Using matrix notation, denote profits by $\Pi$, revenues by $R$, and the explanatory variables by $\mathbf X$.
Assuming a linear setup, we look at
$$\mathbf \Pi = \mathbf X\mathbf a + \mathbf u \tag{1}$$
and
$$\mathbf R = \mathbf X \mathbf b + \mathbf v \tag{2}$$
Are profits correlated with Revenues? Experience say they are. So there is also a relationship
$$\mathbf \Pi = \gamma \mathbf R + \mathbf \varepsilon \tag{3}$$
Inserting $(2)$ into $(3)$ we get
$$\mathbf \Pi = \mathbf X(\gamma\mathbf b) + \gamma \mathbf v + \mathbf \varepsilon \tag{4}$$
Looking at $(1)$ and $(4)$, we have the equivalence
$$\mathbf a = \gamma \mathbf b \tag{5}$$
Will we obtain it through estimation? Not that easily.
Least -squares estimation will give us, for $(1)$
$$ \mathbf {\hat a} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \Pi \tag{6}$$
and for $(2)$
$$\mathbf {\hat b} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf R \tag{7}$$
Insert $(3)$ into $(6)$ to get
$$\mathbf {\hat a} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\left(\gamma \mathbf R + \mathbf \varepsilon\right) $$
$$\implies \mathbf {\hat a} = \gamma \mathbf {\hat b} + \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \varepsilon \tag{8}$$
The interesting realization comes at this point: given the postulated relation $(1)$ it is unlikely that the variables in $\mathbf X$ will be uncorrelated with $\mathbf \varepsilon$, the error term in $(3)$.
This means that even with a large sample, calculating the ratios of the individual coefficients in the vectors $\mathbf {\hat a},\;\mathbf {\hat b}$, we will not recover $\gamma$, since $\left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \varepsilon$ won't converge to zero.
