Inflation, Annuity, Perpetuity

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Last updated 1:44 PM on 5/29/26
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7 Terms

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2 Methods to dealing with Inflation: Nominal Method

  • Use face value of money and market interest rate (You don’t change anything)

    • Inflation already accounted for in market interest rate

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2 Methods for Inflation: Real Approach

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3 Term Structures:

  1. Flat: Same rate over t

  2. Upward Sloping (Normal): Rate increases over t

  3. Downward Sloping (Inverted): Rate decreased over t

Dealing with: Each cashflow is discounted with equivalent t rate

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Perpetuity

  • Cash flow stream → Pays at end of year to eternity

<ul><li><p>Cash flow stream → Pays at end of year to eternity</p></li></ul><p></p>
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Annuity

  • Cash flow stream —> Pays at end of year for certain period of time

  • You can envision this as difference between two perpetuities

    1. Get value of annuity payment as a perpetuity

    2. Discount it by amount of years of the annuity, Subtract A-B

<ul><li><p>Cash flow stream —&gt; Pays at end of year for certain period of time</p></li><li><p>You can envision this as difference between two perpetuities</p><ol><li><p><span style="background-color: transparent;">Get value of annuity payment as a perpetuity</span></p></li><li><p><span style="background-color: transparent;">Discount it by amount of years of the annuity, Subtract A-B</span></p></li></ol></li></ul><p></p>
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Long/Short lived projects

  • Projects are unique, one might take a lot longer and have a slightly higher NPV (Is this really optimal? No) —> We need Equivalent Annual Cashflow (EAC)

<ul><li><p>Projects are unique, one might take a lot longer and have a slightly higher NPV (Is this really optimal? No) —&gt; We need Equivalent Annual Cashflow (EAC)</p></li></ul><p></p>
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Zero Coupon Bonds

  • Pays no interest, just face value at end of term

  • Therefore you pay less than face value

  • Formula: PV=Coupon/(1+r)^t

  • If you want the spot rate you make it so that r is alone on one side and solve for it