# FCFE question using forecasting

Do Pham is evaluating Phaneuf Accelerateur by using the FCFF and FCFE valuation approaches. Pham has collected the following information (currency in euros):

• Phaneuf has net income of €250 million, depreciation of €90 million, capital expenditures of €170 million, and an increase in working capital of €40 million.
• Phaneuf will finance 40% of the increase in net fixed assets (capital expenditures less depreciation) and 40% of the increase in working capital with debt financing.
• Interest expenses are €150 million. The current market value of Phaneuf’s outstanding debt is €1,800 million.
• FCFF is expected to grow at 6.0% indefinitely, and FCFE is expected to grow at 7.0%.
• The tax rate is 30%.
• Phaneuf is financed with 40% debt and 60% equity. The before-tax cost of debt is 9%, and the before-tax cost of equity is 13%.
• Phaneuf has 10 million outstanding shares.

Using the FCFF valuation approach, estimate the total value of the firm, the total market value of equity, and the per-share value of equity.

My question is regarding using the forecasting method to derive FCFE and consequently the market value of equity.

My calculations using this method is as below,

FCFE = NI - [(1-DR)(Capex-Dep)] - [(1-DR)(Change in WC)] = 250 - (0.6)(170-90) - (0.6)(40) = 178

Market value of equity = [(178)(1.07)]/(0.13-0.07) = 3,174

May I check why the equity value using the forecasting method differs from the prescribed solution of 3966?

Noted there are no non cash charges other then depreciation in this question which would have made the forecasting method inaccurate.

Additionally, if we use the equity ratio of 60% X firm value (0.6 X 5766 = 3460), we get a different value from the answer as well.

Any inputs would be greatly appreciated!

Your calculation is FCFE, but the question specifically tells you to use the FCFF approach.

The reason these result in different answers is because:

1. The discount rates for FCFF and FCFE will be different. With FCFF you are discounting using WACC (since FCFF represents both debt and equity capital), meanwhile FCFE will discount only with the cost of equity.
2. FCFF and FCFE have different projected growth rates. This will also affect the discount rate of (r - g).
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Appreciate the input.

Since FCFE can be derived from FCFF itself, should we not be able to use the different methods to calculate FCFE and derive at the same value?

A major shortcoming of the Discounted Cash Flow approach (including with FCFF/E) is that small changes in r and g can wildly change the end result, that’s why there are separate models for FCFF and FCFE.
Even if the growth rate for FCFF and FCFE were the same, it is very unlikely if not impossible for the cost of equity to be the exact same as the WACC.

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