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Tutorial 5 _Ans_

Tutorial 5 _Ans_ - Problem 7.9 Companies X and Y have been...

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Unformatted text preview: Problem 7.9. Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment: Fixed Rate Floating Rate Company X 8.0% LIBOR Company Y 8.8% LIBOR Company X requires a fixed-rate investment; company Y requires a floatingrate in- vestment. Design a swap that will net a bank, acting as intermediary, 0.2% per annum and will appear equally attractive to X and Y. The spread between the interest rates efiered to X and Y is 0.8% per annum on fixed rate investments and 0.0% per annum on floating rate investments. This means that the total apparent benefit to all parties from the swap is 0.8% per annum. Of this 0.2% per annum will go to the bank. This leaves 0.3% per annum for each of .X and Y. In other words, company X should be able to get a fixed-rate return of 8.3% per annum while company Y should be able to get a floating—rate return LIBOR + 0.3% per annum. The required swap is shown in Figure S7 .3. The bank earns 0.2%, company X earns 83%, and company Y earns LIBOR + 04.3%. —H~—v— 8 3% ————-— 8 5% ——-fi H #— __....._____ 8 30/0 __ _____ Company BANK Company _ , LIBOR X —-~V~Wi , WV, on, ,7? Y 7, A, , LIBOR l,,,,v,,.,_ _ LIBOR ,,_,V____ Figure 87.3 Swap for Problem 7.9 Problem 7.11. Companies A and B face the following interest rates (adjusted for the differential impact of taxes): A B ufsiiouars (floating rate) LIBOR + 0.5% LIBOR + 1.0% Canadian dollars (fixed rate) 5.0% 6.5% Assume that A wants to borrow US. dollars at a floating rate of interest and B wants to borrow Canadian dollars at a fixed rate of interest. A financial institution is planning to arrange a swap and requires a 50—basis—point spread. If the swap is equally attractive to A and B. what rates of interest will A and B end up paying? Company A has a comparative advantage in the Canadian dollar fixed—rate market. Company B has a comparative advantage in the US. dollar floating—rate market. (This may be because of their tax positions.) However, company A wants to borrow in the US. dollar floating—rate market and company B wants to borrow in the Canadian dollar fixed-rate market. This gives rise to the swap opportunity. The differential between the US. dollar floating rates is 0.5% per annum, and the differential between the Canadian dollar fixed rates is 1.5% per annum. The difference between the differentials is 1% per annum. The total potential gain to all parties from the swap is therefore 1% per annum, or 100 basis points. If the financial intermediary requires 50 basis points, each of A and B can be made 25 basis points better off. Thus a swap can be designed so that it provides A with US. dollars at LIBOR + 0.25% per annum, and B with Canadian dollars at 6.25% per annum, The swap is shown in Figure 57.4. ct: 5% ~~-~——— cs 625% «~— Company B Financial Institution Company US$' LIBORH‘Vo U53: LEBOR+1% U33: LIBOR+0 25% Figure 37.4 Swap for Problem 7.11 Principal payments flow in the opposite direction to the arrows at the start of the life of the swap and in the same direction as the arrows at the end of the life of the swap. The financial institution would be exposed to some foreign exchange risk which could be hedged using forward contracts. Problem 7.20. Company A, a British manufacturer, wishes to borrow US. dollars at a fixed rate of interest. Company B, a US. multinational, wishes to borrow sterling at a fixed rate of interest They have been quoted the following rates per annum (adjusted for differential tax efiects): Sterling Company A 11.0% 7.0% Company B 10.6% 6.2% Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and that will produce a gain of 15 basis points per annum for each of the two companies The spread between the interest rates offered to A and B is 0.4% (or 40 basis points) on sterling loans and 0.8% (or 80 basis points) on US. dollar loans. The total benefit to all parties from the swap is therefore 80 — 40 = 40 basis points It is therefore possible to design a swap which will earn 10 basis points for the bank while making each of A and B 15 basis points better off than they would be by going directly to financial markets. One possible swap is shown in Figure M7.1. Company A borrows at an effective rate of 6.85% per annum in US. dollars. Company B borrows at an effective rate of 10.45% per annum in sterling. The bank earns a 10—basis—point spread. The way in which currency swaps such as this operate is as follows. Principal amounts in dollars and sterling that are roughly equivalent are chosen. These principal amounts flow in the opposite direction to the arrows at the time the swap is initiated. Interest payments then flow in the same direction as the arrows during the life of the swap and the principal amounts flow in the same direction as the arrows at the end of the life of the swap. Note that the bank is exposed to some exchange rate risk in the swap. It earns 65 basis points in US. dollars and pays 55 basis points in sterling. This exchange rate risk could be hedged using forward contracts. £2 ll 0% £: 10.45% £: 11 09/ . . o Fmanc1al ~-—— Institution $2 6 85% Figure M7.1 One Possible Swap for Problem 7.20 Problem 7.21. Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive three-month LIBOR in return on a notional principal of $100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. The average of the bid and alter fixed rates currently being swapped for three—month LIBOR is 12% per annum for all maturities. The three-month LIBOR rate one month ago was 11.8% per annum. All rates are compounded quarterly. What is the value of the swap? The Swap can be regarded as a long position in a floating-rate bond combined with a short position in a fixed—rate bond. The correct discount rate is 12% per annum with quarterly compounding or 11.82% per annum with continuous compounding. Immediately after the next payment the floating—rate bond will be worth $100 million. The next floating payment (‘35 million) is 0.118 x 100 X 0.25 = 2.95 The value of the floating-rate bond is therefore 102.95e—0‘1182x2/ 12 = 100.941 The value of the fixed—rate bond is 2.56—0.1182x2/12 +2.5e—01182X5/12 + 2.56—0.1182X8/12 +2.56701182x11/12 + 10258—01182x14/12 = 98.678 The value of the swap is therefore 100.941 — 98.678 2 $2.263 million As an alternative approach we can value the swap as a series of forward rate agree— ments. The calculated value is (2.95 w 2,5)5—01182X2/12 + (3.0 _ 2.5)e"0 1182x5/12 -~l—(30 -—-— 2_5)30 1182X8/12 + (30 _ 2.5)8—0 1182x11/12 +(3-0 — 2.5)6’0‘1182X14/12 = $2.263 million ...
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