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Monday, November 22, 2010

What is Present Value?

The DIY investor needs to become comfortable with the relationship between bond prices and interest rates. Especially today, with rates at historically low levels.

I start one of my intro to macroeconomics classes each semester with the announcement that tonight my students will earn their MBAs. This, of course, is tongue-in-cheek; but it does give a hint to the importance of the concept to be discussed - present value. After all, present value is at the foundation of finance.

I begin by sketching out a problem on the board that involves figuring out how much to pay for an apartment building. There is a stream of rental payments, a need to factor in costs, and the estimating of inflation involved.

Later I stress the similarity to a bond and even to stocks. In fact, it comes to the point where students realize the need to value a future stream of payments is all around us. I jokingly point out that with their MBA they can go out and consult at $600/hour on valuing businesses - not far from the truth.

Before the night is over, though, we get into some mathematics. We talk about compound interest and derive the formula FV = PV(1+r)^t (where FV is future value and PV is present value) and then flip it around to solve for the all important present value PV = FV/(1+r)^t.

I'm a firm believer that students have to get their hands dirty to gain understanding. I have seen too many students over the years who thought they understood concepts until they had to apply them. In other words, it looks easy up at the board. Along these lines, I give them a homework assignment based on a group who won a $1 million lottery. The story is that a bunch of old guys pooled their money and when they showed up for the prize they were told it was $50,000/year for 20 years. The assignment is to calculate the present value of the 20-year income stream using a discount rate of 3% and again using 4%.

This illustrates forcefully the difference between cash in hand and a stream of future payments. It also illustrates why the old guys proceeded directly to court on the grounds of misleading advertising.

The real point of the exercise is to get at how bonds work - it shows, in a fun sort of way, the important idea that the value of a stream of payments moves in the opposite direction of interest rates. In particular, it is why bond prices fall when interest rates rise and bond prices rise when interest rates fall - a concept that is difficult for some investors and students to grasp.

The clever DIYer can extend the exercise to show why longer maturity bond prices are more volatile, the impact of discounting using yields on the yield curve etc.


  1. Great post Robert. Well worth the read for any DIY investor :)

  2. Robert,

    As always, I'm very impressed by your willingness to teach and empower.

    Do you mind if I mention RW Investments in my book? It's going to be published in May, by Wiley & Sons, with the current working title, The Millionaire Teacher.

    There's a short section on finding an advisor without a conflict of interest. I'd like to mention you, along with Vanguard, Assetbuilder and Aperio, if that's OK. Of course, there are others, but if I can cover Maryland, Texas, California and Pennsylvania, I'll have a nice, broad U.S. example of some of (what I believe) are the best operators out there.
    I'm very impressed by the work you're doing.

  3. Re: Financial Cents Did this comment come from Argentina? Thanks for the comment.
    Re: Andrew I would be honored to be mentioned in your book which, by the way I can't wait to read. I'm in the process of putting together a talk for High Schoolers in April (financial literacy month in the U.S.) and have been getting some ideas from your old posts. I'm thinking of asking a bunch of blogers for their best single tip for someone graduating high school. What do you think?

  4. How about a quiz related to what most millionaires pay for certain items, Thomas Stanley style? I think it would surprise students to know that 90% of American millioniares live in homes worth less than a million; their favorite watches are Timex and Seikos; their latest car purchases amounted to an average less than $32,000. I think this sort of info would serve as a fine backbone. And 90% of U.S. millionaires are first generation rich. Oh, and people who receive handouts don't end up with as much money as those who don't (Stanley refers to this as economic outpatient care) Thoughts?

  5. The quiz is a really good idea. I actually subscribe to, a make your own quiz/game software package that has a "win a million dollars" type quiz that might make this ideal for either part of the presentation or to draw people in.

  6. I remember PV from business school. It provides a framework built around certain assumptions (interest rates, inflation, income/earnings) on how to value a bond, stock, business, etc. based on discounted cash flow. Thanks for the refresher.

  7. Great post, Robert. It's definitely important to learn these concepts, as there are many places where they can be applied.