## **Learning Outcomes**

After reading this article, you will be able to calculate and explain the market value and yield to maturity of bonds, both redeemable and irredeemable, for ACCA FM exam purposes. You will also learn how to evaluate the features of convertible (hybrid) instruments, understand coupon rates, and apply post-tax cost of debt formulae in exam-style scenarios.

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

For ACCA Financial Management (FM), you are required to understand how bonds and hybrid instruments are valued and how their yields are determined. Specifically, you should be confident with:

- Defining the main types of debt and hybrid (convertible) instruments
- Calculating the market value of redeemable and irredeemable bonds (loan notes/debentures)
- Determining the required return (yield to maturity) for both investors and companies
- Explaining the effect of tax on the cost of debt
- Calculating the cost of hybrid instruments such as convertible bonds
- Understanding the difference between coupon rate and yield to maturity
- Recognising the features and implications of convertible debt as a hybrid security

## **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 primary difference between the coupon rate and the yield to maturity of a bond?
2. How is the market value of irredeemable debt calculated?
3. Briefly explain how tax affects the cost of debt to the company.
4. What makes a convertible bond a “hybrid” instrument for exam purposes?
5. True or false? Investors always receive the coupon rate as their required return.

## **Introduction**

Debt instruments and hybrids like convertible loan notes are central to business finance and often tested in the ACCA FM exam. Understanding how to value these securities and interpret their yields is essential when calculating the cost of capital or evaluating sources of finance.

This article covers the pricing techniques for redeemable and irredeemable bonds, explains the yield to maturity concept, and examines key hybrid instruments such as convertibles.

> **Key Term: bond (loan note, debenture)**
> A long-term debt security issued by a company, usually with a fixed interest (coupon) and a specified repayment date.

## **BOND FEATURES AND TERMINOLOGY**

Bonds (also called loan notes or debentures) are issued by companies to raise long-term finance. Investors pay the market price and receive periodic coupon payments until receive their principal back at redemption.

> **Key Term: coupon rate**
> The fixed annual interest paid on a bond, expressed as a percentage of its nominal (face) value.
>
> **Key Term: yield to maturity (YTM)**
> The annualised return an investor expects if they purchase a bond at its current market price and hold it to redemption.
>
> **Key Term: irredeemable debt**
> A bond with no fixed maturity date; coupon payments are made indefinitely.
>
> **Key Term: redeemable debt**
> A bond with a fixed date on which the nominal value is repaid.

## **BOND PRICING PRINCIPLES**

The market value of a bond is based on the present value of all expected future cash flows, discounted at the investor’s required return (YTM). The company’s cost of debt generally reflects the yield to maturity, adjusted for tax.

### Valuing Irredeemable Debt

An irredeemable bond pays interest in perpetuity and, unless tax is involved, its market value is:

$$
MV = \frac{\text{Annual coupon}}{\text{Investor's required return}}
$$

### Valuing Redeemable Debt

A redeemable bond is valued as the present value of all future coupon payments plus the present value of its redemption payment:

$$
MV = \sum \left( \frac{I}{(1 + r)^t} \right) + \frac{R}{(1 + r)^n}
$$

Where:

- $I$ = annual coupon
- $r$ = yield to maturity (YTM)
- $t$ = time period
- $R$ = amount repaid (often nominal value)
- $n$ = years to redemption

For exam purposes, YTM is often found using trial and error or interpolation.

> **Key Term: redemption premium**
> Any amount paid above nominal value when a bond is repaid.

## **THE COST OF DEBT: INVESTOR AND COMPANY VIEWPOINTS**

The investor’s return is the YTM, calculated as above. For the company, interest payments are typically tax deductible, so the post-tax cost is used when calculating the weighted average cost of capital (WACC):

$$
\text{Post-tax cost of debt} = \text{YTM} \times (1 - T)
$$

Where $T$ is the tax rate.

### **Worked Example 1.1**

A company issues \$100 nominal, 8% irredeemable bonds, trading at \$80 ex-interest. Corporation tax is 25%. What is:

- (a) the return required by debt holders?
- (b) the company’s post-tax cost of debt?

> **Answer:**
> (a) \$8 \div 80 = 10\%$ (pre-tax yield)
> (b) \$8 \times (1 - 0.25) \div 80 = 6\%$ (post-tax cost of debt)

### **Worked Example 1.2**

Redeemable loan notes (\$100 nominal, 6%, redeemable in 3 years at par) are trading at \$95. Calculate the approximate yield to maturity to the investor.

> **Answer:**
> Use PV tables or interpolation. Discount the annual \$6 coupon and \$100 redemption at different rates to equate the PVs to \$95, then interpolate between them to find YTM. (Workings omitted for brevity.)

### **Exam Warning**

> Always use ex-interest (or ex-coupon) market prices in bond valuation calculations unless otherwise specified in the exam.

## **HYBRID INSTRUMENTS: CONVERTIBLES AND WARRANTS**

Some securities combine features of both debt and equity and are known as hybrids.

> **Key Term: convertible bond**
> A bond giving the holder the right, but not the obligation, to convert into a fixed number of ordinary shares, usually at set times and predetermined prices.
>
> **Key Term: warrant**
> A separate security granting the holder the right to purchase shares at a specified price before a set date.

Convertible bonds typically pay a lower coupon than similar straight debt, reflecting the value of the future conversion option.

At maturity, holders choose between conversion and redemption, selecting whichever is more valuable. The cost of convertible debt to the company must take account of the conversion value if conversion is likely.

### **Worked Example 1.3**

A \$100, 5-year, 5% convertible is redeemable at par or can be exchanged for 20 shares. Market share price at maturity is expected to be \$6. The bond currently trades at \$98 and the company pays 30% tax. What is the post-tax cost of this debt if conversion is expected?

> **Answer:**
> Expected conversion value = \$6 × 20 = \$120. Use PV of post-tax coupons and the \$120 conversion value, discounting at estimated rates, then interpolate for the IRR.

## **Summary**

Bond pricing involves discounting all future payments by the investor’s required yield. The yield to maturity may differ from the coupon rate if market price is above or below nominal value. For the company, after-tax cost of debt is required for capital budgeting. Hybrids like convertibles must be carefully evaluated according to their likely redemption or conversion outcomes.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Defining bonds, coupon rates, yield to maturity, irredeemable and redeemable debt
- Calculating market value and YTM of bonds for both investor and company viewpoints
- Recognising the effect of tax on the post-tax cost of debt
- Explaining the unique risks and valuation of convertible bonds and warrants
- Understanding the distinction between coupon rate and yield to maturity

## **Key Terms and Concepts**

- bond (loan note, debenture)
- coupon rate
- yield to maturity (YTM)
- irredeemable debt
- redeemable debt
- redemption premium
- convertible bond
- warrant

Debt and hybrid instruments - Bond pricing and yield to maturity