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

0
1
PV
FV
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FUNDAMENTAL TVM EQUATIONS

• Present and Future Values of a Single Cash Flow
• PV FV ? PVIFr,t where PVIFr,t 1/(1 r)t
  (1 r) - t
• FV PV ? FVIFr,t where FVIFr,t (1 r)t
• Example
• Your lottery ticket hits for 1 million, payable
  in one year. You need the cash now. If the going
  rate of interest is 10, what is the most you can
  sell it for?

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TIPS ON USING THE HP 10B

• 1. Always clear the registers before working a
  problem.
• gold
• CLEAR ALL
• 2. Use at least 6 decimal places in TV problems.
• gold
• DISPLAY
• 6
• 3. Set the number of payments to 1 payment per
  year.
• 1
• 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 ? -100.001
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TVM PART 1 SUMMARY

• Fundamental Theorem of Valuation
• V f(size, timing, risk) of future cash flows
• Economic theory (and behavioral psychology)
  transforms a purely mathematical relationship
  into a financial relationship.
• The fundamental theorem of valuation requires
  knowledge of all three variables.
• The fundamental theorem allows us to value any
  asset on the basis of its future cash flows.

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Problem 5-9

• Youre trying to buy a new 120,000 Ferrari. You
  have 40,000 today that can be invested at 4
  percent annually. How long will it take before
  you have enough to buy the car?

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Problem 5-10

• Imprudential, Inc. has an unfunded pension
  liability of 425 million that must be paid in 20
  years. If the relevant discount rate is 8, what
  is the present value of this liability?

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Problem 5-17

• Youre still committed to owning to a 120,000
  Ferrari. If you can earn 9 percent, and you want
  to buy the car in 10 years, how much must you
  invest today?