Secure computation with penalties aims to achieve fairness in secure computation protocols by imposing monetary penalties on adversarial parties. A fundamental problem to constructing a protocol that involves monetary entities is how to formalize them in the computational model. Bentov and Kumaresan (Crypto 2014) introduced a new computational model with special atomic entities called coins that capture currency and showed a protocol for secure computation with penalties in the model. Their model, secure computation with coins, assumes coins have several properties that are natural in the sense of expressing currency. However, on the other hand, it also requires the unnatural assumption “all coins are indistinguishable from each other” for a technical reason to accomplish the security proof. The motivation of this work is to remove the assumption from the coins to make the model a more general. We propose a new model, secure computation with color coins, such that coins have identifiable colors and do not hold the indistinguishability property. Furthermore, our model allows us to set different prices for each color. We show that secure computation with penalties can be realized in our model. To do this, we make some modifications to the ideal functionality of secure computation with penalties to adapt it to our model without losing the essence, i.e., fairness with penalties.