• Add a swap to a loan to change loan’s type
• Plain vanilla interest rate swap – domestic
currency denominated but involving
different loan structures, fixed vs. floating
• Plain deal foreign currency swap – same
loan structure, fixed interest rate, but
Interest Rate Swap
• Swap interpretation: investing in one type
and financing in another type
• Types = fixed versus floating rate
• Coy. B, due to higher credit rating, has an
absolute advantage in both types
Plain Vanilla Interest Rate Swap
• Coy. B has comparative advantage in fixed
rate, interest advantage is greater
• Coy. A has comparative advantage in
floating rate!!, interest disadvantage is less
• Coys. A and B, each has a comparative
advantage in the type of loan each does not
• Preconditions of a viable swap
Interest Rate Swap
• Page 2 depicts a specific swap
• Other swaps are possible: triangular region
specified by the 3 inequalities on page 3
• On border of triangle, one party does not
gain; on vertex, two parties do not gain
• Gain = 65 basis points for all swaps
• Canuck Avions de Ligne, Ltée Case
• Comparative advantage requirement for a
viable swap is satisfied
• CAL has comparative advantage in real,
Garota has comparative advantage in C$
• But CAL wants C$, Garota wants reais
• Add FX swap to financing in one currency;
result: financing in the other currency
• Interpretation: A portfolio (5-pack) of
forward contracts with different maturities
• CAL buys real forward to hedge real loan
• Garota buys C$ forward to hedge C$ loan
• Implied forward rate common to all 5
maturities is BR7.824/C$ vs. spot rate of
BR7.366/C$, qualitatively consistent with
FX Swap Effects
• Garota obtains real financing at its
prespecified required rate of 15%, this built
into swap cash flow calculations
• CAL obtains C$ financing at 9.61%,
calculated using the Excel’s IRR function
• CAL reduces its C$ financing cost by 89
Viñas de Valdivia, SA
• Determine the reference currency (Chilean
peso) cost of financing in another currency
(U$) via ex-post Uncovered Interest Parity
• Technique applies only to pure discount
• UIP: (1+ KU$) = (1+10%)(1+a) where KU$
is the Chilean peso cost of U$ financing and
a is the annual appreciation of U$
Viñas de Valdivia, SA
• Construct sensitivity analysis graph: gauge
sensitivity of Chilean peso cost to a
• Breakeven value of a is 36.36%, where the
peso costs are equalized
• At projected a, peso debt is cheaper
• Better to borrow at 50% than at 10%!!!!
• 10% in U$’s is 65% in Chilean pesos.
• Must use IRR function, cannot use ex-post
Uncovered Interest Parity, since loan not
pure discount arrangement
• Complication: issue costs
• Issue cost % applies to the gross financing
• Gross-up the net financing
• Yen cash flows must be forward hedged
• FX loan: sell loan proceeds at Bid, buy debt
service at Ask
• Criterion: Minimize cost of financing in the
reference currency (U$)
• Technique: determine vector of U$ cash
flows, then apply IRR function
Hedging FX financing cash flows
• Canuck Avions case: one swap.
• Bling-Bling case: five forward contracts
• Bling-Bling must buy JY288,659,794
forward for years 1, 2, 3, 4, 5 and
JY7,216,494,880 for year 5.
• Valid comparison of reference currency vs.
FX financing requires that the latter be fully
• 0. Zero-Coupon-type: only 1 debt service date.
• 1. Bond-type: pay only interest; at maturity repay
• 2. Mortgage-type: fully amortized with equal
annual debt service (blend of interest and principal
• 3. Type-3: Principal repaid in equal annual
installments; debt service declines during loan life.
• Ranked from fastest to slowest pace of principal
repayment: 3, 2, 1, 0.
Equal annual repayment of
principal (type 3 loan)
• Borrow $1 at 10% over two years.
• Principal repayment = 0.5 per year.
• Interest payments: year1 = $1 x 10% = .1;
year2 = $.5 x 10% = .05
• Debt service: year1 = .5 + .1 = .6; year2 = .5
+ .05 = .55
• Cash flows: 1; -.6; -.55. IRR = 10%
Tabular format for type 3 loan
Year Principal Principal Interest Debt
@Start Repay. Payment Service
1 1 .5 .1 = .6
2 .5 .5 .05 = .55
Effect of up-front fee on pace of principal
repayment to minimize all-in cost
• Borrow $1 over 2 years: 10% interest rate, 5% up-front fee
• Grossed-up principal = 1.05263 = 1/(1-.05)
• Mortgage-type loan: 1; -0.6065; -0.6065 implies cost =
• Pure-discount bond: 1; 0 ; -1.27368 implies cost = 12.86%
• Choose slow pace of principal repayment to amortize up-
front loan processing fee over longer effective time
Effects of loan processing fee (F)
Situation Pace of Principal
Repayment to Reduce
Incur F; no FX Slow
No F; appreciating FX Fast
No F; depreciating FX Slow
Financing in FX
• If FX is projected to depreciate or exhibits a
forward discount, repay principal sloooowly
(bond-type is best), other things equal.
• If FX is projected to appreciate or exhibits a
forward premium, perhaps repay principal ASAP
(type-3 is perhaps best), other things equal.
• Why perhaps? In presence of loan processing
fees, it is better to postpone principal repayment.
• High interest rate currency trades at a
forward discount and will depreciate.
• Low interest rate currency trades at a
forward premium and will appreciate.
• The two effects work at cross purposes: one
raises, the other lowers the cost of financing
in the reference currency.
• Implication: Apply Excel’s IRR function!
Dubious Rules of Thumb
• Definitions: soft currency, likely to
depreciate; hard currency, likely to
• Always finance in a soft currency. Problem:
such a currency exhibits high interest rate.
• Always finance in a low interest currency.
Problem: such a currency will likely
appreciate. Low interest currencies are hard.
Attaching FX Derivatives
• An arbitrage play: firm seeking financing must
be able to sell the FX derivative at a higher price
than that at which it buys the same FX derivative
• Financial institutions must face regulatory
restrictions which preclude them from direct
purchase of the FX derivative
• Dual currency or currency option bonds