# Free Cash Flow Valuation | FCFE from NI using different formulas give different answer!

Kaplan Qbank Question ID 1209806 - Q 36 is to calculate FCFE from Net income.
FCFE from Net Income has two formulas that must give same answer

Formula 1: FCFE = NI + NCC - FCInv - WCInv + net borrowing
Formula 2: FCFE = NI - ((1-DR)(FCInv - Dep) - ((1-DR)WCInv), given that DR = Debt/Assets

The answer is given using formula 2 and the answer is 3.8.
However, if you try to solve the question using formula 1 you’ll get different answer (which is 3.35)!!! why!!!

The given data:

• Earnings per share = €4.50.
• Capital Expenditures per share = €3.00.
• Depreciation per share = €2.75.
• Increase in working capital per share = €0.75.
• Debt financing ratio = 30.0%.
• Cost of equity = 12.0%.
• Cost of debt = 6.0%.
• Tax rate = 30.0%.
• Outstanding shares = 100 million.
• New debt borrowing = €15.0 million.
• Debt repayment = €30.0 million.
• Interest expense = €7.1 million.
Calculate FCFE for the base year

If you want to reconcile the answers with Formula 1, then just ignore the New debt borrowing and debt repayment.

Earnings = €450 mil
FCInv = €300 mil
Depreciation = €275 mil
WCInv = €75 mil

Borrowing to fund net CAPEX and WCINV
= 30\% \times (300 ~mil - 275 ~mil) + 30\% \times 75 ~mil
= 7.5 ~mil + 22.5 ~mil
= 30 ~mil

So, to ensure the debt ratio remains at 30%, the Net borrowing is \$30 million (inclusive of the new debt borrowing of 15 mil and debt repayment of 30 mil).

Formula 1:
FCFE = NI + NCC - FCInv - WCInv + Net Borrowing
FCFE = 450 + 275 - 300 - 75 + 30
FCFE = 380 million

Thank you, but how should I come up with the idea of ignoring the given data regarding the net borrowing which is (-15), and do the above calculation?!! What’s the justification?? Do you think the question is poorly written? I mean in the exam if anyone encounters such problem, how come they will dare to ignore given data as you suggest!

My bad. Poor choice of words.

My explanation above was just to reconcile the figures between Formula 1 and 2.

Formula 2 assumes that Net Borrowing will only involve the borrowing to fund (FCInv - Dep) and WCInv, and maintaining the debt ratio; and assume there are no other new debt issued/repayment. You can say the question is written poorly.

You sure you didn’t leave out any part of the question that could have provided more information?

This part maybe provide related info: “The financial leverage for the firm is expected to be stable. Hiller uses IFRS accounting standards and records interest expense as cash flow from financing (CFF).”

Okay, that means to maintain the debt financing ratio at 30%.

If you refer to page 312 of the Volume 4 textbook, it states:

By assuming a target DR, we eliminated the need to forecast net borrowing and can use the expression

Net borrowing = DR(FCInv – Dep) + DR(WCInv)

By using this expression, we do not need to forecast debt issuance and repayment on an annual basis to estimate net borrowing.

So, in maintaining the financial leverage (which is to maintain the debt financing ratio of 30%), we just use: 30% x (FCInv - Dep) + 30% x WCInv.

That’s very clear now. Thank you so much!

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