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International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

Page

1

Of Haircuts and Extensions: An Analysis of Greek Government Debt1

Mathias Moersch Carolin Schmidt*

Abstract

In light of the current negotiations concerning the Greek debt, this paper conducts a valuation

analysis based on the Present Value (PV) method. We explain the rationale for the PV method

and use it to model a simplified representation of the Greek debt situation. We illustrate the

effects of changes in the variables in the PV function and show that if the Greek loan interest rate

was decreased by 50 basis points and the maturity of the debt was extended from 30 to 50 years,

the effect would be equivalent to a haircut of roughly 59%.

The Greek Government Debt crisis of the early 2010’s has served as a microcosm of the various

political, economic and social factors at play as the world emerges from the Great Recession. It

has served as a battleground for future Eurozone policies, European integration and global

monetary policy. Sparked by events across the Atlantic, Greece’s attempts to improve its fiscal

situation represent the greater challenges and decisions that sovereigns and their creditors face

today.

The financial problems arising from the housing crisis were not limited to the US, as the

interlinked global financial system caused many of these multinational companies to spread the

problem overseas, aided by heavy investment from China and Europe into the US housing

market, directly or indirectly through mortgage-backed securities (Holt, 2009). Eurozone

countries were ostensibly able to weather any financial storm, with the strict restrictions of the

Maastricht Treaty keeping long-term interest rates, inflation, debt-to-GDP ratios, and budget

deficits within certain ranges (EC, 2014). However some countries, including Greece, had

benefited from their ascension into the Eurozone with lower interest rates than they normally

would have received. Taking advantage of this situation, Greece borrowed heavily in the run-up

to the financial crises, limiting their borrowing capabilities during the recession. Greece ran huge

budget deficits from 2004-2009, rapidly expanding the public sector and increasing government

spending (Ministry of Finance, 2010). Bolstered by a steadily growing economy and low

Eurozone interest rates, Greece consistently used a fiscal policy that bumped up against the

edges of the Maastricht criteria, even utilizing swaps and other forms of creative accounting to

artificially keep themselves within the agreed bands (Balzli, 2010).

After the financial crisis spread to Greece, its fiscal policy began to unravel. With the Greek

economy quickly contracting, the European Union began to investigate as concerns grew about

the need for a possible bailout. Eurostat accused Greece of manipulating data which, combined

with the announcement of the Greek government that its projected 2009 budget deficit was being

revised upwards from 3.7% to a staggering 12.5%, caused the bond markets to respond quickly

(White, 2010). By April 2010, Greece’s credit rating had dropped to junk status and its short-

term borrowing costs had risen to 14%, about 1,000 basis points higher than Germany’s

1 This paper is based on a study done by DZ BANK Research. We thank the authors of the study for their valuable

input that helped us develop this teaching case.

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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(Wachman, 2010). With Greece now breaking multiple criteria for Eurozone financial stability,

the EU and IMF began to consider emergency measures. This began with a €110 billion financial

aid program in May 2010 funded mainly by Eurozone countries, followed by another €130

billion package finalized in February 2012 after austerity measures were passed by the Greek

Parliament (Pratley, 2012). A key portion of this package was a bond swap agreed to by the

Greek government and bondholders, reducing Greece’s debt by trading €200 billion of Greek

sovereign debt for a mixture of cash and long-term bonds, avoiding a sovereign default by

Greece (Kollowe, 2012). Further negotiations have ensued with creditors over further loan

relief, including a potential extension of loan maturities from 30 years to 50 years, along with

lowering the interest rate on the loans by half a percentage point (Bloomberg, 2014).

Using the present value concept, which is a common approach to value investments in finance,

this case study will show that the proposed maturity extension and the reduction of the interest

rate is equivalent to cutting the original outstanding loan by approximately 59%. Section I will

introduce the present value formula and its derivation, and discuss the formula for a finite series

of cash flows in detail. Later on, in section II , we will apply this concept by taking a simplified

version of the potential Greek debt haircut as an example. We will show that the actual debt

burden would be decreased considerably, should a debt extension of the discussed form be

implemented. Section III will summarize the results.

I. The Present Value Of Cash Flows

A. The time value of money

The present value (PV) is a standard concept in finance that determines today’s value of a stream

of cash flows that occur in the future. It takes into account that 100 euros received today have a

different value from 100 euros to be received in the future. The reasons for this difference in

values are, for example, inflation, risk, or an attractive investment opportunity that is forgone

today because of a lack of capital. The 100 euros could be invested today and yield a positive

return (i.e., a future value that is greater than the 100 euros) at the end of the investment period.

B. From compounding to discounting

The starting point for the PV is compound computation of interest. The 100 euros invested today

at a rate of, say, 5% lead to a future value (FV) of 105 euros in one year’s time:

(

)

10505.1100 1==FV (1)

Conversely today’s value, the so-called present value (PV) of the 105 euros is

( )

100

05.1

105

1==PV (2)

That is, the calculation of a present value is just undoing a compound interest calculation. This is

called discounting. All other things equal, it is not hard to imagine how to compute the present

value of a cash flow of 105 euros that occurs not in one but in two years’ time:

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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( )

24.95

05.1

105

2==PV (3)

The general formula for the present value of a cash flow in the future is thus

( )

t

t

t

i

CF

PV

+

=1, (4)

where PV: Present value of a future cash flow

CFt: Cash flow occurring in time t

it: Interest rate applicable to period t, so-called discount factor

Please note the subscript t in the interest rate i, since interest rates might not be constant over the

investment period. The choice of the applicable discount factor depends on the risk of the

investment. For low-risk investments, the rates of return on government bonds can be used. If the

risk is comparable to the risk of a portfolio of shares, stock market returns like that of the S&P

500 can be used. In either case, the risk of the investment which should be valued must be

adequately captured by the discount factors.

The usage of the PV is not limited to the valuation of single cash flows. If we think of a whole

series of future cash flows, we can add up all the individual present values and aggregate them

into a single present value:

( ) ( ) ( )

∑

=+

=

+

++

+

+

+

=

T

t

t

t

t

T

T

T

i

CF

i

CF

i

CF

i

CF

PV

1

2

2

2

1

1

1

)1(

1

...

11 (5)

This present value gives us the value of all the cash flows that occur at different points in time in

the future. In a nutshell, the PV helps to make cash flows from different points in time

comparable to each other.

Let us now assume that we have taken out a 10-year loan of 10,000 euros with a yearly 5%

interest rate. That means that we have to pay 500 euros in interest every year and redeem the

borrowed amount of 10,000 euros in 10 years:

Table I: Interest payments and principal of a loan with maturity in 10 years

t 1 2 3 4 5 6 7 8 9 10

Interest 500 500 500 500 500 500 500 500 500 500

Redemption 10,000

Assume a constant interest rate of 10%. We can use the PV formula in Equation (5) to determine

the total amount of money that we would have to set aside today for 10 years at a 10% interest

rate in order to pay off the entire loan without further action:

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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( ) ( ) ( ) ( )

72.927,6

1.1

500,10

1.1

500

1.1

500

1.1

500

1092 =++++= ...PV (6)

That is, if today we deposited an amount of 6,927.72 euros in an account that yields a 10%

interest rate per year, we could entirely pay off the interest payments and the principal. To put it

differently, we can say that the present value of 6,927.27 euros is the actual credit burden of the

debtor.

Let us now assume a yearly interest payment of 500 euros over 100 years to understand the

contribution that a single future cash flow makes to the whole PV: the further in the future a

payment occurs, the less value it has today. Economically, this means that we have to save very

little today to end up with 500 in the far future due to interest on interest over a long period of

time. Mathematically, this is because we discount the 500 euros over many periods, which makes

the denominator of the PV formula bigger and thus the whole fraction smaller the later the cash

flow occurs. Equation (7) reports the amounts of money that would have to be deposited today to

reach 500 euros in t years, e.g. 3.628 cents saved today will accumulate to 500 euros over a

period of 100 years at an interest rate of 10%.

( )

( )

( )

( )

03628.0

1.1

500

...

77.192

1.1

500

...

22.413

1.1

500

55.454

1.1

500

100

10

2

1

==

==

==

==

PV

PV

PV

PV

(7)

Figure 1 shows the present values of 500 euros that occur at different future points in time

t=1,…,100.

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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Figure 1: Present value of 500 euros occurring at different future points in time t

The present values of payments diminish quickly the further in the future they occur. These

considerations help understand the effect of a longer term to maturity on the present value of the

Greek debt, assuming for simplicity that the coupon that is to be discounted remains fixed.

II. Valuing THE Greek Debt

In this section, several scenarios of a potential loan relief are discussed, and their effects on the

credit burden are analyzed. The debt burden – computed as the present value of all interest

payments and the redemption of the principal of a loan – is a function of three variables: the cash

flows, CFt; the applicable discount factors, it; and the points in time, t, in which the payments

occur. A change in any of these variables alters the present value, or, in our example, the amount

of money that Greece would have to save today in order to service its loans. The effect on the

credit burden will be discussed in the following subsections.

A. Valuing the Greek debt: The status quo

At the time of discussing the above mentioned debt reliefs, Greece had several loans with

different maturities outstanding. For the sake of simplicity, we assume that the bailout loans have

a principal of €240 billion, as reported by Reuters (2014), which mature in 30 years. In order to

show the effects of a change in variables, we should keep our assumptions as simple as possible.

We therefore assume the interest rate on the Greek debt to be 3%, which corresponds to a yearly

interest payment of €240 billion x 0.03 = €7.2 billion. We modeled a curve of discount factors

which is illustrated in Figure 22 and follow the common assumption of an upward-sloping yield

curve of interest rates, as returns on securities normally tend to increase with maturities3. This

assumption is discussed further in section II. B.2.

2 Data and spreadsheet calculations available on request.

3 This is often justified by the fact that investors require a so-called term premium for holding longer-term securities

(e.g., Cox et al. (1985)).

0

100

200

300

400

500

600

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

92

96

100

PV of €500

occurring in t

t

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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Figure 2: Modeled yield curve of discount rates for different terms to maturity

These data define the base case. The present value, or the debt burden, of this loan is (in billions

of euros):

239.7

)03300.1(

2402.7

...

)00640.1(

2.7

)00485.1(

2.7

)00420.1(

2.7

3032 =

+

++++=PV (8)

If Greece saved €239.7 billion today, it could pay off its entire debt within 30 years.

B. Valuing the Greek debt: Scenario analysis

In this section, two effects should be analyzed: first, a decrease of 50 bps in the yearly coupon

that Greece has to pay on the loan; second, a maturity extension of the Greek debt from 30 to 50

years. We will first show the separate effects in the following subsections, and combine them in

a final subsection to show the overall effect. Table 2 summarizes the assumptions made in the

scenarios.

Table 2: Summary of the assumptions made in each scenario

N: Face value

[billions of euros]

c: Coupon rate

[percent]

C: Coupon

[billions of euros]

T: Maturity

[years]

Base case 240 3.00 7.20 30

Scenario 1 (II. B.1) 240 2.50 6.00 30

Scenario 2 (II. B.3) 240 3.00 7.20 50

Scenario 3 (II. B.4) 240 2.50 6.00 50

B.1 Scenario 1: The effect of a decrease in the coupon rate by 50 basis points

In the current debate on the extension of the Greek debt, one of the suggestions was to decrease

the interest rate that Greece has to pay on the loan by 50 basis points (bps), or 0.5 percentage

points.

If Greece has to pay only 2.5% interest on the outstanding loan and everything else remains

unchanged, the debt burden is

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 5 10 15 20 25 30 35 40 45 50

Discount rate in %

applicable to time

t

Time to maturity in years

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

Page

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.85.214

)03300.1(

2406

...

)00640.1(

6

)00485.1(

6

)00420.1(

6

3032 =

+

++++=PV (9)

That is, the original credit burden of €239.7 billion falls by roughly 10.37% if the yearly coupon

is lowered by 50 bps. Error! Reference source not found. shows a comparison of the present values

of the 30 coupon payments of the base case and the scenario discussed in this subsection. It is

evident that the present values of the reduced payments are smaller than the original payments

and that the credit burden (which is just the sum of the present values) is thus lower when less

interest has to be paid.

Figure 3: Base case (3% coupon rate) versus Scenario 1 (decrease in the coupon rate by 50 bps)

B.2 The impact of the shape of the term structure of interest rates

The ideas in this subsection are not directly related to the case of Greece, since the discount rates

are not affected by the potential loan extension. However, it is helpful to take a look at the shape

of the term structure of interest rates, or yield curve, which is often used to value investments, in

order to fully understand the effects of a loan extension on the PV of the loan.

If the interest rate for our bank account falls from 10% to 8%, then we have to save more money

today in order to have a specific amount of money in the future, since the interest we receive on

this amount of capital will be lower than expected. The same applies to loans and the debt

burden: the lower the rate of return in the bank account, the more has to be laid aside today in

order for the debtor to be able to pay back the loan in the future. Also, the later the principal has

to be paid back, the higher is the interest rate at which this payment is discounted; and thus, the

lower the value that has to be saved today.

The different rates of return on an investment, depending on the lifetime of the investment, are

shown in the yield curve of interest rates, as depicted in Figure 2. In most cases, one can observe

that interest rates increase with time (so-called ‘normal’ shape of the yield curve). This means

0

10

20

30

40

50

60

70

80

90

100

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Present value

of cash flows

Time to maturity in years

Base case Scenario 1

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

Page

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that the longer our capital is tied up in an investment, the higher the returns should be. Only

occasionally can a falling or ‘inverse’ yield curve be observed (in particular before recessions,

e.g. Ang et. al, 2006; Cwik, 2005). Therefore, when there is a normal, upward-sloping yield

curve, a cash flow that occurs at the so-called long end of the term structure has a lower value

today than the same cash flow that occurs in the intermediate or short term because later

payments are discounted at a higher interest rate.

B.3 Scenario 2: The effect of a loan extension to 50 years

In subsection B.1, the effect of a decrease in the yearly coupon that the Greek government has to

pay on the loan was discussed. This of course causes a decrease in the credit burden. In this

subsection, an extension of the loan to 50 years is discussed. Having to pay more coupon

payments (namely 50 rather than 30) means an increase in the credit burden.

From the considerations in the previous subsection on changing discount factors (and assuming

an upward-sloping yield curve) we know that longer terms to maturity come along with higher

interest rates at the long end. That is, having to pay back the principal 20 years later does not

only cause a decrease in the PV simply because of the fact that we discount over 20 more

periods; it also decreases the PV because this very last, huge payment is discounted at a higher

interest rate (3.97%) than when it was discounted in t=30 (3.3%). This additionally drives the PV

down.

If we only assume that the outstanding loan is due in 50 rather than in 30 years, but leaving all

other assumptions unchanged, the credit burden is

85.214

)03970.1(

2402.7

...

)03300.1(

2.7

..

)00485.1(

2.7

)00420.1(

2.7

50302 =

+

+++++=PV (10)

That is, due to the higher number of interest payments (50 rather than 30) and more discounting,

the credit burden decreased by roughly 9.7% compared to the status quo – even though 20 more

interest payments have to be made. Note that an upward sloping yield curve is assumed to come

to this conclusion. Figure 4 compares the present values of the coupon payments of the base case

and this subsection’s scenario.

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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Figure 4: Base case (3% coupon, 30 years) vs. Scenario 2 (3% coupon, 50 years)

The results would be different in the case of a downward-sloping yield curve. Then it would be

disadvantageous for the debtor to move the face value of the loan into the future since the

interest rates at which the face value was discounted would be very low. As a consequence, the

discounted face value would be higher and the debtor would have to save more today in order to

pay back the face value in the future. However, whether or not the sum of all payments would be

higher than in the base case is not clear without knowing the concrete yield curve, since the NPV

depends on the difference between the interest rates at the short end and the long end.

B.4 Scenario 3: The combined effect on the credit burden

To see the full effect when the previous assumptions are combined, we compute the present

value of the Greek loans, taking together all the manipulations from the previous subsections,

i.e., decreasing the coupon rate by 50 bps and extending the maturity to 50 years. The debt

burden for this scenario is

08.186

)03970.1(

2406

...

)03300.1(

6

..

)00485.1(

6

)00420.1(

6

50302 =

+

+++++=PV (11)

This is equivalent to a reduction of the original credit burden by more than 22%. The base case is

graphically compared to this scenario in

Figure 5.

0

10

20

30

40

50

60

70

80

90

100

1

6

11

16

21

26

31

36

41

46

Present value

of cash flows

Time to maturity in years

Base case

Scenario 2

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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Figure 5: Base case (3%, 30 years) versus Scenario 3 (2.5%, 50 years)

C. The haircut

In the introduction we posited that the scenario in which the coupon rate is only 2.5% and the

maturity is extended to 50 years leads to the same credit burden as a haircut of the original loan

of roughly 59%. To come to this conclusion, we just have to solve the following equation4 for X:

302 )03300.1(

2.7

..

)00485.1(

2.7

)00420.1(

2.7

08.186 X

+

+++= (12)

Equation (12) allows us to compute the principal X that leads to the same credit burden as the

combined scenario. Note that this is still the status quo except for the principal X which we are

trying to compute.

Solving the above equation for X leads to a principal X of €97.994 billion. That is, if the Greek

debt – as it is currently outstanding – had a principal of only €97.994 billion while the euro

interest payments remained unchanged, this would be equivalent to the scenario of an interest

rate decrease and a maturity extension:

302 )03300.1(

994.972.7

..

)00485.1(

2.7

)00420.1(

2.7

08.186

+

+++= (13)

That is, these two measures together – i.e. a decrease in the coupon rate of 50 bps and a loan

extension to 50 years – lead to the same loan relief as a haircut of the original principal (€240

billion) of more than 59%.

III. Conclusion

In this case study, we introduced the PV as a method to value investments and explained the

general idea behind this concept. We showed that two measures that appear rather unimpressive

at first sight have a considerable effect on the credit burden of Greece and that, assuming a

normal shape of the yield curve, these two measures have an effect that is equivalent to a haircut

of the original loan of more than 59%.

4 Note that we assume that the coupon does not change even though the face value of the loan changes.

0

10

20

30

40

50

60

70

80

90

100

1

6

11

16

21

26

31

36

41

46

Present value

of cash flows

Time to maturity in years

Base case Scenario 3

International Research Journal of Applied Finance ISSN 2229 – 6891

Vol. VI Issue – 8 August, 2015 Case Study Series

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References

Ang, Andrew, Piazzesi, Monika and Min Wei, 2006, What does the yield curve tell us about

GDP growth? Journal of Econometrics 131, 359-403.

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Spiegel, http://www.spiegel.de/international/europe/greek-debt-crisis-how-goldman-sachs-

helped-greece-to-mask-its-true-debt-a-676634.html

Bloomberg View, February 13, 2014, Greece needs Debt Forgiveness, Businessweek,

http://www.businessweek.com/articles/2014-02-13/europe-should-extend-greece-some-debt-

relief

Cox, John C., Ingersoll, Jonathan E., and Stephen A. Ross, 1985, A Theory of the Term

Structure of Interest Rates, Econometrica 53, 385-408.

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http://www.theguardian.com/world/2012/feb/19/how-does-greece-debt-swap-work

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10/01_programme/el_2010-01-15_sp_en.pdf

Pratley, Nils, February 21, 2012, Greece bailout: six key elements of the deal, The Guardian,

http://www.theguardian.com/business/2012/feb/21/greece-bailout-key-elements-deal

Reuters, March 27, 2014, Euro zone not preparing third Greek bailout so far: official,

http://www.reuters.com/article/2014/03/27/us-eurozone-greece-idUSBREA2Q2B420140327

Wachman, Richard, and Nick Fletcher, April 27, 2010, Standard & Poor's downgrade Greek

credit rating to junk status, The Guardian,

http://www.theguardian.com/business/2010/apr/27/greece-credit-rating-downgraded

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http://web.archive.org/web/20101007143658/http://abcnews.go.com/Business/wireStory?id=9

541636

Author

Mathias Moersch, PhD

Professor of Financial Economics, Heilbronn University, Max-Planck-Straße 39, 74081

Heilbronn, Germany, mathias.moersch@hs-heilbronn.de

Carolin Schmidt*

Research associate and lecturer, Heilbronn University, Max-Planck-Straße 39, 74081 Heilbronn,

carolin.schmidt@hs-heilbronn.de

*corresponding author