## **Learning Outcomes**

After reviewing this article, you will be able to:

- Define and explain the free cash flow (FCF) approaches to equity valuation as required for ACCA Financial Management (FM).
- Distinguish between free cash flow to equity (FCFE) and free cash flow to the firm (FCFF) models.
- Calculate business and equity values using FCF models and apply them to exam-style scenarios.
- Recognise the situations where these valuation methods are most appropriate and understand key exam considerations.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand the main approaches to equity valuation—especially those based on free cash flow. It is important to be able to:

- Discuss and apply cash flow-based models for valuing shares, including the use of the discounted cash flow basis.
- Calculate the value of a business or equity using free cash flow methods, including the distinction between free cash flow to equity (FCFE) and free cash flow to the firm (FCFF).
- Identify the circumstances where a free cash flow approach is appropriate.
- Discuss the strengths and weaknesses of free cash flow valuation methods.
- Apply these models in calculating values in exam scenarios, interpreting results accurately.

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. What is the main difference between free cash flow to equity (FCFE) and free cash flow to the firm (FCFF) approaches in equity valuation?
2. Which discount rate should you apply when valuing the whole firm using free cash flow models?
3. True or false? Free cash flow models can be used when firms do not pay dividends but have stable, predictable cash flows.
4. Briefly explain when you might use a free cash flow valuation approach instead of a dividend-based model.

## **Introduction**

Equity valuation is a core topic in ACCA Financial Management. While dividend valuation models are suited to companies with predictable dividend patterns, they fall short for firms that either do not pay dividends or retain much of their earnings for reinvestment.  
Free cash flow models—specifically free cash flow to equity (FCFE) and free cash flow to the firm (FCFF)—offer alternative ways to estimate the value of equity or the business as a whole, especially when the dividend approach is not viable or when changes in capital structure are expected.  
This article explains how to calculate, apply, and interpret free cash flow-based valuation methods in line with ACCA FM requirements.

## **FREE CASH FLOW VALUATION MODELS**

### Overview

Free cash flow models value a business by estimating and discounting the cash flows available to either the firm’s equity holders (FCFE approach) or all providers of capital (equity and debt—FCFF approach). These models are used particularly when:

- Dividend payments do not reflect the company’s actual distributable earning power.
- The firm retains most profits for business growth.
- The capital structure is likely to change in the future.
- You want to value the whole business (not just equity).

> **Key Term: free cash flow to equity (FCFE)**
> The residual cash flow that could be distributed to equity shareholders after accounting for all business expenses, tax, and payments to debt holders—with necessary adjustments for changes in working capital and capital expenditure.
>
> **Key Term: free cash flow to the firm (FCFF)**
> The cash flow generated by the firm's operations that is available to all providers of capital (both equity and debt), before deducting interest and after capital investments and working capital changes.

### FCFE vs FCFF—What’s The Difference?

- **FCFE** values equity directly. You discount FCFE at the cost of equity ($k_e$) to get the value of equity.
- **FCFF** values the entire firm. You discount FCFF at the weighted average cost of capital (WACC, $k_{wacc}$) to get the value of the business (firm value); then subtract the market value of debt to find the value of equity.

### Calculating Free Cash Flow

#### Step 1: Calculate FCFE

FCFE = Net income  
&ensp;&ensp; + Depreciation/Non-cash charges  
&ensp;&ensp; – Capital expenditure  
&ensp;&ensp; – Increase in working capital  
&ensp;&ensp; + Net new borrowing

Or, as a shortcut:

FCFE = Cash flow from operations – Capital expenditure – Net debt repayments

#### Step 2: Calculate FCFF

FCFF = EBIT × (1–Tax rate)  
&ensp;&ensp; + Depreciation/Non-cash items  
&ensp;&ensp; – Capital expenditure  
&ensp;&ensp; – Increase in working capital

Alternatively, start from operating profit before interest and tax—this gives a pre-financing cash flow.

> **Key Term: weighted average cost of capital (WACC)**
> The average rate of return required by all providers of finance (equity and debt) in proportion to their market values, used to discount free cash flows to the firm.

### Discounting to Find Value

- For FCFE: Value of equity = Present value (PV) of all forecast FCFE discounted at $k_e$.
- For FCFF: Total firm value = PV of all forecast FCFF discounted at WACC ($k_{wacc}$).  
  &ensp;&ensp;Then: Equity value = Firm value – Market value of debt.

#### Perpetuity Model

When free cash flows are expected to grow at a constant rate ($g$):

- FCFE Model: $ \text{Equity Value} = \dfrac{\text{FCFE}\_1}{k_e - g} $
- FCFF Model: $ \text{Firm Value} = \dfrac{\text{FCFF}_1}{k_{wacc} - g} $

Where $_1$ denotes the expected free cash flow in one year’s time.

### When to Use Each Model

Use FCFE:

- When dividends do not match the firm's true payout ability (e.g., high retentions).
- When valuing the equity directly.

Use FCFF:

- When valuing the entire business (frequently for takeovers, mergers or when assessing changing capital structures).
- When both debt and equity holders are paid from the business' cash flows.

### **Worked Example 1.1**

Valiant Ltd has the following information:

- Net income (after tax): \$2,100,000
- Depreciation: \$400,000
- Capital expenditure: \$500,000 (annual, no growth)
- Increase in working capital: \$100,000 per year
- Net new debt raised: \$0 (no change in debt)
- Cost of equity: 12%
- Expected perpetual cash flow (no growth)

Calculate the value of equity using FCFE.

> **Answer:**
> FCFE = \$2,100,000 + 400,000 – 500,000 – 100,000 + 0 = \$1,900,000$  
> Value of equity = \$1,900,000 / 0.12 = \$15,833,333$

### **Worked Example 1.2**

Suppose Orion plc generates \$2,500,000 yearly in FCFF, forecast to grow at 3% per year. The company’s WACC is 9%. Market value of its debt is \$8,000,000.

Calculate:
a) Total firm value  
b) Value of equity

> **Answer:**
> a) $ \text{Firm Value} = 2,500,000 / (0.09 - 0.03) = 41,666,667 $  
> b) Equity value = \$41,666,667 - 8,000,000 = \$33,666,667$

### **Exam Warning**

> Using the wrong discount rate is a common exam mistake.  
> For FCFE methods, always discount at the cost of equity ($k_e$). For FCFF (firm value) methods, always discount at WACC.

### **Revision Tip**

> Practice converting between FCFF and FCFE, especially when exam questions provide net income, capital expenditure, and changes in working capital. Remember: FCFF is before finance payments; FCFE is after debt servicing.

## **Summary**

Free cash flow valuation is essential when dividends don’t reflect true earning power, when companies retain most profits, or when valuing entire firms.

- FCFE discounts cash available to equity holders at the cost of equity to value equity.
- FCFF discounts total firm cash flows at the WACC and subtracts debt to find equity value.  
  These models are particularly suited to companies with non-standard dividend policies or undergoing capital structure changes.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define and distinguish free cash flow to equity (FCFE) and free cash flow to the firm (FCFF).
- Calculate equity value and firm value using free cash flow models.
- Identify appropriate discount rates (cost of equity for FCFE, WACC for FCFF).
- Apply perpetuity (growth) models in free cash flow valuation.
- Recognise when to use each free cash flow valuation approach.
- Understand common pitfalls and typical exam requirements for these models.

## **Key Terms and Concepts**

- free cash flow to equity (FCFE)
- free cash flow to the firm (FCFF)
- weighted average cost of capital (WACC)

Equity valuation models - Free cash flow approaches