TIME VALUE OF MONEY: THE UNIVERSAL TOOL

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TIME VALUE OF MONEYTHE UNIVERSAL TOOL
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TIME VALUE OF MONEY FUNDAMENTAL PRINCIPLES

• Opportunity Rates and Equilibrium Prices
• Risk, Return, and Value
• Time Lines and the Equivalence Theorem
• The Fundamental Time-Value Equations

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FUNDAMENTAL TVM EQUATIONS

• Present and Future Values of a Single Cash Flow
• Valuing a Series of Cash Flows
• Equal Payments - Ordinary Annuities, Annuities
  Due
• Unequal Payments
• Deferred Annuities
• Perpetuities

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TIPS ON USING THE HP 10B

• 1. Use at least 6 decimal places in TV problems.
• number
• gold
• ./,
• 2. Set annuity payments at beginning or end of
  period.
• gold
• beginning (or end)
• 3. Set frequency of payments (annually, monthly,
  etc.)
• number (check gold, clear all)
• gold
• P/YR

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TIME VALUE OF MONEY EXAMPLE

• Present Value of a Lump Sum (PV)

1
0
100
PV
Equation Approach PV 100 PVIF(10,1) PV
100 1/(1.10)1 PV 100 .9091 90.91
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 1, N 100, FV PV ? -90.91
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TIME VALUE OF MONEY EXAMPLE

• Future Value of a Lump Sum (FV)

1
0
FV
90.91
Equation Approach FV 90.91 FVIF(10,1) FV
90.91 (1.10)1 FV 90.91 1.10 100
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 1, N 90.91, PV FV ? -90.91
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TIME VALUE OF MONEY EXAMPLE

• Present Value of an Annuity (PVA)

0
1
2
3
100
100
100
PVA
Equation Approach PVA 100 PVIFA(10,3) PVA
100 1 - 1/(1.10)3/.10 PVA 100 2.4868
248.68
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 3, N 100, PMT PV ? -248.6851
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PVA EXAMPLE

• Youve just been notified that you hold the
  winning ticket in the Missouri lottery. The
  jackpot is 1 million. You are given the option
  of receiving 450,000 today, or 50,000 annually
  at the end of each of the next 20 years. Assume
  your opportunity rate is 10, and that taxes are
  not an issue. Which option should you take?

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TIME VALUE OF MONEY EXAMPLE

• Future Value of an Annuity (FVA)

0
1
2
3
100
100
100
PVA
Equation Approach FVA 100 FVIFA(10,3) FVA
100 (1.10)3 - 1/.10 FVA 100 3.31 331
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 3, N 100, PMT FV ? -331
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TVM APPLICATIONRETIREMENT PLANNING
Waldo is 35 and wishes to retire in 30 years. He
would like to make 25 100,000 withdrawals from
his IRA, the first at age 66. Waldo also needs to
accumulate enough money to put his four-year-old
daughter, Laura, through college. He believes
she will require 25,000 at the beginning of each
of her four years in college. Assume Waldo can
earn a 9 after-tax return on his invested
capital, and plans to make 30 equal annual
deposits, the first to occur one year from today.
How large must each deposit be for Waldo to
accomplish his goals?
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SOLVING COMPLEX TIME VALUE PROBLEMS

• MARTINS METHOD
• Step 1 Draw a timeline, detail the cash
  inflows and outflows
• Step 2 Choose a focal point on the timeline
• Step 3 Equate the inflows and outflows at
  the focal point solve for the unknown.

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TVM APPLICATION ANNUITIES

• First Security Insurance offers the following
  annuity to Wally, who is 25 years old. Pay the
  firm 1000 today, and the firm will pay him 1000
  (guaranteed) monthly for life, beginning at age
  65. Wally believes that his opportunity rate is
  approximately 10. Wally thinks the last payment
  he will collect will be at age 75.
• On a purely financial basis, should Wally
  purchase the annuity?
• What other factors should Wally consider in
  making his decision?

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TVM APPLICATIONRETIREMENT PLANNING

• Assume yesterday was your 40th birthday. You wish
  to accumulate enough money at age 55 in order to
  retire. Your after-tax opportunity rate is 8.
  (You plan to commence monthly withdrawals one
  month after reaching age 55.)
• How much must you accumulate if (a) you wish to
  draw 2000 monthly from the account, and (b) you
  expect to live to age 80?
• If you plan to start making equal monthly
  investments today, how much must you set aside
  each month? (Assume that the last investment will
  occur one month prior to the first withdrawal.)

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TVM SUMMARY