The trouble with discount rates

Discount rates are an elegant way to whittle a three dimensional concept down to one dimension. But they are inexact.

For starters, a brief definition of a discount rate: A discount rate is a percentage amount by which you reduce future cash flows to calculate what they would be worth today. (My definition)

Investopedia's definition:
The interest rate used in discounted cash flow analysis to determine the present value of future cash flows. The discount rate takes into account the time value of money (the idea that money available now is worth more than the same amount of money available in the future because it could be earning interest) and the risk or uncertainty of the anticipated future cash flows (which might be less than expected).

Pretty good definition.

Ok. So which would you rather have - one dollar today, or one dollar and ten cents next year? Discount rates attempt to tackle that problem.

 

In terms of an investment, your cash and assets today is the "first dimension."

There are two risks that discount rates account for. 1. The risk that you will not be paid tomorrow (uncertainty/variance of cash flows, the "second dimension") and 2. The risk that inflation will make money tomorrow worth less than it is today, (risk of time and inflation, the "third dimension")

Now, what you are really looking at, in reality is a series of cash flows with a probability associated with each one.  Let's say you have one dollar today, and you can invest that in a loan that 95% of the time will pay you $1.10 next year and 5% of the time will pay you $0 next year.  A discount rate takes the $1.10 and reduces it by the risk of default. The higher the probability that you are paid $0, the higher the discount rate. If you determine your discount rate is 10%, then it is a theoretically neutral present value project, with a $1 net present value and a $1 price. An investor should be ambivalent.

The trouble is that the probability trees of payments on investments are not shaped the same. Some investments are all-or-nothing, like the one above. Some are closer to normal probability curves. Some are oddly shaped. For example, as used in a post mentioned before, the future cash flows of USEC, Inc. are dependent on whether it receives a loan guarantee from the U.S. Department of Energy. Any future income projections for five years from now will be skewed away from the average because the loan will have such a big impact on the results of the company. But that might have the same discount rate as a set of returns that are highly volatile and centered around a mean. And those might share the same discount rate as a junk bond with probability skewed toward either full repayment or zero payment. But to investors, the differences between these returns are meaningful. Investors have different capital needs, so they care whether their returns are more centered or skewed toward 0.  So that's the first way discount rates can fail: they take different arrays of returns in a fixed period of time and try to put a single price on them. Taking two dimensions and bringing it to one.

The third dimension of cash flows is the timing. Discount rates put a single price on differently timed cash flows. So if you have one investment of $1 that pays $1.10 next year, and another one that pays $1.46 in four years, a discount rate might find these two investments of equal value. But to an investor, there is a big difference. Some people need money earlier, and some people can wait and are more long-term investors.

In addition to providing a little too much simplicity, discount rates are difficult to calculate. Wall Street uses a CAPM formula, but that formula is incorrect, as discussed in a previous post. I have put a lot of thought into the correct way to determine a discount rate for an investment, and I have yet to figure it out. One day I'll come up with something.

Until then...

The most accurate way to analyze an investment is to project the actual cash flows into the future, without discounting them. Note the shape of the probability curve, and the timing of the cash flows. If you foresee everything being normalized, with nothing skewed in terms of the probability curve or the timing of returns, then apply a discount rate based on the chance that inflation will reduce your spending power, and the spread, or standard deviation of the probability curve. The longer you have to wait for your returns, and the greater the standard deviation, the higher the discount rate should be. As a baseline, a discount rate low-risk, constant payment, such as an annuity from a company with good credit, should be in the 5-8% range.