How to derive the formula of FCFE in Question 6 CFAI book 4

CFA Level II Equities
#1

The question 6, EOC of the reading 31 Free Cashflow Valuation

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The solution states that

FCFE=Net income−(1−DR)(Capitalexpenditures−Depreciation)−(1−DR)(Investmentinworkingcapital)

with: Capitalexpenditures = FCInv = 35% , Depreciation =9% , DR = debt ratio = 20%, Investmentinworkingcapital = WCInv = 6%

I don’t know how to derive this formula. In fact, I just know that

FCFE=Net income + NonCashCharge - FCInv - WCInv

So, I suppose

NonCashCharge = DR * FCInv + Depreciation* (1−DR) + DR * WCInv

But why???

Many thanks in advance.

#2

The formula with the DR part in it is for a mature company - a combination of Debt and Equity which is equal to (1-Debt) are used to pay for the Investment in WC and FC.

So of the WC amount spent to buy Working Capital -> (1-DR) * WC is equity spend, while DR * WC is the Debt Spent (Net Borrowing Part).

When it comes to FC - you have a portion that you actually do not spend which is the Depreciation Part. So (1-DR)*(FC-Depr) = Equity Spend on FC, while DR*(FC-Depr) = Debt Spend (Net Borrowing).

So

Net Result =>

Equity Spending = WC * (1-DR) + (FC-DEPR) * (1-DR)

Debt Spend (Net Borrowing) = DR * WC + DR * (FC-Depr)

and Non Cash Charge = Depr

===

You add up the Equity Spend and the Debt Spend -> you end up with WC + FC

#3

So, there is the Net Borrowing which is equal to DR * WCInv + DR * (FCInv-Depr).

It’s clear now. Thank you!