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
(IBM pays USD, receives EUR)
:
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
info about
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!
)
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