I'm working with the following information trying to work through a valuation exercise and I'm absolutely stuck. How can I find ∆WC and CAPX with this information?
Cap ex can come directly from the CF statement. Looks like you explicitly have it listed as a % of sales. Your change in WC can't be estimated without either corresponding % sales figures of either 1) current asset and current liability accounts or 2) net WC as a % sales. Using #2, you would find the NWC at the end of a year required to support the coming year's sales and calculate the change as the additional investment required to bring the existing WC balance to meet that figure.
You don't provide enough information. Yet, if you provide a little more information it might be possible. In theory -- one may recreate a statement for the source and use of funds (i.e., delta balance sheet) from an income statement and cash flow statement. The following adjustments provides a simplified example of the IFRS balance sheet taxonomy, and it is not significantly different for US GAAP:
-(Impairments + Net_Disposals) = NetPPE_New - AdditionsToPPE + DepAmort - NetPPE_Old AdditionsToPPE - Gross_Disposals = GrossPPE_New - GrossPPE_Old Accum_Disposals - Impairments = AccumDDA_Old - AccumDDA_New + DepAmort (AdditionsToPPE - Gross_Disposals) + (Accum_Disposals - Impairments) = (GrossPPE_New - GrossPPE_Old) + (AccumDDA_Old - AccumDDA_New + DepAmort)
Note, AdditionsToPPE (above) is roughly analogous to CapEx.
Recreating a delta balance sheet becomes a lot more complicated when you enter the real world. The real world is fraught with nuanced accounting adjustments. One must account also for asset disposals, impairments, write-offs, and M&A activity.