I/Y 9.00% 9.00%N 1 2PV (1,834.86) (2,525.04)

Page 121: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

CF 1 CF 2 CF 3FV 2,000 3,000 1,000I/Y 9.00% 9.00% 9.00%N 1 2 5PV (1,834.86) (2,525.04) (649.93)

Total PV (5,009.83)

Page 122: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

• Alternative Two – Use the CF Register

1. Draw Time Line

2. Input Cash Flows into CF Register

3. Go to NPV Register1. Input Rate of Return

2. Compute NPV

Page 123: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 1 – Alternative Two

1. Draw Time Line

2. Push CF button

3. Clear CF register

2nd CLR Work

4. Input Cash Flows

Page 124: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Cash Flow Register

• Inputs– CF0 = Investment, Price, Cost at Time 0

We are solving for PV so CF0 should be 0

Since CF0 already = 0, – C01 = Cash Flow at the end of Period 1

– F01 = Frequency of C01

The number of times that C01 occurred consecutively

Page 125: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 1

1. Draw Time Line

2. Clear the CF Register

3. Input Cash Flowsa. CF0 = 0, b. C01 = 2,000; F01 = 1, c. C02 = 3,000; F02 =1, d. C03 = 0; F03 = 2, e. C04 = 1,000; F04 = 1,

Page 126: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 1

1. Check Inputs

2. Go To NPV Register

3. Input I 9 ENTER,

4. CPT NPV = 5,009.83

Page 127: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 2

What would you be willing to pay for a real estate investment that has the following expected cash flows: Yr. 1 $500, Yrs. 2-6 $1,000, Yr. 7-10 $1,500, and Yr. 11 $30,000? Assume your required return for this type of investment is 17.0%.

Page 128: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 2

1. Draw Time Line

2. Input Cash Flowsa. CF0 = 0

b. C01 = 500; F01 = 1c. C02 = 1,000; F02 = 5d. C03 = 1,500; F03 = 4e. C04 = 30,000; F04 = 1

Page 129: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 2

3. Check your Inputs

4. Go to “NPV” Register

1. Enter I = 17.0;

2. Press “CPT”

NPV = ?

Page 130: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows Example 2

NPV = 10,100.25

Page 131: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

• The CF Register can also be used to find the rate of return associated with uneven cash flows.

• This cannot be done easily any other way.

Page 132: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Uneven Cash Flows

• Inputs–CF Register Steps are the same–Go to IRR Register

CPT IRR

IRR = the Internal Rate of Return

IRR = the rate of return on the investment

Page 133: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Effective Interest Rate Calculation

Page 134: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Effective Interest Rate Calculation

The annual rate of return actually earned when

compounding or payment periods are less than 1 year.

Page 135: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Effective Interest Rate

• Nominal rate = i –The nominal rate is the rate

“named” in the information.–“The credit card rate is for 18.0%

compounded monthly.”• 18.0% is the nominal rate

Page 136: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR Calculations

What is the Effective Interest Rate for a credit card with an 18% nominal interest rate if the card is not paid off each month?

Page 137: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

Effective Interest Rate with Compounding Periods < 1 Year

100*1m

i1Rate Int. Eff.

m

Where m = the number of compounding periods within the year.

Page 138: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR Calculations

100*112

.181

12

EIR

Page 139: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR Calculations

100*1015.1 12 EIR

Page 140: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR Calculations

100*11956.1 EIR

Page 141: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR Calculations

%56.19EIR

Page 142: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

EIR CALCULATIONS

Use “I Conv” Register for easy Effective Interest Rate calculations.

Page 143: Time Value of Money Introduction. TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????

I Conv Register

• Steps1. 2nd I Conv

2. Input Nominal Rate, ENTER

3. Arrow Down Twice

4. Input C/Y • (Compounding Periods per Year)

5. Arrow Up

6. CPT EFF (Effective Interest Rate)


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