Abstract
Business choices typically entail tradeoffs between potential growth rates and the risk of failure. This note applies recent results from the theoretical valuation literature to characterize, as a benchmark, the terms of that tradeoff sufficient to leave the expected value of discounted cash flows unchanged. The central result indicates that risk-neutral investors could accept sizeable increases in risk in exchange for modest improvements in expected growth rates. The benchmark result can be used to rank projects in terms of their impact on the value of the firm's equity.
Notes
1 Equivalent forms of this expression can be derived if instead cash flows occur at the end of each year, in midyear, or at multiple times during the year.
2 The technical reason for this independence is that the numerator in equation (Equation1) is independent of g, the denominator is linear in g, and common factors in g cancel out in the numerator and denominator of dp/dg when applying the implicit function theorem.