## **Learning Outcomes**

After reading this article, you will be able to define and compute the cost of debt, explain the weighted average cost of capital (WACC), distinguish WACC from marginal cost of capital, and select the appropriate rate for investment appraisal. You will learn when to use WACC, understand how the cost of debt affects WACC, and appreciate the impact on project and company valuations for ACCA FM.

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

For ACCA Financial Management (FM), you are required to understand the measurement and application of the cost of capital. In particular, this article covers:

- Calculation of the cost of debt, both before and after tax, for irredeemable and redeemable debt
- Calculation and interpretation of the weighted average cost of capital (WACC)
- Distinction between average (historic) and marginal (future) cost of capital
- When and how to use WACC and marginal cost of capital in investment appraisal
- The impact of tax on the cost of debt and WACC
- Implications of using WACC for project evaluation

## **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. Explain why the cost of debt to a company is usually lower than the return required by debt investors.
2. What is the main difference between calculating WACC and marginal cost of capital?
3. True or false? The post-tax cost of debt is always used when calculating WACC for investment appraisal.
4. Under what circumstances should the marginal cost of capital be used in project appraisal rather than the historic WACC?

## **Introduction**

Investment appraisal requires an accurate discount rate reflecting the company’s cost of finance. This means calculating not just the cost of equity, but also the cost of debt – and understanding how to combine these costs, usually by calculating the weighted average cost of capital (WACC).

A further consideration is whether to use the existing WACC or to calculate the marginal cost of capital for new investments. This article clarifies the calculation of the cost of debt, the mechanics and interpretation of WACC, and helps you decide between WACC and marginal cost for appraisal in the ACCA exam context.

> **Key Term: cost of debt**
> The effective annual percentage cost to a company for borrowing, typically after adjusting for tax relief on interest payments.
>
> **Key Term: weighted average cost of capital (WACC)**
> The overall average cost of the company's sources of finance, weighted by their proportional market values in the company’s capital structure.
>
> **Key Term: marginal cost of capital**
> The cost of raising one extra unit of capital, reflecting the current costs (and mix) of new equity and/or debt needed for an additional investment.

## COST OF DEBT—BASICS AND TAX IMPACT

Debt finance is attractive to firms because interest payments are tax-deductible, reducing the effective cost. When calculating the company’s cost of debt for inclusion in WACC, you must adjust for tax.

### Pre-tax vs Post-tax Cost

- **Investors** in debt require a return based on the stated coupon or prevailing market yields—this is the **pre-tax cost of debt**.
- **Companies** benefit from the tax deductibility of interest, resulting in a lower **post-tax cost of debt**. This is the relevant figure for WACC, as it reflects the actual cash outflow.

> **Key Term: post-tax cost of debt**
> The after-tax annual percentage cost to the company for servicing its debt, calculated as interest × (1 – tax rate).

### Irredeemable Debt

For debt with no maturity (perpetuity):

- **Pre-tax cost:**
  $$K_d = \frac{I}{MV}$$
  where $ I $ is annual interest (before tax), $ MV $ is the current market value.

- **Post-tax cost:**
  $$K_d(1-T) = \frac{I(1-T)}{MV}$$
  where $ T $ is the corporate tax rate.

### Redeemable Debt

For debt repayable at a future date, the annual cost is calculated as the internal rate of return (IRR) of all future cash flows (interest payments and redemption amount), using post-tax interest payments.

## THE WEIGHTED AVERAGE COST OF CAPITAL (WACC)

WACC is the average annual rate a company is expected to pay to all its long-term capital providers (both equity and debt), weighted by proportion in the current capital structure.

**Formula:**
$$\text{WACC} = \frac{V_e}{V_e+V_d}k_e + \frac{V_d}{V_e+V_d}k_d(1-T)$$
Where:

- $ V_e $, $ V_d $: market values of equity and debt
- $ k_e $: cost of equity
- $ k_d $: cost of debt
- $ T $: tax rate

### Calculating WACC: Key Points

- Use **market values**, not book values, to weight the costs.
- Always use the **post-tax cost of debt**—interest is tax-deductible.
- Preference shares, if present, are treated like debt for weighting.
- WACC represents the average rate paid on the existing mix of finance.

### When to Use Historic WACC

- The company's capital structure is not expected to change substantially.
- The new investment is similar in risk to existing projects.
- New finance will be raised in roughly the same proportions as existing funds.

### **Worked Example 1.1**

A company has:

- \$4 million equity (market value), cost of equity 12%
- \$2 million bonds (market value), 8% annual coupon, tax rate 25%
  Calculate WACC.

> **Answer:**
>
> 1. **Cost of debt (post-tax):**
>    $$8\% \times (1 - 0.25) = 6\%$$
> 2. **WACC:**
>    $$\frac{4}{6} \times 12\% + \frac{2}{6} \times 6\% = 8\% + 2\% = 10\%$$
>    The company's WACC is 10%.

## WACC VS MARGINAL COST OF CAPITAL

### What is Marginal Cost of Capital?

WACC reflects the **historic, weighted** average cost of all existing capital. Marginal cost of capital (MCC) refers to the **expected cost of raising the next dollar (or other currency unit) of new finance**.

- If new funds can be raised at the same rates and proportions as current funds, MCC ≈ WACC.
- If the company must offer higher returns (e.g., pay a higher rate to attract new capital, or issue new equity at a discount), the MCC will be higher.

### When is MCC Higher Than WACC?

- Existing sources of cheap finance have been exhausted (e.g., all retained earnings invested).
- Incremental debt requires a higher coupon rate due to increased company risk or market rates have risen.
- Additional equity must be issued at a lower price (e.g., rights issue discount, flotation costs), raising the effective cost.

### **Worked Example 1.2**

A company currently has a WACC of 9%. To fund a large new project, it must issue debt at 12% (post-tax) and new equity costing 15%. If the additional finance will be raised entirely through these new issues, what is the marginal cost of capital?

> **Answer:**
> The marginal cost of capital for the new funds is a weighted average of the new equity and debt costs (using the planned proportions). If new capital is 50% equity, 50% debt:
>
> - $15\% \times 0.5 + 12\% \times 0.5 = 7.5\% + 6\% = 13.5\%$
>   The MCC is 13.5%, much higher than the historic WACC.

## APPLICATION: WHICH RATE TO USE IN INVESTMENT APPRAISAL?

### Use Historic WACC If

- The size of the investment is small relative to the company's existing capital base.
- The company can raise funds for the project at existing rates and proportions.

### Use Marginal Cost of Capital If

- The investment is large and will require funds at higher rates than the existing capital.
- The project will cause a significant change in capital structure.
- The company must raise new finance with different risk/cost characteristics.

> **Key Term: investment appraisal discount rate**
> The rate used to discount expected project cash flows, reflecting the opportunity cost of capital for the project.

### **Exam Warning**

> Do not assume WACC is always the correct rate for new investments. For major projects or when new capital will be raised at new rates, you must justify and, if appropriate, use the marginal cost of capital in appraisals.

### **Revision Tip**

_Always adjust the cost of debt for tax in WACC calculations. The tax shield is a key component in reducing the effective cost to the company._

## **Summary**

- The cost of debt to the company must be calculated after tax.
- WACC is the average long-term cost of financing, weighted by market values.
- Marginal cost of capital is the cost to raise the next unit of finance, which may differ from current WACC.
- Use WACC for most investment appraisals, unless raising new funds at different costs—then use MCC.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define and calculate the cost of debt, adjusting for tax effects
- Calculate WACC using appropriate market values and costs
- Explain the difference between historic WACC and marginal cost of capital
- Recognise when to use WACC versus MCC in project evaluation
- Understand the impact of new financing costs on investment appraisal

## **Key Terms and Concepts**

- cost of debt
- weighted average cost of capital (WACC)
- marginal cost of capital
- post-tax cost of debt
- investment appraisal discount rate

Cost of debt and WACC - WACC vs marginal cost of capital