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Chapter7: Introduction to Risk and Return

7-5 Diversification and Value Additivity

We have seen that diversification reduces risk and, therefore, makes sense for investors. But does it also make sense for the firm? Is a diversified firm more attractive to investors than an undiversified one? If it is, we have an extremely disturbing result. If diversification is an appropriate corporate objective, each project has to be analyzed as a potential addition to the firm's portfolio of assets. The value of the diversified package would be greater than the sum of the parts. So present values would no longer add.

   Diversification is undoubtedly a good thing, but that does not mean that firms should practice it. If investors were not able to hold a large number of securities, then they might want firms to diversify for them. But investors can diversify.32 In many ways they can do so more easily than firms. Individuals can invest in the steel industry this week and pull out next week. A firm cannot do that. To be sure, the individual would have to pay brokerage fees on the purchase and sale of steel company shares, but think of the time and expense for a firm to acquire a steel company or to start up a new steel-making operation.

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   You can probably see where we are heading. If investors can diversify on their own account, they will not pay any extra for firms that diversify. And if they have a sufficiently wide choice of securities, they will not pay any less because they are unable to invest separately in each factory. Therefore, in countries like the United States, which have large and competitive capital markets, diversification does not add to a firm's value or subtract from it. The total value is the sum of its parts.

   This conclusion is important for corporate finance, because it justifies adding present values. The concept of value additivity is so important that we will give a formal definition of it. If the capital market establishes a value PV(A) for asset A and PV(B) for B, the market value of a firm that holds only these two assets is

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A three-asset firm combining assets A, B, and C would be worth PV(ABC) = PV(A) + PV(B) + PV(C), and so on for any number of assets.

   We have relied on intuitive arguments for value additivity. But the concept is a general one that can be proved formally by several different routes.33 The concept seems to be widely accepted, for thousands of managers add thousands of present values daily, usually without thinking about it.

32One of the simplest ways for an individual to diversify is to buy shares in a mutual fund that holds a diversified portfolio.

33You may wish to refer to the Appendix to Chapter 31, which discusses diversification and value additivity in the context of mergers.

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