## **Learning Outcomes**

By studying this article, you will be able to explain the core theories of capital structure, focusing on Modigliani and Miller’s (MM) propositions with and without tax. You will interpret the impact of gearing on firm value, the cost of capital, and the practical limits in applying theory. After reading, you should be able to discuss WACC behaviour, optimal capital structure, and evaluate MM’s assumptions for ACCA AFM.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand how capital structure theory informs financing decisions. Focus particularly on the following areas for your revision:

- The effect of gearing on the weighted average cost of capital (WACC) and company value
- The principles and conclusions of Modigliani and Miller (MM) propositions—both with and without tax
- Practical considerations and real-world limitations of capital structure theory
- The concept of optimal capital structure and how bankruptcy risk or agency costs influence it
- Application of MM formulae in numerical scenarios to evaluate capital structure choices

## **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. Which of the following, according to MM (without tax), is true regarding the value of a firm when gearing increases?
   a) The firm’s value increases.
   b) The firm’s value decreases.
   c) The firm’s value remains unchanged.
   d) The firm’s value depends on project risk.

2. What effect does introducing corporate tax have in MM’s theory of capital structure?
   a) No effect on WACC.
   b) It increases the optimal proportion of equity.
   c) It makes higher gearing more attractive by reducing WACC.
   d) It makes agency problems disappear.

3. True or false? In MM theory without tax, WACC is affected by the company’s capital structure.

4. Calculate the post-tax WACC for a company funded 60% by equity (cost 12%) and 40% by debt (cost 6%) with tax at 25%.

5. Briefly explain a practical limitation of MM’s theoretical conclusions about gearing.

## **Introduction**

Capital structure theory addresses the impact of the mix of debt and equity on a company’s value and cost of capital. This question is central to financial management because financing choices determine both the risk and return profile facing shareholders. Modigliani and Miller (MM) developed propositions that form the starting point for examining this area. You are expected to explain and apply MM’s theory both with and without corporate taxation, as well as evaluate their assumptions in light of real-world factors such as bankruptcy risk, tax exhaustion, and agency issues.

> **Key Term: capital structure**
> The mix of debt and equity used to finance a company’s assets.

## **MM PROPOSITIONS WITHOUT TAX**

Modigliani and Miller’s first proposition, in a world without tax, is that a company’s value is not affected by its gearing. Their reasoning is that, in perfect capital markets, investors can create their own gearing through personal borrowing (“homemade gearing”), so the choice of capital structure by the company becomes irrelevant.

> **Key Term: MM Proposition I (no tax)**
> The value of a firm is independent of its capital structure if there are no taxes or other market imperfections.

Expanding on this, MM’s second proposition states that, although using more debt increases the risk (and therefore required return) to equity holders, the benefit from lower-cost debt is exactly offset by the increase in equity cost, so WACC remains unchanged.

> **Key Term: weighted average cost of capital (WACC)**
> The average rate of return required by all providers of a company’s capital, weighted by their market values.

### **Worked Example 1.1**

A company has two financing options:

- Option A: 100% equity
- Option B: 60% equity, 40% debt (interest rate equals risk-free rate)

Assume all capital markets are perfect and no taxes exist. What happens to company value and WACC if Option B is chosen rather than Option A?

> **Answer:**
> According to MM (no tax), firm value and WACC remain unchanged. Cheaper debt is offset by greater risk to equity, pushing up required equity returns so overall WACC is constant.

### **Exam Warning**

> Be careful: In the exam, do not conclude that increasing debt in a no-tax environment automatically lowers WACC. MM’s theory requires you to show that WACC is constant if their assumptions hold.

## **MM PROPOSITIONS WITH TAX**

When considering corporate tax, MM revised their theory. Interest payments are tax-deductible, creating a “tax shield.” The benefit of this shield means that the total value of a geared firm rises as borrowing increases.

> **Key Term: tax shield**
> The reduction in taxable profits due to the deductibility of interest on debt, resulting in a lower effective cost of debt for companies.

This leads to the conclusion under MM with tax that a company’s value increases with more debt, and WACC falls as gearing rises. Their formula for the value of a geared firm ($V_g$) is:

$$V_g = V_u + T \times D$$

Where:

- $V_g$ = value of the geared firm
- $V_u$ = value of an equivalent ungeared firm
- $T$ = corporate tax rate
- $D$ = market value of debt

Similarly, the MM formula for the cost of equity with tax is:

$$k_e = k_{ei} + (1 - T)(k_{ei} - k_d)\frac{D}{E}$$

### **Worked Example 1.2**

A company is valued at \$500m if it had no debt (unleveraged). It introduces \$200m of debt, and the corporate tax rate is 30%. What is the theoretical total value of the firm after adding the debt under MM with tax?

> **Answer:**
> Tax shield = \$200m \times 30\% = \$60m$. Therefore, total value = \$500m + \$60m = \$560m$.

### **Revision Tip**

> Always include the tax shield in valuation and WACC calculations when working with MM theory under corporate tax. The difference is significant and frequently tested.

## **PRACTICAL LIMITATIONS**

While MM provide logical building blocks, their strict assumptions rarely hold in reality. Problems arise from:

- Bankruptcy risk: Lenders demand higher returns or restrict lending as gearing rises, increasing the real cost of debt at high gearing.
- Agency costs: Managers may have different goals than shareholders or debt holders, affecting risk.
- Tax exhaustion: If companies become highly geared, they may not have enough taxable profits to benefit from the full tax shield.
- Debt covenants: Lenders can impose restrictions, reducing financial flexibility.

> **Key Term: optimal capital structure**
> The combination of debt and equity that minimizes WACC and maximizes firm value, considering real-world factors like default risk.

In practice, firms tend to target a moderate gearing—balancing debt’s tax benefits with the rising costs related to financial distress.

### **Worked Example 1.3**

A firm raises increasing amounts of debt. Initially, WACC falls as cheap debt is used. Eventually, lenders demand higher risk premiums and non-interest cash costs such as covenants rise. At high gearing, the cost of both debt and equity rises, WACC starts to climb, and company value may fall. Does the MM with-tax prediction of an ever-decreasing WACC hold in reality?

> **Answer:**
> No. In practice, WACC falls at first but rises again at high gearing. Most companies seek a point where tax and risk effects are balanced—this is their target or “optimal” capital structure.

## **Summary**

- MM’s no-tax theory predicts capital structure irrelevance for firm value and WACC in perfect markets.
- Introducing tax (interest deductibility) means firm value should rise with gearing, and WACC should fall as more debt is used.
- Real-world issues (bankruptcy, tax exhaustion, agency costs) mean that beyond a certain point, increasing debt increases total cost of capital.
- Most companies set a “target” capital structure, balancing risk and tax shields.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain MM’s capital structure propositions with and without tax
- Describe WACC behaviour as gearing increases under both versions
- Calculate the impact of a tax shield on firm value
- Identify real-world constraints limiting gearing
- Outline the optimal capital structure concept

## **Key Terms and Concepts**

- capital structure
- MM Proposition I (no tax)
- weighted average cost of capital (WACC)
- tax shield
- optimal capital structure

Capital structure theory and practice - MM propositions with and without tax