Investment Theory and Risk Management, + Website

Discount Rates Redux

Recall from Chapter 1 the discussion of the role of the discount rate in computing present value. There, we stated that this is the rate at which we are willing to trade present for future consumption. This is the role that the term r in the dividend discount model implicitly plays. Specifically, the one period discount rate is , where r is the relevant interest rate. The discount rate tells us how valuable a dollar one period into the future is to us today. If r = 10 percent, then that dollar feels like about $0.92 today. If r = 5 percent, it feels a little more like $0.95 today. As interest rates fall, the present value of a dollar to be received one year out means more to us. Stated differently, as r falls, we need less tomorrow to compensate us for giving up a dollar today. That is, as r falls to zero, the opportunity cost of consuming a dollar today is zero; there is no foregone payoff by failing to save for the future. In the limit, r equal to zero means we are indifferent between a dollar today and a dollar in the future; the discount rate in this case is one. Therefore, high discount rates follow from lower interest rates. In general, high discount rates are consistent with the idea that the market doesn't value the future as much and this preference shows in the form of low market rates (usually consistent with lots of liquidity, that is, money supply). ...