Intro to Time Value of Money

CFA® Exam: Level 1 / Quantitative Methods / Time Value of Money: Intro



Time Value of Money (TVM) Explained

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Present Value, Future Value



Time Value of Money (TVM) Explained

USD 100 is worth more today than in a year or two.

So USD 100 today > USD 100 in one year's time > USD 100 in two year's time, and so on...

interest rate = price of money

interest rate = real risk-free interest rate + inflation premium + default risk premium + liquidity premium + maturity premium



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Interpreting Interest Rates

Interest rates can be perceived as:

  • required rates of return what are the expected future profits from an investment?
  • discount rates what is the present value of a certain future amount?
  • opportunity costs what future profits do we forgo in favor of current consumption?

Present Value (PV) & Future Value (FV): Formulas


Formula for the future value:

\(FV_N=PV\times(1+r)^N\)

Formula for the present value:

\(PV=\frac{FV_N}{(1+r)^N}\)


Where:

\(FV_N\) – future value,

PV – present value,

r – periodic interest rate,

N – number of periods.




Characteristics of PV and FV

A number of relations characterize the present value and the future value:

  • The higher PV, the higher FV.
  • The higher FV, the higher PV.
  • The higher N, the higher FV.
  • The higher N, the lower PV.
  • The higher r, the higher FV.
  • The higher r, the lower PV.
  • The more frequent the compounding, the higher the FV.
  • The more frequent the compounding, the lower the PV.

There's more on TVM on our blog!

To continue with time value of money, read about different types of annuity and see how to apply the CF and NPV worksheets for TVM exam-type problems.




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