Stokey and Zeckhauser Chapter 10 - Discounting
  • Need a way of comparing desirability of outcomes with consequences that occur at different times in the future.
  • Need to extend the model of choice to enable systematic comparison between costs and benefits incurred and realized at different stages in time.
  • Discounting is the standard procedure developed for this.

Discounting

  • Reduces a stream of costs and/or benefits to a single amount, which is the present value, by using compound interest.
  • Net benefit = “the present value of the discounted stream of net benefits.”
  • Rationale – people prefer $1 now to $1 a year from now
    • Money can be invested to produce earnings
    • Waiting carries a cost in the form of lost opportunity. Ignores risk.
  • Usually for dollar amounts, can be used for any stream with same units

Mechanics

  • If discount rate is 5%, invest $100 today, it will become $105 a year from now.
  • Arithmetically the same as interest rate.
  • Initial Sum = Sum (after 1 year)/(1 +r), where r = discount rate.
  • Rate is chosen by the person doing the analysis.

PV = S(n)/(1 +r)^n

Present value of a Sum(n) payable n years from now.

Stream of Benefits

  • Normal situation – a stream of costs and benefits is generated over time.
  • Present value of the stream is the sum of the present values of the individual items.
  • When choosing between two projects, a high discount rate will favor the one where the costs are postponed.

When choosing projects:

  • Internal Rate of Return - The discount rate at which the present value of a project becomes zero.
    • For a yes-no decision on a single project, choose the project if its internal rate of return is greater than the appropriate discount rate. A project should be done if its rate of return is greater than the rate at which money can be borrowed. Only for situations where there is an initial outflow of funds and then a stream of returns.
    • For choosing among multiple projects, choose the project with the highest internal rate of return. Won’t always produce correct decision. Can still be inferior to doing nothing.

Present Value criterion and internal rate of return criterion lead to accepting and rejecting same projects only if there are NO budget limitations, if they do NOT preclude one another and if streams of returns are first negative and then positive.

Proper criterion = Choose the mix of projects with the highest present value.

The Choice of a Discount Rate

  • What is the appropriate discount rate for projects?
    • For public projects – the opportunity cost is the correct discount rate. If the present value is positive, the project uses the funds to better advantage than they are currently being used in the private sector.
    • A low discount rate implies that marginal opportunities for investment in private sector are not very promising
    • Should be separately determined for individual projects