The lattice approach derived by Broadie and Kaya (J Financ Quant Anal 42(2):279–312, 2007) has traditionally been used to determine the capital structure of a firm in economies with constant interest rates; however, this study argues that the capital structure of a firm should be determined by considering the state of its debt simultaneously with the randomness of interest rates. This study extends the Hilliard et al. (J Financ Res 19(4):585–602, 1996) bivariate binomial model to determine the capital structure of firms, taking into account stochastic interest rates and their correlation with the asset value of the firm. Our simulation results suggest that taking stochastic interest rates into consideration reduces the equity value of a firm while increasing its debt value. The stronger the correlation between variations in the asset value of the firm and the short rate, the stronger the impact of this correlation on the capital structure of the firm.