## **Learning Outcomes**

After studying this article, you will be able to distinguish between the required return for debt providers and the actual cost of debt to a company after tax. You will understand how to calculate the after-tax cost for both irredeemable and redeemable debt, explain the impact of weighting choices (book vs. market values) when determining the weighted average cost of capital (WACC), and apply these concepts in investment appraisal calculations.

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

For ACCA Financial Management (FM), you are required to understand how to determine the cost of debt and apply WACC in investment appraisal. This includes:

- Calculate the cost of irredeemable and redeemable debt, accounting for tax relief
- Distinguish between pre-tax and after-tax cost of debt to the company
- Explain the impact of tax relief on WACC and investment appraisal discount rates
- Select and justify appropriate weighting methods (book value vs. market value) when calculating WACC
- Calculate a company’s WACC using both book value and market value weightings

## **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. When calculating WACC, why is the after-tax cost of debt used rather than the pre-tax cost?
2. Which formula gives the post-tax cost of irredeemable debt to a company?
   a) $K_d = \frac{I}{MV}$
   b) $K_d (1 - T) = \frac{I (1 - T)}{MV}$
   c) $K_d = \frac{I (1 + T)}{MV}$
   d) $K_d = \frac{I}{MV (1 - T)}$
3. True or false? The use of market value weightings in WACC more accurately reflects what investors expect than book value weightings.
4. Briefly explain the main difference between redeemable and irredeemable debt when assessing its cost in the WACC calculation.

## **Introduction**

When companies raise debt finance, the true cost to the business differs from the headline coupon rate paid to debt holders. This article explains how corporation tax reduces the effective cost of debt, and how this affects the weighted average cost of capital (WACC)—a key discount rate for investment appraisal. You will also see why the way weights are chosen (book or market values) impacts the relevance of the WACC calculation.

> **Key Term: Cost of debt**
> The return required by debt holders, adjusted for the tax benefit a company receives from being able to deduct interest payments when calculating taxable profit.
>
> **Key Term: Weighted Average Cost of Capital (WACC)**
> The average rate a company expects to pay for using various sources of long-term finance, weighted by their proportions, incorporating the after-tax cost of debt.

## **The After-tax Cost of Debt**

Interest paid to debt holders is a tax-deductible expense for companies. This reduces the firm's actual financing cost below the interest payment received by investors.

### Irredeemable Debt

For debt that is never repaid (perpetuity), the pre-tax cost to the company is:

$$K_d = \dfrac{I}{MV}$$

Where:

- $K_d$ = required return (yield) for debt holders (pre-tax)
- $I$ = annual interest payment
- $MV$ = current market value of the debt

However, for the company, the after-tax cost is reduced by the tax relief on interest:

$$K_d (1 - T) = \dfrac{I (1 - T)}{MV}$$

Where $T$ is the corporate tax rate (as a decimal).

### Redeemable Debt

For debt that is repaid after a set period, the after-tax cost is found by calculating the internal rate of return (IRR) on post-tax interest payments and principal repayment, discounted to the current market price.

- Use after-tax interest payments ($I \times (1 - T)$) each year until redemption
- Discount these plus the redemption payment at the required IRR to match the market price

### **Worked Example 1.1**

A company has \$100,000 of irredeemable 8% loan notes quoted at \$90 per \$100 nominal. Corporation tax is 25%. What is:

a) The pre-tax cost of debt?
b) The post-tax cost of debt?

> **Answer:**
> a) Pre-tax cost: $K_d = \frac{8}{90} = 8.89\%$
>
> b) Post-tax cost: $K_d (1 - T) = \frac{8 \times (1 - 0.25)}{90} = \frac{6}{90} = 6.67\%$

### **Worked Example 1.2**

A company issues \$1,000,000 of 6% redeemable bonds, trading at \$95 per \$100 nominal, redeemable at par in 4 years. Corporation tax is 20%. Calculate the post-tax cost of debt using two discount rates (7% and 5%) and estimate the IRR.

> **Answer:**
> Calculate PV at both rates using after-tax interest (\$6 \times 0.8 = \$4.8 per year):
>
> At 5%: PV (4 years of \$4.8, plus \$100 at year 4) = [\$4.8 × 3.546] + [\$100 × 0.823] = \$17.03 + \$82.30 = \$99.33
>
> At 7%: [\$4.8 × 3.387] + [\$100 × 0.763] = \$16.26 + \$76.30 = \$92.56
>
> Market price is \$95. Use interpolation:
>
> IRR = 5% + [(\$99.33 - \$95)/(\$99.33 - \$92.56)] × (7% - 5%) = 5% + [4.33/6.77] × 2% ≈ 5% + 1.28% = 6.3%
>
> The post-tax cost of debt is approximately 6.3%.

## **Why Use the After-tax Cost in WACC?**

The tax saving on interest reduces the firm's true cost of debt. As WACC is used as a discount rate for project appraisal, failing to adjust for tax would overstate financing costs and could reject viable projects.

### **Exam Warning**

> Interest in WACC calculations must always be taken net of tax for debt, unless the exam question states the firm pays no tax. Forgetting this adjustment often leads to an inflated WACC.

## **Choosing Weightings in WACC Calculations**

When calculating WACC, the sources of finance are weighted according to their share in the company’s capital structure. The choice of weighting—market value or book value—affects the usefulness of the WACC as a discount rate.

### Market Value Weightings

- Reflect the current value that investors place on securities
- More accurately represent investor expectations and opportunity cost
- Market values change constantly, reflecting changes in perceived risk and income potential

### Book Value (Nominal Value) Weightings

- Based on historical accounting values from the balance sheet
- Do not reflect current investor expectations or market conditions
- May be required when market values are unavailable or in certain reporting contexts

> **Key Term: Market value weighting**
> Using current traded prices of debt and equity to determine capital structure proportions when calculating WACC.
>
> **Key Term: Book value weighting**
> Using nominal or accounting values from the statement of financial position to determine the proportions of finance sources for WACC.

### **Worked Example 1.3**

A company has the following capital structure:

- \$5m ordinary shares (market value \$2.50/share, nominal value \$1/share)
- \$2m 10% bonds (market value \$80 per \$100 nominal)

Calculate the WACC using both market value and book value weights. Cost of equity is 12%; post-tax cost of debt is 7% (tax already factored).

> **Answer:**
> Market value equity = \$5m × \$2.50 = \$12.5m; market value debt = \$2m × \$80/\$100 = \$1.6m
> Total = \$14.1m
>
> Market value weights: equity 88.7%, debt 11.3%
> WACC = (0.887 × 12%) + (0.113 × 7%) ≈ 10.44% + 0.79% = **11.23%**
>
> Book value weights: equity 71.4%, debt 28.6%
> WACC = (0.714 × 12%) + (0.286 × 7%) ≈ 8.57% + 2.00% = **10.57%**
>
> Note how the weighting choice changes WACC.

### **Revision Tip**

> Market value weightings are generally preferred for WACC, as they reflect current investor expectations and opportunity costs.

## **Summary**

The relevant cost of debt for a company is always net of tax, reflecting the actual cash outflow after corporation tax relief on interest. For irredeemable debt, use the after-tax interest divided by market price. For redeemable debt, use the IRR of post-tax flows. WACC must combine each source’s current after-tax cost, weighted by its proportion in the capital structure—ideally using market values for accuracy.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Distinguish pre-tax from after-tax cost of debt, and explain the impact of tax deductions for interest
- Calculate the after-tax cost of irredeemable and redeemable debt
- Understand why WACC uses post-tax cost of debt
- Identify the difference between market value and book value weightings in WACC
- Calculate WACC using both weighting methods—recognising when each is appropriate

## **Key Terms and Concepts**

- Cost of debt
- Weighted Average Cost of Capital (WACC)
- Market value weighting
- Book value weighting

Cost of debt and WACC - After-tax cost and weighting choices