So far, the estimation of discount rates required by entrepreneurs has remained a mystery. Mongrut and Ramirez (2006) made a contribution to this area by deriving the lower bound discount rate for a non-diversified entrepreneur in an emerging market. However, they used a quadratic utility function, which does not have desirable assumptions. In this research one extends the previous work by deriving expressions of discount rates using a Hyperbolic Absolute Risk Aversion (HARA) utility function that includes the quadratic and the logarithmic forms as special cases. Furthermore, one also assumes the entrepreneur with the lowest risk-aversion that invests almost all his capital in his project or firm and whose level of wealth approaches to zero. One finds that both expressions depend upon entrepreneur’s risk-aversion and a measure of the project total risk. Maintaining constant the risk-free rate, we simulate the expressions of discount rate for the quadratic form and the logarithmic form. As expected, the entrepreneur’s required returns (discount rates) are highly sensitive in both specifications and all values were lower than 50% and most of them were lower than 25%, but higher than the assumed risk-free rate.