Expected Present Discounted Value

nominal vs real interest rates -  

• nominal interest rates (it) - in terms of currency, how interest is naturally expressed
  • borrow $M this year, pay $M(1+it) next year
• real interest rates (rt) - in terms of basket of goods
  • borrow M basket of goods, pay M(1+rt) basket of goods next year
• 1+rt = (1+it) Pt / Pet+1
  • Pt - present cost/price
  • Pet+1 = expected price next year
• rt ~ it - pet
  • w/o inflation, real interest rate equals nominal interest rate
  • inflation usually positive >> real interest less than nominal interest
  • higher inflation >> lower real interest rate

expected present discounted value - value today of expected future payments  

• expresses future values in terms of present values
• $M next year = $M / (1+it) this year
• $M in 2 years = $M / [(1+it)(1+it+1)] this year
• discount factor - constant multiplied by future value to get present discounted value
  • discount rate = it
• $Vt = $zt + $zt+1 / (1+it) + $zt+2 / [(1+it)(1+it+1)] + ...
  • future costs/payments usually estimated by expected values
  • constant interest rates >> it = it+1 >> discount factors equal to 1/(1+i)n
  • constant interest rates and payments
    • $Vt = $z (1-[1/(1+i)n]) / (1-[1/(1+i)])
  • constant interest rates and payments, continuing forever
    • $Vt = $z/i
  • 0 interest rates >> present value equal to sum of expected values