This preliminary report studies a graphical version of Plotkin's call-by-value equational theory, in particular its soundness with respect to operational semantics. Although an equational theory is useful in safe program transformation like compiler optimisation, proving its soundness is not trivial, because it involves analysis of interaction between evaluation flow and a particular sub-program of interest. We observe that soundness can be proved in a direct and generic way in the graphical setting, using small-step semantics given by a graph-rewriting abstract machine previously build for evaluation-cost analysis. This would open up opportunities to think of a cost-sensitive equational theory for compiler optimisation, and to prove contextual equivalence directly in the presence of language extensions.