## **Learning Outcomes**

After reading this article, you will be able to explain how the duration of debt instruments measures interest rate risk, distinguish between debt and hybrid instruments, and describe how these concepts affect financial management decisions. You will learn to calculate basic duration and interpret interest sensitivity for bonds and convertibles, with a focus on exam requirements.

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

For ACCA Financial Management (FM), you are required to understand the characteristics of debt and hybrid instruments as well as their sensitivity to interest rate changes. In particular, you should be able to:

- Explain the nature and features of debt and hybrid instruments (e.g., bonds, convertible bonds, preference shares)
- Describe how the duration of a debt instrument measures interest rate sensitivity
- Apply basic calculations and interpretations of duration to bonds and hybrid instruments
- Evaluate the impact of duration and interest sensitivity on the choice of finance and risk management in business decisions

## **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 instruments is typically most sensitive to changes in market interest rates?
   a) A short-term loan
   b) Long-term irredeemable debt
   c) A 5-year bond
   d) Equity share
2. What does the duration of a bond measure?
   a) The time to final maturity
   b) The average time to receive the bond’s cash flows
   c) The risk of default
   d) The coupon rate
3. True or false? A convertible bond is considered a hybrid instrument because it has features of both debt and equity.
4. Briefly explain why a bond with a longer duration presents higher price volatility to interest rate changes.
5. If interest rates rise, what happens to the market value of a fixed-rate bond, and why?

## **Introduction**

Corporate financial managers routinely issue or invest in debt instruments, such as bonds, and increasingly encounter newer hybrid securities with both debt and equity characteristics. Evaluating the risk and value of these instruments requires understanding not only their structure but also how their prices respond to interest rate changes. Duration is an essential tool for this purpose—a central concept in managing financing risk and making sound investment choices.

> **Key Term: Debt instrument**
> A financial obligation requiring periodic payments of interest and repayment of principal at maturity, typically in the form of bonds or loan notes.
>
> **Key Term: Hybrid instrument**
> A financial security combining features of both debt and equity, such as convertible bonds or preference shares.

## **Debt and Hybrid Instruments Explained**

Debt instruments—such as loan notes and bonds—are contractual obligations to pay interest and, eventually, repay the amount borrowed. Hybrids, like convertible bonds and preference shares, combine aspects of debt (fixed interest, priority in payments) with potential conversion or participation in equity.

### Features of Debt Instruments

- Fixed interest (coupon) payments
- Defined maturity date for principal repayment
- Ranks above equity on liquidation
- Market value affected by changes in interest rates

### Features of Hybrid Instruments

- Pay fixed or variable income (as with debt)
- Offer potential for conversion into shares (as with equity)
- May provide capital appreciation
- Price sensitivity depends on both debt and equity features

> **Key Term: Convertible bond**
> A type of hybrid instrument giving the bondholder the right to exchange the bond for a predetermined number of shares in the issuing company.

## **Interest Rate Sensitivity and Duration**

The market value of fixed-income securities changes inversely with market interest rates. The longer the maturity and lower the coupon, the more sensitive the security is to rate changes.

> **Key Term: Duration**  
> The weighted average time to receive all the cash flows (interest and principal) from a security, used as a measure of interest rate risk.

### Why Duration Matters

- **Low duration:** Price changes little when interest rates move (low risk)
- **High duration:** Price changes significantly with rate movements (higher risk)

> **Key Term: Interest rate risk**
> The risk that a security’s market value will fluctuate due to changes in prevailing interest rates.

### Calculating Duration (Modified and Macaulay Duration)

The most common measure for ACCA is the Macaulay Duration:

$$
\text{Duration} = \sum_{t=1}^N \left( \frac{\text{PV of cashflow}_t}{\text{Bond price}} \times t \right)
$$

Where:

- $ t $ = time period (years)
- $ N $ = total number of periods
- PV of cashflow_t = present value of the bond’s payment in year t, discounted at the market yield

Typically, the longer the bond’s remaining life, and the lower its coupon, the higher its duration.

### **Worked Example 1.1**

A company issues a \$100,000, 6% annual coupon bond with 5 years to maturity. The current yield to maturity is 6%. What is the Macaulay duration?

> **Answer:**
> Each annual coupon is \$6,000, and principal of \$100,000 is repaid at year 5. Discounting at 6%:
>
> PV of cashflows:
>
> - Year 1–4: PV = \$6,000 / (1.06)^t
> - Year 5: PV = (\$6,000 + \$100,000) / (1.06)^5
>
> Bond price = \$100,000 (since coupon rate = market rate)
>
> Duration ≈ 4.21 years (for a 5-year, 6% coupon bond at par)
>
> The duration is less than 5 years due to the annual coupon payments.

### **Worked Example 1.2**

Suppose a non-convertible preference share pays \$4 every year, is irredeemable, and the current market yield is also 4%. What is the duration?

> **Answer:**
> For irredeemable instruments (perpetuities), Duration = (1 + yield)/yield. Here, (1 + 0.04)/0.04 = 25 years.
>
> This is much higher than a redeemable bond, reflecting higher sensitivity to interest rates.

## **Interpreting Duration for Business Finance Decisions**

Duration provides a practical measure of risk: The higher the duration, the greater the percentage price change for a given change in yield.

For example, a bond with a duration of 5 years would see its value fall by approximately 5% if market interest rates rise by 1%.

Hybrid instruments such as convertible bonds are more complex. Initially, their duration is closer to that of straight debt; as they approach conversion into equity or redemption, their interest rate sensitivity changes, increasingly reflecting equity characteristics.

## **Managing Interest Rate Exposure**

Companies, pension funds, and investors use duration to align investment strategy with risk tolerance:

- Shorter duration for less exposure to rate changes (preferred if rising rates anticipated)
- Longer duration to seek higher yield but with higher risk (suitable if stable/falling rates are expected)
- Matching duration of assets and liabilities reduces net interest rate risk

### **Worked Example 1.3**

A company expects to make a large payment in 7 years. To minimize interest rate risk, should it invest in bonds with high or low duration?

> **Answer:**
> The company should match the duration of its assets to the timing of the liability, i.e., invest in bonds with duration close to 7 years. This immunizes the investment from interest rate changes.

### **Exam Warning**

> Be careful: Duration is not simply the average maturity. Bonds with the same maturity can have very different durations if their coupon rates differ.

### **Revision Tip**

> For ACCA FM calculations, you may be asked to estimate or compare duration and interest sensitivity—focus on the logic, knowing that longer terms and lower coupons increase duration.

## **Summary**

- Debt instruments and hybrids differ in structure and risk
- Duration measures how sensitive a bond’s price is to interest rate changes
- Longer duration means higher interest rate risk
- Hybrid instruments have variable sensitivity depending on their terms
- Managing duration helps reduce interest rate risk in financing decisions

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define and distinguish between debt and hybrid instruments
- Explain the concept and practical use of duration
- Relate duration to price sensitivity and risk
- Apply basic duration calculations to bonds and preference shares
- Understand duration’s role in financial management decisions
- Recognize the interest sensitivity of hybrid instruments

## **Key Terms and Concepts**

- Debt instrument
- Hybrid instrument
- Convertible bond
- Duration
- Interest rate risk

Debt and hybrid instruments - Duration and interest sensitivity basics