*“Ultimately investors must choose sides. One side – the wrong choice is a seemingly effortless path that offers the comfort of consensus.” – Seth Klarman (Trades, Portfolio)*

I was fortunate enough to obtain a copy of Seth Klarman (Trades,Portfolio)’s “Margin of Safety” at the end of last week and read through most of it in one sitting. I found a few chapters very informative and worth sharing with others that may not have a copy themselves or have not read the book.

If you have read “The Intelligent Investor,” “Security Analysis” or the Berkshire letters you will see a lot of repetition, but the repetition has a modern touch from Klarman as it was published in 1991. The examples given are also different but the reoccurring themes are the same: margin of safety, intrinsic value, crowd behavior, competitive advantages, valuation tactics, etc.

Chapter 8 is “The Art of Business Valuation.” The chapter was one of my favorites (I will write a post or two about the others) and talks about the elusive precision of NPV, DCF and IRR, how a ** valuation range** should be used, various ways of valuing a business, how to choose a discount rate and the reflexivity of market prices. The following is an excerpt from a section titled “

**The Choice of a Discount Rate**,” as a question was recently received from a reader asking about the discount rate, specifically, should it be adjusted depending on both the certainty (or uncertainty) of future cash flows and the risk free rate?

*(Spoiler: Yes it should, but let us hear it from the horse’s mouth.)*

*“The other component of present-value analysis, choosing a discount rate, is rarely given sufficient consideration by investors. A discount rate is, in effect, the rate of interest that would make an investor indifferent between present and future dollars. Investors with a strong preference for present over future consumption or with a preference for the certainty of the present to the uncertainty of the future would use a high rate for discounting their investments. Other investors may be more willing to take a chance on forecasts holding true; they would apply a low discount rate, one that makes future cash flows nearly as valuable as today’s.*

*There is no single correct discount rate for a set of future cash flows and no precise way to choose one.** The appropriate discount rate for a particular investment depends not only on an investor’s preference for present over future consumption but also on his or her own risk profile, on the perceived risk of the investment under consideration, and on the returns available from alternative investments.”*

- Klarman explains how we can essentially view a discount rate as an opportunity cost and that depending on the certainty of the opportunity (or lack of) we should adjust the discount rate up and down accordingly. An example of this may be discounting a company with relatively known cash flow like Wal-Mart or Coca-Cola at something like 6% to 8% while a company like Tesla or 3D Systems Corp. might be discounted at 13% to 14%.

*“Investors tend to oversimplify; the way they choose a discount rate is a good example of this. A great many investors routinely use 10 percent as an all-purpose discount rate regard- less of the nature of the investment under consideration. Ten percent is a nice round number, easy to remember and apply, but it is not always a good choice.*

*The underlying risk of an investment’s future cash flows must be considered in choosing the appropriate discount rate for that investment. A short-term, risk-free investment (if one exists) should be discounted at the yield available on short-term U.S. Treasury securities, which, as stated earlier, are considered a proxy for the risk-free interest rate. Low-grade bonds, by contrast, are discounted by the market at rates of 12 to 15 percent or more, reflecting investors’ uncertainty that the contractual cash flows will be paid.*

*It is essential that investors choose discount rates as conservatively as they forecast future cash flows.** Depending on the timing and magnitude of the cash flows, even modest differences in the discount rate can have a considerable impact on the present-value calculation.”*

Take the table below illustrating the difference of $1 discounted at 6% through 14% over a 10-year period. The longer the time frame the larger the discrepancies become between the discount rate used — until a certain point.

To further illustrate this *threshold* being reached we can look at the difference of cash flows at years 15, 20, 25 and 35 discounted at 14%.

$1,000,000 discounted over 15 years is equal to roughly 14% or 140k.

$1,000,000 discounted over 20 years is equal to roughly 7.2% or 72k.

$1,000,000 discounted over 25 years is equal to roughly 3.8% or 38k.

$1,000,000 discounted over 35 years is equal to roughly 1% or 10k.

As we can see after about 15 years (at 14%), the bulk of the cash flow has already been discounted and our interpretation from there on out becomes negligible (from a DCF perspective, the durable moat still matters!)

Discount Rate | 6% | 7% | 8% | 9% | 10% | 11% | 12% | 13% | 14% |

Year | |||||||||

1 | $0.94 | $0.93 | $0.93 | $0.92 | $0.91 | $0.90 | $0.89 | $0.88 | $0.88 |

2 | $0.89 | $0.87 | $0.86 | $0.84 | $0.83 | $0.81 | $0.80 | $0.78 | $0.77 |

3 | $0.84 | $0.82 | $0.79 | $0.77 | $0.75 | $0.73 | $0.71 | $0.69 | $0.67 |

4 | $0.79 | $0.76 | $0.74 | $0.71 | $0.68 | $0.66 | $0.64 | $0.61 | $0.59 |

5 | $0.75 | $0.71 | $0.68 | $0.65 | $0.62 | $0.59 | $0.57 | $0.54 | $0.52 |

6 | $0.70 | $0.67 | $0.63 | $0.60 | $0.56 | $0.53 | $0.51 | $0.48 | $0.46 |

7 | $0.67 | $0.62 | $0.58 | $0.55 | $0.51 | $0.48 | $0.45 | $0.43 | $0.40 |

8 | $0.63 | $0.58 | $0.54 | $0.50 | $0.47 | $0.43 | $0.40 | $0.38 | $0.35 |

9 | $0.59 | $0.54 | $0.50 | $0.46 | $0.42 | $0.14 | $0.36 | $0.33 | $0.31 |

10 | $0.56 |
$0.51 | $0.46 | $0.42 | $0.39 |
$0.35 | $0.32 | $0.29 | $0.27 |

We can also see the large differences between the best case, the base case and the worst case. The best case results with a value of 56% of the original cash flow, while the worst-case results in 27% of the original cash flow. For simplicity a simple present value formula was used with $1 as the original cash flow. (Best, base and worst cases are bolded at year 10.)

*“Business value is influenced by changes in discount rates and therefore by fluctuations in interest rates. While it would be easier to determine the value of investments if interest rates and thus discount rates were constant, investors must accept the fact that they do fluctuate and take what action they can to minimize the effect of interest rate fluctuations on their portfolios.*

*How can investors know the ‘correct’ level of interest rates in choosing a discount rate? I believe there is no ‘correct’ level of rates. They are what the market says they are, and no one can predict where they are headed. Mostly I give current, risk-free interest rates the benefit of the doubt and assume that they are correct. Like many other financial-market phenomenathere is some cyclicality to interest rate fluctuations. High interest rates lead to changes in the economy that are precursors to lower interest rates and vice versa. Knowing this does not help one make particularly accurate forecasts, however, for it is almost impossible to envision the economic cycle until after the fact.*

*At times when interest rates are unusually low, however, investors are likely to find very high multiples being applied to share prices.** Investors who pay these high multiples are dependent on interest rates remaining low, but no one can be certain that they will. This means that when interest rates are unusually low, investors should be particularly reluctant to commit capital to long-term holdings unless outstanding opportunities become available, with a preference for either holding cash or investing in short-term holdings that quickly return cash for possible redeployment when available returns are more attractive.*

*Investors can apply present-value analysis in one of two ways. They can calculate the present-value of a business and use it to place a value on its securities. Alternatively, they can calculate the present-value of the cash flows that security holders will receive: interest and principal payments in the case of bondholders and dividends and estimated future share prices in the case of stockholders.”*

- A common stock is essentially a bond with a variable coupon and no maturity; figuring out what the coupon payments will be is the inherently tough part of the business.

*“Calculating the present value of contractual interest and principal payments is the best way to value a bond. Analysis of the underlying business can then help to establish the probability that those cash flows will be received. By contrast, analyzing the cash flows of the underlying business is the best way to value a stock. The only cash flows that investors typically receive from a stock are dividends. The dividend-discount method of valuation, which calculates the present value of a projected stream of future dividend payments, is not a useful tool for valuing equities; for most stocks, dividends constitute only a small fraction of total corporate cash flow and must be projected at least several decades into the future to give a meaningful approximation of business value. Accurately predicting that far ahead is an impossibility.”*

- Although Klarman does not state an exact time frame to use when discounting cash flow, my assumption is that it would be in the five, 10 and 15-year intervals with various ranges (sensitivity analysis of cash flows), using various discount rates. He clearly does not use several decades, as he says it is an impossibility to predict and as our previous experiment has shown above, the cash flows become arguably negligible around years 15 to 20.

*“Once future cash flows are forecast conservatively and an appropriate discount rate is chosen, present value can be calculated. In theory, investors might assign different probabilities to numerous cash flow scenarios, and then calculate the expected value of an investment, multiplying the probability of each scenario by its respective present value and then summing these numbers. In practice, given the extreme difficulty of assigning probabilities to numerous forecasts, investors make do with only a few likely scenarios. They must then perform sensitivity analysis in which they evaluate the effect of different cash flow forecasts and different discount rates on present value. If modest changes in assumptions cause a substantial change in net present value, investors would be prudent to exercise caution in employing this method of valuation.”*

Best case, base case and worst case is all you need in terms of probabilities and expected values. Complexity does not usually produce a more accurate representation. There was a great write-up a week or two ago on GuruFocus by Grahamites about “Cultivating an Expected Value Mindset” where the reader will find additional information about components of the *“subjectivity analysis” *the value investor must conduct.

*“Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.” – Isaac Newton*