New Zealand Applied Business Journal
Volume 1, Number 1, 2002
A FLOW CHART APPROACH TO UNDERSTANDING INTEREST RATE SWAPS
Edwin D. Maberly
Professor of Finance
Department of Accountancy, Finance and Information Systems
University of Canterbury
Christchurch, New Zealand
e.maberly@afis.canterbury.ac.nz
Abstract: Over the last 20 years, financial engineers have created many value
enhancing financial products. Today the curriculum for intermediate finance papers
includes a discussion of both interest rate and currency swaps, but due to their
complexity, many students fail to grasp these concepts. This paper is pedagogical in
nature as its purpose is to enhance the understanding of interest rate swaps. The
methodology employs a flow chart approach incorporating both visual and verbal
teaching aids. A logical extension applies to currency swaps.
Key words: Finance, pedagogy, education.
INTRODUCTION
A swap is a transaction in which two counterparties exchange payment streams of different
character based on an underlying notional principal amount. For example:

One party desires a fixed rate loan, while the other desires a variable rate loan. In this
case, the potential exists for an interest rate swap between counterparties.

One party desires to exchange Australian dollars for New Zealand dollars at some time in
the future, while the other desires to exchange New Zealand dollars for Australian
dollars. In this case, the potential exists for a currency swap between counterparties.
STANDARD LOAN AGREEMENT
Jill and Tom are two businesspersons with operations based in Auckland, New Zealand (NZ),
and both are undertaking a business expansion to be financed by a 5-year $1,000 bank loan.
However, given the characteristics of each operation, Jill prefers a 5-year fixed rate loan,
while Tom prefers a 5-year variable rate loan. In other words, Jill’s preferred habitat is a
fixed rate loan, while Tom’s preferred habitat is a variable rate loan. The loan size is known
as the loan’s notional principle, which at $1,000 is identical for both counterparties. Jill and
Tom are currently negotiating with the Bank of New Zealand (BNZ), and the BNZ is willing
to make the 5-year $1,000 loan on terms depicted in Table 1—Jill and Tom’s preferred
habitat being in bold type. Henceforth, the NZ bank rate is abbreviated as NZBR.
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New Zealand Applied Business Journal
Jill
Tom
Fixed
10.00%
9.00%
Variable
4.05% + NZBR
3.25% + NZBR
Difference
1.00%
0.80%
Table 1
Both Jill and Tom accept the terms offered by BNZ. Internal BNZ documents indicate that
Tom is considered the better credit risk. For pedagogical reasons assume that the NZBR
does not fluctuate over the 5-year period, with the rate currently at 3.75%. However, in
reality the NZBR, which is a variable rate, could rise or fall considerably. Given these
assumptions, Table 2 outlines the interest payments paid by both counterparties.
Jill
Tom
Total
Total Amount Borrowed
1
$100
70
$170
2
$100
70
$170
3
$100
70
$170
4
$100
70
$170
5
$100
70
$170
$2,000
$2,000
$2,000
$2,000
$2,000
Fixed interest
Variable interest
Table 2
Annual interest payments: NZBR constant at 3.75% over the 5-year period
Ex post Tom appears smart by borrowing at a variable rate for 5-years. However, the
situation changes if the NZBR increases say by 3% each year over the 5-year period of the
loan. In this fluctuating interest rate environment, the NZBR at the end of the 1st year
increases to 6.75% and so forth for other years. The revised annual interest payments are
depicted in Table 3. From Table 2, Tom’s variable rate is initially lower and therefore looks
attractive. But remember there is “no free lunch in financial markets.” Under the revised
scenario depicted in Table 3, ex post Jill’s fixed rate loan is the more attractive loan scheme.
Jill
Tom
Total
Total Amount Borrowed
1
$100
70
$170
2
$100
100
$200
3
$100
130
$230
4
$100
160
$260
5
$100
190
$290
$2,000
$2,000
$2,000
$2,000
$2,000
Fixed interest
Variable interest
Table 3
Annual interest payments: NZBR increases annually by 3%
COMPARATIVE ADVANTAGE
From Table 1,Tom’s variable rate is lower than Jill’s variable rate and similarly for Tom’s
fixed rate. Thus, Tom is said to have an absolute advantage over Jill of borrowing at both a
fixed and variable rate. However, bothTom and Jill are forced to “specalized,” that is each
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Volume 1, Number 1, 2002
borrows $1,000 at either a variable or fixed rate, but not both. For the interest rate swap
problem, absolute advantage is superseded by comparative advantage. The concept of
comparative advantage is defined by solving Problem 1.
Problem 1: Tom borrows $1,000 for 5 years and similarly for Jill. From Table 1, what type
of loan (e.g., fixed or variable) should Tom and Jill individually select to minimize total
interest paid to the BNZ? Note that the total amount of money borrowed equals $2,000.
Answer: From Table 1, to minimize the total interest paid Jill borrows at a variable rate and
Tom borrows at a fixed rate. Thus, we say that Jill has a comparative advantage of borrowing
variable and Tom a comparative advantage of borrowing fixed.
SOLUTION:
Case 1: Assume that Jill borrows at the variable rate and Tom at the fixed rate as depicted in
Table 1. Therefore, Jill pays 4.05% plus NZBR and Tom 9.00%.
Sum of the two loans = 13.05% plus NZBR.
Case 2: Assume that Jill borrows at the fixed rate and Tom at the variable rate as depicted in
Table 1. Therefore, Jill pays 10.00% and Tom 3.25% plus NZBR.
Sum of the two loans = 13.25% plus NZBR.
Since 13.05% plus NZBR < 13.25% plus NZBR, Case 1 minimizes the interest expense of
the two combined loans.
INTEREST RATE SWAP
The total amount borrowed by both counterparties equals $2,000. From Table 2, if Tom and
Jill borrow basis their preferred habit, annually interest payments total $170. Relaxing the
assumption of a constant NZBR over the 5-year period, then annual interest payments total
$132.50 plus $1,000 times the NZBR for a particular year.
Consider the following scenario where Tom borrows $1,000 at a fixed rate and Jill borrows
$1,000 at a variable rate basis the terms depicted in Table 1, which by the way is not Jill and
Tom’s preferred habitat. Table 4 outlines the interest payments paid by both counterparties
over the 5-year loan period.
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New Zealand Applied Business Journal
Jill
Tom
Total
Total Amount Borrowed
1
$78
90
$168
2
$78
90
$168
3
$78
90
$168
4
$78
90
$168
5
$78
90
$168
$2,000
$2,000
$2,000
$2,000
$2,000
Fixed interest
Variable interest
Table 4
As before, the total amount borrowed is $2,000, but the annual interest payments are
reduced from $170 to $168, which represents a potential savings of $2 on the $2,000 notional
principal. Although conceptually $2 is not a large sum of money, if both counterparties
borrow $100,000,000 instead of $1,000, the potential savings amounts to $200,000 on the
$200,000,000 notional principal.
A. Swap agreement
It turns out that Jill and Tom are old college friends and meet together at least once a week to
lawn bowl, weather permitting. After discussing their business plans and terms of the 5-year
$1,000 loan offered by BNZ, Jill and Tom enter into the following contractual agreement.
Tom borrows $1,000 from BNZ for 5 years at a fixed rate of 9%, while Jill borrows $1,000
from BNZ for 5 years at a variable rate of 4.05% plus the NZBR (for pedagogical reasons,
the NZBR is held constant at 3.75%). However, since Tom has a preferred habitat of a
variable rate and Jill a fixed rate, they agree to swap annual interest payments as follows:
Jill agrees to pay Tom an annual fixed payment of $99, which equates to a 9.90% fixed rate
on the notional principal of $1,000.
Tom agrees to pay Jill an annual variable payment of 3.15% plus the NZBR on the notional
principal of $1,000, which equates to $69 assuming that the NZBR remains constant at 3.75%
over the 5-year loan.
Observe that both parties are better off under the swap agreement versus borrowing $1,000
from BNZ basis their preferred habitat. For both parties, annual interest payments are
reduced by $1. In particular, Jill is able to borrow $1,000 at a fixed rate of 9.9% instead of
10%, and Tom is able to borrow $1,000 at a variable rate of 3.15% plus the NZBR instead of
3.25% plus the NZBR.
B. Issues of interest
A swap agreement is not risk free as it contains counterparty risk. BNZ ultimately looks to
Jill for an annual variable interest payment of 4.05% plus the NZBR on the notional principal
and conversely to Tom for an annual fixed payment of 9% on the notional principal. In
addition, both parties are responsible for repayment of their loan’s notional principal at
maturity. Jill incurs the counterparty risk that Tom will default on the terms outlined in the
swap agreement and conversely for Tom.
In the previous example, Jill and Tom shared equally the potential gains from an interest rate
swap, but the profit-split ratio net of any commission paid to a middleman could be 0.60:0.40
or any other ratio whose component parts sum to 1.00. The profit-split ratio, which is
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Volume 1, Number 1, 2002
indeterminate, is based on bargaining power, credit risk of the two counterparties and other
related factors.
In the previous example, a middleman is not used to facilitate the transaction. However,
assume that Jill and Tom do not know each other and/or have no knowledge of interest rate
swaps. In this case, a portion of the potential savings must be paid to a middleman whenever
such services are utilized, and there is nothing to preclude BNZ from acting as the middleman
and thus deriving a commission for their services in this capacity.
In many interest-rate swap agreements, the variable portion of the loan is stated for example
as 3.25% plus LIBOR. LIBOR stands for the London Interbank Offered Rate (the deposit
rate applicable to interbank loans in London). LIBOR is used as the reference rate for many
international interest rate transactions.
This paper’s methodolgy to understanding interest rate swaps is converted to a flow chart
approach containing the following learning objectives:

The potential for an interest rate swap exists only if both counterparties are better off
under the swap arrangement ignoring counterparty risk.

Why preferred habitat and comparative advantage must be different for an interest
rate swap to occur.

How to construct the swap payments given the potential savings and the profit-split
ratio net of commissions.

How the introduction of a middleman alters the swap payments via commissions paid
for their services.
FLOW CHART APPROACH
Statement of problem: Firm 1 prefers a fixed rate loan while Firm 2 prefers a variable rate
loan. In each case, the loan is for $1,000 over a period of 10 years.
Firm 1
Firm 2
Fixed
12.00%
9.00%
Difference
3.00%
Variable
6.25% + LIBOR
4.05% + LIBOR
2.20%
Example 1
SEE APPENDIX 1
Circle preferred habitat of each firm, which for Firm 1 is the fixed rate loan and Firm 2 the
variable rate loan.
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New Zealand Applied Business Journal
1. Insert the interest rate corresponding to the preferred habitat loan. Based on the
information from Example 1,
Firm 1: x = 12.00%.
Firm 2: y = 4.05% + LIBOR%.
2. Calculate the interest paid on preferred habitat loan.
Firm 1: $X = x* notional principle = [0.12]*[$1,000].
Firm 2: $Y = y* notional principle = [0.0405 + LIBOR]*[$1,000].
3. Determine the total interest paid on preferred habitat loans.
$X + $Y = Total interest paid on preferred habitat loans.
$X + $Y = [0.1605 + LIBOR]*[$1,000].
SEE APPENDIX 2
1. Determine the comparative advantage loan for each firm and circle appropriate loan
where indicated. Basis the solution to Problem 1, Firm 1 has a comparative advantage of
borrowing variable while Firm 2 has a comparative advantage of borrowing fixed.
2. Insert interest rate on comparative advantage loan. Based on the information from
Example 1,
Firm 1: v = 6.25% + LIBOR%.
Firm 2: w = 9.00%.
3. Calculate interest paid on comparative advantage loan.
Firm 1: $V = v* notional principle = [0.0625 + LIBOR]*[$1,000].
Firm 2: $W = w* notional principle = [0.09]*[$1,000].
4. Determine the total interest paid on comparative advantage loans.
$V + $W = Total interest paid on comparative advantage loans of the two firms.
$V + $W = [0.1525 + LIBOR]*[$1,000].
5. Calculate $Z. Based on the information from Example 1,
$Z = [$X + $Y] – [$V + $W]
$Z = [0.1605 + LIBOR]*1,000 – [0.1525 + LIBOR]*1,000
$Z = [0.80]*$1,000 = $8.00 > 0.
SEE APPENDIX 3
Appendix 3 introduces the roll of a middleman and presents an overview of the interest rate
swap agreement. The profit-split ratio (a:b) must be specified where a and b denote the
percentage of the saving accruing to Firm 1 and Firm 2, respectively net of commissions.
Given the risk profile of the two firms as indicated in Example 1, assume that a = 0.40 and b
= 0.60.
For pedagogical purposes, assume that the middleman’s commission is expressed as a
percentage of the savings ($Z), and the symbol c represents this percentage. Also assume
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Volume 1, Number 1, 2002
that both counterparties contribute equally to the middleman’s commission where c = 0.10 in
Example 1.
Another way of expressing the middleman’s commission is in basis points relative to the
notional principle where 1% represents 100 basis points. For example, assume that the
middleman’s commission equals 8 basis points. Therefore, based on a notional principle of
$1,000, the middleman’s commission equals $0.80.
Calculate the middleman’s commission.
c*[$Z] = [0.10]*[$8] = $0.80
Calculate the dollar interest rebate to Firm 1 and Firm 2.
Interest rebate Firm 1: $A = a*[$Z - $0.80] = [0.40]*[$7.20] = $2.88
Interest rebate Firm 2: $B = b*[$Z – 0.80] = [0.60]*[$7.20] = $4.32
Calculate the net cost of the loan to both counterparties.
Net cost of loan to Firm 1:
$X - $A = $120.00- $2.88 = $117.12 or
11.712%.
Net cost of loan to Firm 2:
$Y - $B = [$40.50 + LIBOR*$1.000] - $4.32
$36.18 + LIBOR*$1,000 or
3.618% + LIBOR.
DEFINITION
$Z = [$X + $Y] – [$V + $W], which is the potential $ savings from entering into an interest
rate swap.
A necessary and sufficient condition for an interest rate swap between two counterparties is
$Z > 0.
Whenever $Z > 0 the preferred habitat loan  comparative advantage loan.
CONCLUSION
Confirm from Example 1 that both counterparties have reduced their interest payments via
the interest rate swap agreement and that each loan has the desired characteristics—fixed
versus variable terms.
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New Zealand Applied Business Journal
APPENDIX ONE
Preferred Habitat Loan
Bank
Firm 2
borrows
$1000 from
Bank
Firm 1
borrows
$1000 from
Bank
Firm 2
pays $Y
to Bank
Firm 1
pays $X
to Bank
Bank
Firm 1
Firm 2
Firm 1
Firm 2
1. Circle preferred habitat loan: fixed/variable
2. Interest rate on preferred habitat loan = x percent
1. Circle preferred habitat loan: fixed/variable
2. Interest rate on preferred habitat loan = y percent
3. $X = [x percent]*[notional principle of loan]
3. $Y = [y percent]*[notional principle of loan]
4. $X + $Y= Total interest paid on preferred habitat loans.
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APPENDIX TWO
Comparative Advantage Loan
Bank
Firm 2
borrows
$1000 from
Bank
Firm 1
borrows
$1000 from
Bank
Firm 2 pays
$W to
Middleman
Firm 1 pays
$V to
Middleman
Firm 1
Firm 2
Middleman
Firm 1
Firm 2
1. Circle comparative advantage loan: fixed/variable
1. Circle comparative advantage loan: fixed/variable
2. Interest rate on comparative advantage loan = v
percent
2. Interest rate on comparative advantage loan = w
percent
3. $V = [v percent]*[notional principle of loan]
3. $W = [w percent]*[notional principle of loan]
4. $V + $W = Total interest paid on comparative advantage loans.
5. $Z = [$X + $Y] – [$V + $W] > 0 necessary and sufficient condition for interest rate swap.
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APPENDIX THREE
Comparative Advantage Loan
Bank
Firm 1 pays
$X to
Middleman
Firm 1
Net Cost of loan = $X-$A
Middleman
$C = Commission
Interest Rebate
= $A
Firm 2
borrows
$1000 from
Bank
Middleman
pays $V+$W
Firm 1
borrows
$1000 from
Bank
Firm 2 pays
$Y to
Middleman
Firm 2
Net Cost of loan = $Y-$B
Interest Rebate
Assume Zero
Credit Risk for
Middleman
= $B
Counter Party Risk
1. Calculate the middleman’s commission: c*[$Z] = $C; Z=[$X+$Y] – [$V+$W].
2. Calculate the dollar interest rebate to Firm 1 and 2: $A = a*[$Z-$C]; $B = b[$Z-$C].
3. Calculate the net cost of loan both counterparties. Firm 1: $X - $A; Firm 2: $Y - $B.
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