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We have come a long way. We began by defining wealth and income, then traced the origins of money. We learned to value a risk-free project and built a toolkit for measuring risk. We even quantified the cost of risk . Now, we arrive at the culmination of our journey: determining the value of a risky project. This chapter synthesizes everything we have learned. It introduces the crucial distinction between diversifiable and irreducible risk , presents the final formula for Net Present Value under uncertainty, and explores the profound implications of this framework for understanding everything from corporate finance to the value of cryptocurrencies . 7.1 Only Irreducible Risk Has a Cost In Chapter 5, we learned about diversification . By combining projects that are not perfectly correlated, an investor can reduce overall portfolio risk. This process has a profound implication for the valuation of individual projects. Consider two types of risk associated with any project: Diversifia...

In the previous chapter, we developed the tools to calculate and measure risk. We learned about probability distributions , expected values , covariance , and the power of diversification . But we left a critical question unanswered: what is the cost of risk ? We stated that investors are risk-averse and require a risk premium , but we did not quantify it. This chapter tackles that challenge head-on. We will explore how to calculate the cost of risk, examine common mistakes in doing so, and finally, consider the other side of the coin: the potential benefit that risk can bring. 6.1 The Cost of Risk The cost of risk is not a physical cost like a raw material or a wage. It is an opportunity cost. It represents what investors give up, or the extra return they demand, to bear uncertainty. To understand this, imagine two projects: Project A: A risk-free bond that guarantees a return of €100 in one year. Project B: A risky venture with an expected return of €100 in one year, but with a...