CHAPTER 5 Discounting to Present Value

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10 years comprises only 2 percent (H48) of the present value of the annuity Of course, the amounts and the percentages change with the appropriate discount rate At a 5 percent discount rate again, that is appropriate for discounting US Treasury bonds the present value is $1537 (B36), which is more than three times the present value at a 20 percent discount rate Intuitively, this is reasonable, because, as noted earlier, the US Treasury is a risk-free17 loan, and we require less interest income and thus a lower discount rate to part with our money than we would with investing in a private business For the 5 percent discount rate, the last 10 years accounts for 19 percent (B48) of the present value of receiving one dollar every year for 30 years, which is much higher than the 2 percent (H48) at a 20 percent discount rate Since the US Treasury is a risk-free loan, we discount the future much less than we do for a private business Thus, it makes intuitive sense that the more distant cash flows in Years 21 to 30 matter more to us when we loan to the US Treasury than when we invest in a private business Another way of looking at it is that with an investment in a private business, we are much more likely to discount the piein-the-sky forecasts of having sales in the hundreds of millions of dollars 30 years now and focus on the bird in the hand, ie, the forecast cash flows in the first 5 to 10 years In valuing a startup business, where a 30 percent discount rate is appropriate, 93 percent (M46) of the present value comes from the first 10 years of forecast cash flows, and the last 10 years contribute no material present value, ie, M48 appears as zero percent (which means that it is less than 05 percent of the present value of the 30 years of cash flows)

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17 It is risk-free in the sense that there is no material risk of the US Treasury defaulting on its loans There is still term risk in the longer loans For example, a 30-year Treasury bond paying 5 percent when originally purchased would become an unattractive investment if interest rates rise to 6 percent In hindsight, it would have been better for the investor to buy a short-term Treasury bill until interest rates rose, then buy the long-term bond This is covered in greater detail later in the chapter

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PART ONE Business Valuation

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The next step mechanically in the mathematics is to multiply the PVF by the forecast cash flow(s) If we expect $1 million of cash flow every year for 30 years, and 20 percent is the appropriate discount rate for the specific investment we are valuing, then its present value is $1 million $498 (H36) $498 million If we are expecting cash flows only for two years, then we would be willing to pay $1 million $83 (H6) $830,000 for the first year s expected cash flow, plus $1 million 069 (H7) $690,000 for the second year s cash flow, for a total of $1,520,000, which is the present value of the two years of expected cash flows

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CALCULATING DISCOUNT RATES

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Calculating discount rates is a topic about which many hundreds of thousands of pages of scholarly and professional literature have been written For the sake of practicality, we will keep it relatively short and useful In this section, we discuss some fundamentals of finance that will be helpful in understanding business discount rates on a deeper level Later in this chapter you will see that small firms are more volatile and therefore riskier than large firms For starters, we ll look at the components of equity returns One of the few and most powerful laws of finance is the greater the risk, the greater the expected reward that investors will demand Note that there is a significant difference between the expected reward (return) on a security before we invest in it and the actual return after the fact

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