a finance/math question: economic profit = invested capital * (ROIC-WACC)

Hello. There is this equation economic profit = invested capital * (ROIC-WACC)
Since ROIC= NOPLAT/Invested capital, we can say:

Economic Profit= NOPLACT -(Invested Capital *WACC)

I can check that it's correct with numbers but I don't get the math by how they do this. Thanks!!

First, let's declare some variables. I believe this may make it easier to follow. Let Alpha (α) be the Invested Capital. Let Beta (β) be the ROIC. Let Gamma (γ) be the WACC. And let Delta (δ) be the NOPLAT. So, the equation says:

\(\displaystyle \text{Profit}=\alpha \cdot \left(\beta -\gamma \right)\)

And we know that:

\(\displaystyle \beta =\frac{\delta }{\alpha }\)

So make the appropriate replacement:

\(\displaystyle \text{Profit}=\alpha \cdot \left(\frac{\delta }{\alpha }-\gamma \right)\)

\(\displaystyle \text{Profit}=\alpha \cdot \frac{\delta }{\alpha }-\alpha \cdot \gamma \)

\(\displaystyle \text{Profit}=\delta -\alpha \cdot \gamma \)

Thus, Profit = NOPLAT - (Invested Capital * WACC). Make sense now?