Calculating Present Values (PV)

• PV

  • One Period
    
    

  • Two Periods
    
    

  • t periods
    
    

    where is called the discount factor.

  • 
    
    

• Time-varying Discount Rates;
  
  

• Net PV:
  
  where is usually negative.

• Perpetuity. E.g., Bonds with no termination date, which just promised to pay a fixed sum every year forever.
  
  

  Multiplying through by
  
  Substracting () from ()
  
  
  
  

• Growing Perpetuities. A growing perpetuity is like a perpetuity except the payment grows at a rate of g per period instead of being constant through time.
  
  

  Multiplying through by
  
  Substracting () from ()
  
  
  
  

• Annuities. There are a number of assets, such mortgage, annuities and so on, which involve a fixed payment for a specified number of years.
  
  

  The PV of an annuity is found by splitting it into the difference between two perpetuities: