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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?

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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.

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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.

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