# 11/20 Ch 18- Long term financing (continuation)

Software and s/w Development

Oct 30, 2013 (4 years and 8 months ago)

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Ch18
-
c.
1

11/20

Ch 18
-

Long term financing

(continuation)

Bonds

Swaps

Interest rate swaps

Currency swaps

(
Fixed by fixed
)

Why does the value of the
IBM currency
swap change?

The value is a function of the coupon, the exchange rate (USD
/EUR
), and interest rates
(
i
EU
R

and
i
USD
).

V
IBM

= f(coupon
EUR
, coupon
USD
, S
t
, i
EU
R
, i
USD
, T)

Only t
he exchange rate and interest rates constantly
and randomly
change.

Comparative stat
ics
-
V
IBM

:

If
S
t

falls (USD
appreciates
)

=>

V
IBM

falls
.

If
i
USD

fal
ls =>

V
IBM

falls

If
i
EUR

goes up, =>

V
IBM

falls
.

The opposite happens for the Swap Dealer.

Note:
You can think of currency swaps as a collection of forward currency contracts.
I
BM exchanges USD 4M for EU
R 5.25M
for 2 years
=>implicit S
t

=

.762 USD/EUR

At T=
3
, IBM exchanges USD 204M for EUR 215.25 M

=>
implicit S
3

=
.94 USD/EUR

Decomposition into Forward Contracts

We can d
ecompose the currency swap into a series of forward contracts.

Example
: From last class. IBM swap
:

Semi
-
a
nnual exchanges:

EUR

5.25

= USD
4M

A
t maturity, final exchange:

EUR

215.25

M = USD
204

M

• Each of these payments represents a forward contract.

Recall
IRP formula: F
t,T
j

= S
t

(1+i
d
,Tj
xT
j
/360)/(1+i
f,Tj
xT
j
/360)

:

T
j
: time of the jth settlement date

i
T
j
: interest rate ap
plicable to time
T
j

F
t,Tj
: forward exchange rate applicable to time
T
j
.

IBM’s

NPV
of the forward contract corresponding to t
he exchange of payments at T
j
:

(
EUR 5.25 M x
F
t,Tj

USD 4 M
)/(1+
i
USD,T
j
)
T
j

• Similarly, I
BM
’s NPV

of the forward contract co
rresponding to the exchange of
principal
s

at T (maturity):

(EUR 215.25 M x F
t,T

USD 204 M)/(1+
i
USD,T
)
T
.

Ch18
-
c.
2

=>

The value of a currency swap can be calculated from the term structure of forward rates
and the term structure of domestic interest rates

(yield

curve)
.

Example
: Reconsider
IBM
’s

e
xample
with two payments left

i.e., 1 year to go
.

S
t

=
1
.
0
5

USD/DKK.

T =
1

year

In USD: 6
-
mo= 5%, 12
-
mo=5.1%

In EUR: 6
-
mo= 6%, 12
-
mo=6.2%

Using IPT, the
6
-
mo
,
and
12
-
mo

forward exchange rates are:

F
t,6
-
mo
=
1.0
5

USD
/EUR x (1+.0
5
/2
) /(1+.0
6
/2
) =
1.0449029
USD/EUR

F
t,12
-
mo
=
1.0
5

USD/EUR x (1+.0
51
/2
)
2
/(1+.0
62
/2
)
2

=
1.0388272
USD/EUR

• The exchange of interest involves receiving
EUR 5
.
2
5
M
and paying USD
4 M
.
Then, t
he
value of the forward contracts corresponding t
o the exchange of inte
rest are (in millions
)
:

(
EUR
5
.
2
5 x
1.0449029
USD/EUR

-

USD 4
)/(1+.05
/2
) =

USD
1.4495027

(
EUR
5.2
5 x
1.0388272
USD/EUR

-

USD 4
)/(1+.05
1
/2
)
2

=
USD
1.3824395

F
inal exchange of
principal
s: IBM

receiv
es

EUR 21
0

M

and pay
s

USD
2
0
0

M
. The value
of the forward contract is:

(
EUR
21
0

x
1.0388272
USD
/EUR

USD
20
0
)/(1+.05
1
/2
)
2

=
USD
17
.
262119

• The total value of the swap
(in USD M)
is:

1.4495027

+

1
.3824395

+

17.262119

=
20.094061
(check value from last class!)

=> IBM

would be wi
lling to sell this swap for
USD
20,
094
,061

Financial Engineering

S
ituation for non
-
US commodity markets participants:
Commodity p
rices
are
set in USD.

Problem
: Two sources of uncertainty: commodity price risk and FX risk.

Solution
: Use swaps to fix th
e price of the commodity in terms of the domestic currency.

Example:
Mexic
an Oil Producer

PEMEX

(Petróleos Mexicanos)

Pemex

sells 100M barrels every six months in the Oil Market.

100M barrels

Avg
.

oil price (USD)

The price for oil is set i
n USD. Not in
MXN
. This creates economic exposure.

PEMEX

Oil Market

Ch18
-
c.
3

1.

Commodity price risk
-
taken care of

Avg. oil price (USD)

Fixed oil price (USD)

2.

Exchange rate risk
-
use currency swap

Fixed (USD)

Fixed (
MXN
)

At then end of the two swaps, PEMEX ha
s fixed the price of oil in terms of
MXN.

SWAP
DETAILS

Commodity swap

Dealer pays
2
5 USD/barrel against market price for 2 years
.

Notional = 100M Barrels

Duration
:

2

yrs

Frequency
: semiannual

Currency swap (fixed by fixed)

SD pays
6.5
% in
MXN

against 5%
in USD
.

S
t
= .105

USD/
MXN

i
USD

= 5%

iMEX
=
6.5
%

Duration:

2 yrs

Frequency
: s
emiannual

*

W
e need to find out the fi
xed price of oil in terms of
MXN

1.

Com
modity
Swap

(Notional = 100M Barrels)

Avg. oil price (USD)

USD
2
.5 Billion

2.

C
urrency Swap

USD 2.5 Billion

MXN

?

PEMEX

Swap Dealer

PEMEX

Swap Dealer

PEMEX

Swap Dealer

PEMEX

Swap Dealer

Ch18
-
c.
4

Calculations for the SD
MXN

payments:

(1) Need to determine the Notionals of Swap

Notional of USD part = USD2.5B/.025 = USD 100B

(2) Determine
MXN

payment. (Recall that at inception the Value of the Swap is zero.)

NPV (USD

payments) =

USD
100B

NPV (
MXN

payments
) =

USD
100B/.1
05

USD/
MXN

=
MXN

9
52
.
38
B

=> SD’s
MXN

payment

=
MXN 952.38B
(
.03
2
5
) =

MXN

30.952381
B

Note
: The p
rice

of oil in
MXN

for 2 years has been fix
ed:

P
t

=

MXN

3
0
,
9524
M/100M barrels

=
3
09
.
52

MXN
/Barrel

Chapt
er
20

Short term financing

• Sources of short
-
term financing

Commercial Paper/Bank Notes

Bank Debt

Cost of debt: call a bank. Example for a US MNC
=>

i
USD

=

5%

MNCs can borrow anywhere

Q:
Where should they borrow?

A:

Wherever it is cheaper

(look for
lowest interest rate)
.

Borrow i
n a place that reduces economic exposure

(remember Laker Airlines)

We’ll pa
y attention to the lowest cost
.

Example:

IBM can borrow 5% in the USD or 9% in Mexico. We need more information
to make a decision. Need

the future exchange rate.

IBM will look at the effective borrowing cost

(in USD)
.

R
f
MXN
(in USD)
=

(1+i
MXN
)
*
(1+e
f,t
)

-

1

E[e
f,t

]=

-
8% (The USD

is expected to appreciate against the
MXN
)

R
f
USD

=

i
USD

=

5%

R
f
MXN

=

(
1
+
.09
)*
(1

+(
-
.08)
)

-

1

=

.0028

=>IBM s
hould borrow in Mexico
.

Problem
: e
f,t

is exp
ected.

R
MXN

is also an expected quantity.

There are risks involved!

Note
:
If the forward rate is used to set the expected change, then the effective borrowing
costs would be the same everywhere. (Remember IRP!
)