The complexity of discounted cash flow

Folio: The Magazine for Magazine Management,  Sept, 1985  by Richard M. Koff

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The betting odds

A better method is to use a more intuitively understandable (and mathematically simpler) measure of risk. I suggest that risk be measured in terms of betting odds. If you flip a coin and bet on heads, the chance of losing is one in two, or 50 percent. The return on such a bet, if you win, is 100 percent. Let's start a graph of return against risk (Figure 1) and plot this first return percentage (100 percent) against the risk of loss n50 percent).

If you step up to a parimutuel window and bet on the favorite, the odds may be quoted as six to five. This means that if you win, you will get $1.20 back for each dollar you bet, for a return of 20 percent. The parimutuel computer at the track keeps a count of all bets and, in this case, probably found that, not counting the percentage taken by the track management, for every $5 bet on the favorite there was only $1 bet on all the other horses in the race. Your theoretical Chance of Failure (loss) is only one in six, or 16.67 percent. I say theoretical because there is no way of knowing what the actual Chance of Failure is in a bet on a horserace, since this would take a lot more knowledge about the horses, the weather, the track, and so on than we are likely to have. We can now plot a second point on our graph--a 20 percent return against a 16.67 percent Chance of Failure.

In general, then, we can find what I will call the Risk Premium as determined by the Chance of Failure in the following formula (with all variables expressed as decimal fractions): Risk premium= Chance of failure / 1-Chance of failure

For another example, if you estimate that the Chance of Failure of your magazine start-up is 25 percent, the Risk Premium would be 0.25/(1 - 0.25)=0.333, or 33.3 percent.

This relationship (plotted in Figure 1) is easier to understand and use than the beta factor. Note that at 100 percent Chance of Failure, the Risk Premium would be infinite--no one would willingly invest in any project that is certain to fail. However, we do occasionally invest small sums in something that has close to 100 percent Chance of Failure. For example--when did you last buy a lottery ticket? You spent a dollar or two in an investment that had odds of failure measured in millions to one--but the win would provide a very high return and the consequences of loss are negligible, so you took a flyer. This matter of the consequences of loss adds another dimension to the investment decision, but that is best left to a future article.

Putting it to work

At last we are ready to make our first estimate of a discount rate for our magazine. It starts with a required rate of return equal to the risk-free return of government bonds, includes the effect of inflation, and is modified by our estimate of the riskiness of this investment. If you think the Chance of Failure of a particular magazine is about 15 percent, you multiply the 12 percent risk-free return by the required 17.7 percent Risk Premium from the graph or the equation and get just over 30 percent (1.12 times 1.177 equals 1.318). If this discount rate is applied to the cashflow of Table 1, the net present value is $1,202,000.