Truth-inducing incentive schemes are used to motivate project managers to provide unbiased project information to portfolio manager to reduce information asymmetry between portfolio manager and project managers. To improve the scheme, we identify the proper value of penalty coefficients in the truth-inducing incentive scheme when information asymmetry is present. We first describe the allocation method that achieves budget optimization under certain assumptions and identify the proper coefficients while accounting for the differing perceptions of both portfolio manager and project managers. We report a bound on the ratio between the two penalty coefficients in the truth-inducing incentive scheme and then we conduct a simulation study to narrow down the bound. We conclude that the penalty coefficient for being over budget should be reduced when the portfolio budget is tight and the penalty coefficients should be equivalent to the organizational opportunity costs when the portfolio budget is sufficient.