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Lesson 72

Calculating Interest Rate and Currency Swap Payments

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Introduction

In our last lesson, we delved into the world of options and established the fundamental no-arbitrage relationship of put-call parity. We're now continuing our exploration of derivatives by turning our attention to another major class of financial instruments: swaps.

This lesson addresses a key part of the CB1 syllabus: calculating the cash flows involved in swaps. We will focus on two principal types: interest rate swaps and currency swaps. You will learn how these agreements are structured and, most importantly, how to compute the precise cash flows that are exchanged between the counterparties on each settlement date. This is a highly practical skill, aligning with your preference for numerical application, and is essential for understanding how companies manage financial risk.

1. Interest Rate Swaps (IRS)

An interest rate swap is an agreement between two parties to exchange interest payments on a specified notional principal amount for a defined period. The crucial feature is that one party pays a fixed interest rate while the other pays a floating (or variable) rate. The principal itself is 'notional'—it's only used to calculate the interest payments and is never actually exchanged.

Why would companies do this? There are two main reasons:

  1. Hedging: A company with a floating-rate loan might worry that interest rates will rise. It can enter a swap to pay a fixed rate, effectively converting its unpredictable floating-rate liability into a stable, predictable one.
  2. Comparative Advantage: One company might have access to cheaper fixed-rate financing, while another has access to cheaper floating-rate financing. If their needs are the opposite of what they can get cheaply, they can borrow in their advantageous market and then use a swap to exchange the payments, resulting in a net saving for both.

The following video provides an excellent introduction to the mechanics of an interest rate swap and presents a simple, clear method for calculating the outcomes.

Interest rate swaps finally made easy! In under 20 minutes, learn Andrew's simple 4-step method

The video "Interest rate swaps finally made easy!" by Andrew Mower gives a great overview and then lays out a structured, 4-step method for the calculations.

First, watch the introduction from the beginning up to the end of the analogy to get an intuitive feel for why swaps exist. The KFC voucher analogy is a simple but effective way to think about two parties with complementary but mismatched advantages. Next, watch the segment from the 4-step method. This section outlines a clear, repeatable process for setting up and solving swap problems, which will be the foundation for our calculations.

Calculating Net Payments in an IRS

As the video explained, the power of a swap lies in the potential for mutual benefit. The core calculation you need to master for your exam is determining the payments each party makes and, ultimately, the single net payment that is exchanged on a settlement date.

Rather than both parties sending each other money, the payments are netted. Only the party that owes more makes a payment, equal to the difference between the two obligations.

The following study note provides a formal definition and a concise example of this netting process.

Financial Mathematics Study Note Interest Rate Swaps

This note from the Society of Actuaries (SOA) provides precise definitions and clear examples.

First, quickly read the section "Definitions" to solidify your understanding of terms like counterparties, notional principal amount, and settlement dates. Then, focus on Section 5, "Net Payments". Read this section carefully, paying close attention to Example 8, which shows a straightforward calculation of a net swap payment, and Example 9, which demonstrates how the swap affects the company's overall net interest payment when an underlying loan is involved.

As illustrated in Example 9, by entering the swap, Chloe successfully transformed her floating-rate loan payment into a predictable fixed payment of $17,500 each year, regardless of how LIBOR moved. This is the practical purpose of hedging in action.

Let's now apply the full 4-step method from the video to a complete numerical problem.

Interest rate swaps finally made easy! In under 20 minutes, learn Andrew's simple 4-step method

This is the worked example from Andrew Mower's video, applying the 4-step method to Fredco and Gregco.

Watch the detailed walkthrough from the example. Follow each step of the calculation: Setting up the rates table. Calculating the total saving and splitting it. Determining each company's target rate. Arranging the swap payments to show how the target rates are achieved. Notice how the final table balances, ensuring that both companies end up paying their desired type of interest at a lower effective rate than they could have achieved on their own.

2. Currency Swaps (Cross-Currency Swaps)

A currency swap, or cross-currency swap (XCCY), is similar in spirit to an IRS but with two fundamental differences:

  1. The cash flows being exchanged are in different currencies.
  2. The principal amounts are exchanged at the beginning of the swap and then re-exchanged at the end.

The diagram below shows the typical structure of a currency swap.

This diagram illustrates the three key stages of a cross-currency swap. 1: The initial exchange of notional principals (e.g., Party A gives €420M, Party B gives \$500M). 2: Periodic interest payments in the respective currencies. 3: The final exchange where the original notional amounts are returned.

Why Use a Currency Swap?

Like an IRS, currency swaps are often driven by comparative advantage. A US company might be able to borrow cheaply in USD but needs to fund a project in Europe, requiring EUR. A European company might face the opposite situation. By borrowing in their respective domestic markets and then swapping the proceeds and interest obligations, both can effectively borrow in their desired foreign currency at a lower rate.

The diagram below shows how a currency swap connects two separate loan agreements.

This diagram shows two companies leveraging their borrowing advantages. Company A borrows locally in USD and Company B borrows locally in BRL. They then use a currency swap to exchange these funds and interest obligations, allowing Company A to effectively get BRL financing and Company B to get USD financing, likely at better rates than they could get directly.

Calculating Currency Swap Cash Flows

Calculating the cash flows in a currency swap is straightforward. Unlike an IRS where interest payments are typically netted, in a currency swap the periodic interest payments are usually paid in full by each party, because they are in different currencies.

Let's consider an example based on the structure in the first diagram.

Scenario:

  • Party A (a US firm) and Party B (a European firm) enter into a 5-year currency swap.
  • Notional Principals: USD 500 million and EUR 420 million. At inception, Party A gives Party B €420M, and Party B gives Party A $500M.
  • Interest Rates: Party A agrees to pay a fixed 5% annual interest rate in EUR to Party B. Party B agrees to pay a fixed 4% annual interest rate in USD to Party A.

Calculation of Annual Interest Payments:

  1. Party A's Payment (in EUR):
    This is based on the EUR notional amount.
    Payment = 5% of €420 million = €21 million.
    Party A pays €21 million to Party B each year.

  2. Party B's Payment (in USD):
    This is based on the USD notional amount.
    Payment = 4% of $500 million = $20 million.
    Party B pays $20 million to Party A each year.

Summary of Cash Flows:

  • At Inception (Year 0):
    • Party A pays €420M to Party B.
    • Party B pays $500M to Party A.
  • Each Year (Years 1-5):
    • Party A pays €21M to Party B.
    • Party B pays $20M to Party A.
  • At Maturity (End of Year 5):
    • The principal amounts are re-exchanged.
    • Party A pays $500M back to Party B.
    • Party B pays €420M back to Party A.

The key calculation is simply applying the agreed-upon interest rate to the corresponding currency's notional principal for each period.

Conclusion

In this lesson, we have demystified the mechanics of interest rate and currency swaps, focusing on the practical calculation of the cash flows involved. These instruments are foundational tools in corporate finance for managing risk and optimizing funding costs.

Key Takeaways:

  • Interest Rate Swap (IRS): An agreement to exchange fixed-rate for floating-rate interest payments on a notional principal in a single currency. Only the net difference in interest is paid on each settlement date.
  • Currency Swap (XCCY): An agreement to exchange principal and interest payments in two different currencies. The principals are physically exchanged at the start and returned at the end. The periodic interest payments are typically paid in full, not netted.
  • Calculation: The core of the calculation for both swap types is applying the agreed-upon rates (fixed or floating) to the correct notional principal for the period.

Now that you can calculate the cash flows generated by these swaps, our next lesson will explore their strategic application. We will demonstrate precisely how companies use forwards, futures, and swaps to hedge currency, interest rate, and equity price risks, building directly on the numerical skills you've developed today.