FCFE formula - given D/E target ratio

[andrevc]

Hi all,
On the FCFF model valuation chapter, they give us a formula to use when we want to forecast FCFE and we have a target D/E ratio.
It’s: FCFE = NI - [ (1-DR) (FCinv - Dep) - (1-DR) (WCinv) ]
My question is: I applied the distributive and figured we are reducing FCFE by taking out FCinv and WCinv, but then adding up the DR proportion of both FCinv and WCinv (this would be the net borrowings).
In parallel, we sum up depreciation and subtract the DR x Dep. Why do we decline FCFE by the DR x Dep. What’s the rationale here? I understand that we need to fund long-term capital investment and working capital with the proportionate debt participation. What’s the deal with depreciation?

 

[cpk123]

Net new investment in fixed capital = (New investment in fixed capital - depreciation) as well as Working Capital Investment is financed based on a fixed DR (Debt Ratio).
(This is explained in the CFAI book - right in the section where the write up this formula).
So (FCInv - Depr) * DR = Net Borrowing for FCInv
WC * DR = Net Borrowing for WCInv.
So
FCFE = NI + Depr - FCInv - WCInv + Net Borrowing
= NI - (FCInv - Depr ) - WCInv + DR * (FCInv - Depr) + WCInv * DR
= NI - (1-DR) (FCInv -Depr) - (1-DR) WCInv.

 

[oz001]

Depreciation is related to existing assets, those have already been funded with the target debt ratio. Additional debt participation applies only to incremental new investment (FCInv net of depreciation) hence the target DR is applied to (FCInv - Depr)

 

[andrevc]

Perfect explanation guys. Now its very clear, many thanks!