Discounted-Cash-Flow Value Estimates are Optimistic when Assumptions are Not

Discounted-cash-flow valuations are upward biased even when estimates of market discount rates and cash flow growth rates are unbiased, because both compounding and discounting are convex functions. The upward bias in the estimated value of a long-lived cash flow stream can exceed 25% under plausible assumptions regarding magnitudes of estimation errors, which can equate to upward bias in estimated net present values that exceed 100%. This bias may help to explain the value premium puzzle, observed takeover premia, long run returns after IPOs, and high equity valuations during periods of low real interest rates. A method of correcting value estimates for the bias is proposed.