14.1 Problem Andina, S.A.
From which source should Andina borrow? Assumptions Principal borrowing need Maturity needed, in weeks Rate of interest charged by ALL potential lenders New York interest rate practices Interest calculation uses: Exact number of days in period Number of days in financial year So the interest charge on this principal is Great Britain interest rate practices Interest calculation uses: Exact number of days in period Number of days in financial year So the interest charge on this principal is Swiss interest rate practices Interest calculation uses: Assumed 30 days per month for two months Number of days in financial year So the interest charge on this principal is Values $8,000,000 8 4.000%
56 360 $49,777.78
56 365 $49,095.89
60 360 $53,333.33
Andina should borrow in Great Britain because it has the lowest interest cost.
Problem 14.2 Adelaide Corporation
Compare the alternatives and make a recommendation. Assumptions Principal borrowing need Maturity needed, in years Fixed rate, 2 years Floating rate, six-month LIBOR + spread Current six-month LIBOR Spread Fixed rate, 1 year, then re-fund Values $30,000,000 2.00 5.000% 3.500% 1.500% 4.500% First 6-months #1: Fixed rate, 2 years Interest cost per year Certainty over access to capital Certainty over cost of capital #2: Floating rate, six-month LIBOR + spread Interest cost per year Certainty over access to capital Certainty over cost of capital #3: Fixed rate, 1 year, then re-fund Interest cost per year Certainty over access to capital Certainty over cost of capital Second 6-months $1,500,000 Certain Certain Third 6-months Fourth 6-months $1,500,000 Certain Certain
Certain Certain
Certain Certain
$750,000.00 Certain Certain
$750,000.00 Certain Uncertain
$750,000.00 Certain Uncertain
$750,000.00 Certain Uncertain
Certain Certain
$1,350,000.00 Certain Certain
??? Uncertain Uncertain
??? Uncertain Uncertain
Only alternative #1 has a certain access and cost of capital for the full 2 year period. Alternative #2 has certain access to capital for both years, but the interest costs in the final 3 of 4 periods is uncertain. Alternatvie #3, possessing a lower interest cost in year 1, has no guaranteed access to capital in the second year. Depending on the company's business needs and tolerance for interest rate risk, it should choose between #1 and #2.
Problem 14.3 Raid Gauloises
Given interest rate expectations, which loan is the best deal? Assumptions Principal borrowing need Maturity needed, in years Current euro-LIBOR Banque de Paris' spread & expectation Banque de Paris' initiation fee Banque de Sorbonne's spread & expectation Banque de Sorbonne's initiation fee Values 20,000,000 4.00 4.000% 2.000% 1.800% 2.500% 0.000% Expected Chg in LIBOR
0.500% 0.250%
Raid Gauloises must evaluate both loan proposals under both potential interest rate scenarios. Banque de Paris Loan Proposal Expected interest rates & payments: Expected euro-LIBOR Bank spread Interest rate Funds raised, net of fees Expected interest costs Repayment of principal Total cash flows All-in-cost of funds if: euro-LIBOR rises 0.500% per year euro-LIBOR rises 0.250% per year Banque de Sorbonne Loan Proposal Expected interest rates & payments: Expected euro-LIBOR Bank spread Interest rate Funds raised, net of fees Expected interest costs Repayment of principal Total cash flows All-in-cost of funds if: euro-LIBOR rises 0.500% per year euro-LIBOR rises 0.250% per year Year 0 4.000% 2.000% 6.000% 19,640,000 - 1,300,000 19,640,000 - 1,300,000 - 1,400,000 - 1,400,000 - 1,500,000 - 1,500,000 - 1,600,000 - 20,000,000 - 21,600,000 Year 1 4.500% 2.000% 6.500% Year 2 5.000% 2.000% 7.000% Year 3 5.500% 2.000% 7.500% Year 4 6.000% 2.000% 8.000%
7.7438% 7.1365% Year 0 4.000% 2.500% 6.500% 20,000,000
Found by plugging in .250% in expectations above. Year 1 4.250% 2.500% 6.750% Year 2 4.500% 2.500% 7.000% Year 3 4.750% 2.500% 7.250% Year 4 5.000% 2.500% 7.500%
- 1,350,000 20,000,000 - 1,350,000
- 1,400,000 - 1,400,000
- 1,450,000 - 1,450,000
- 1,500,000 - 20,000,000 - 21,500,000
7.0370% 7.1036%
Found by plugging in .500% in expectations above.
The Banque de Sorbonne loan proposal is actually lower all-in-cost under either interest rate scenario.
Problem 14.4 Felini Motors
Assumptions Principal borrowing need Maturity needed, in years Current LIBOR Felini's bank spread Proportion of differential paid by FRA Cost of FRA If LIBOR Falls 50 Basis Pts Per Year Expected annual change in LIBOR LIBOR Bank spread Interest rate Funds raised, net of fees Expected interest (interest rate x principal) Forward Rate Agreement Repayment of principal Total cash flows All-in-cost of funds (IRR) 4.000% 2.500% 6.500% 5,000,000 - 100,000 4,900,000 7.092% - 300,000 - 25,000 - 325,000 - 275,000 - 50,000 - 325,000 - 250,000 - 75,000 - 325,000 - 225,000 - 100,000 - 5,000,000 - 5,325,000 Values 5,000,000 4.00 4.000% 2.500% 70% 100,000 Year 0 Year 1 -0.500% 3.500% 2.500% 6.000% 3.000% 2.500% 5.500% 2.500% 2.500% 5.000% 2.000% 2.500% 4.500% Year 2 Year 3 Year 4
If LIBOR Rises 50 Basis Pts Per Year Expected annual change in LIBOR LIBOR Bank spread Interest rate Funds raised, net of fees Expected interest (interest rate x principal) Forward Rate Agreement Repayment of principal Total cash flows All-in-cost of funds (IRR)
Year 0
Year 1 0.500%
Year 2
Year 3
Year 4
4.000% 2.500% 6.500% 5,000,000 - 100,000 4,900,000 7.458%
4.500% 2.500% 7.000%
5.000% 2.500% 7.500%
5.500% 2.500% 8.000%
6.000% 2.500% 8.500%
- 350,000 17,500 - 332,500
- 375,000 35,000 - 340,000
- 400,000 52,500 - 347,500
- 425,000 70,000 - 5,000,000 - 5,355,000
This rather unusual forward rate agreement is somewhat one-sided in the favor of the insurance company. When Felini is correct, Felini pays the full difference in rates to the insurance company. But when interest rates move against Felini, the insurance company pays Felini only 70% of the difference in rates. And all of that is after Felini paid $100,000 up-front for the agreement regardless of outcome. Not a very good deal. A final note of significance is that since Felini receives only 70% of the difference in rates, its total cost of funds is not effectively "capped" -- they could in fact rise with no limit over the period as interest rates rose.
Problem 14.5 John Jones
How will John Jones do using interest rate futures? Assumptions Interest rate futures, closing price Effective yield on interest rate futures Values 93.07 6.930% Three Months From Now Floating Rate is Floating Rate is 6.000% 8.000% 6.000% -6.930% -0.930% Loss 8.000% -6.930% 1.070% Gain
John Jones' interest rate payments with futures Interest payment due in three months Sell a future (take a short position) Gain or loss on position
Problem 14.6 Canon Candy Company
Calculate gains or losses from swap position. Assumptions Notional principal LIBOR, per annum Spread paid over LIBOR, per annum Swap rate, to pay fixed, per annum Values $5,000,000 4.000% 2.000% 7.000% First 6-months 0.500% 4.500% Second 6-months Third 6-months Fourth 6-months
Interest & Swap Payments a. LIBOR increases 50 basis pts/6 months Expected LIBOR Current loan agreement: Expected LIBOR (for 6 months) Spread (for 6 months) Expected interest payment Swap Pay Agreement: fixed (for 6-months) Receive floating (LIBOR for 6 months) Net interest (loan + swap) Swap savings? Net interest after swap Loan agreement interest Swap savings (swap cost)
5.000%
5.500%
6.000%
-2.250% -1.000% -3.250%
-2.500% -1.000% -3.500%
-2.750% -1.000% -3.750%
-3.000% -1.000% -4.000%
-3.500% 2.250% -4.500%
-3.500% 2.500% -4.500%
-3.500% 2.750% -4.500%
-3.500% 3.000% -4.500%
$(225,000) (162,500) $(62,500)
$(225,000) (175,000) $(50,000)
$(225,000) (187,500) $(37,500)
$(225,000) (200,000) $(25,000)
b. LIBOR decreases 25 basis pts/6 months Expected LIBOR Current loan agreement: Expected LIBOR (for 6 months) Spread (for 6 months) Expected interest payment Swap Agreement: Pay fixed (for 6-months) Receive floating (LIBOR for 6 months) Net interest (loan + swap) Swap savings? Net interest after swap Loan agreement interest Swap savings (swap cost)
-0.250% 3.750%
3.500%
3.250%
3.000%
-1.875% -1.000% -2.875%
-1.750% -1.000% -2.750%
-1.625% -1.000% -2.625%
-1.500% -1.000% -2.500%
-3.500% 1.875% -4.500%
-3.500% 1.750% -4.500%
-3.500% 1.625% -4.500%
-3.500% 1.500% -4.500%
$(225,000) (143,750) $(81,250)
$(225,000) (137,500) $(87,500)
$(225,000) (131,250) $(93,750)
$(225,000) (125,000) $(100,000)
In both cases Canon Candy Company is suffering higher total interest costs as a result of the swap.
Problem 14.7 Xavier and Zulu
Make a recommendation on potential swaps. Assumptions Credit rating Prefers to borrow Fixed-rate cost of borrowing Floating-rate cost of borrowing: LIBOR (value is unimportant) Spread Total floating-rate Comparative Advantage in Borrowing Xavier's absolute advantage: in fixed rate borrowering in floating-rate borrowing Comparative advantage in fixed rate One Possibility Xavier borrows fixed Zulu borrows floating Xavier pays Zulu floating (LIBOR) Zulu pays Xavier fixed Net interest after swap Savings (own borrowing versus net swap): If Xavier borrowed floating If Xavier borrows fixed & swaps with Zulu Xavier AAA Floating 8.000% 5.000% 1.000% 6.000% Values 4.000% 1.000% 3.000% Xavier -8.000% ---5.000% 8.500% -4.500% Zulu ---7.000% 5.000% -8.500% -10.500% Zulu BBB Fixed 12.000% 5.000% 2.000% 7.000%
6.000% 4.500% 1.500% 12.000% 10.500% 1.500%
If Zulu borrowes fixed If Zulu borrows floating & swaps with Xavier
The 3.0% comparative advantage enjoyed by Xavier represents the opportunity set for improvement for both parties. This could be 1.5% savings for each (as in the example shown), or any other combination which distributes the 3.0% between the two parties.
Problem 14.8 Carlton's Cross Currency Swap: Receive Dollars & Pay Francs
Calculate gains or losses from swap position. Assumptions Notional principal Spot exchange rate, SFr./$ Spot exchange rate, $/euro a) Interest & Swap Payments Receive fixed rate dollars at this rate: On a notional principal of: Carlton will receive cash flows: Exchange rate, time of swap (SFr./$) Carlton will pay cash flows: On a notional principal of: Pay fixed rate Swiss francs at this rate: SFr. 15,000,000 2.01% 2.01% 2.01% SFr. 301,500 SFr. 301,500 SFr. 15,301,500 Values $10,000,000 1.5000 1.1200 Year 0 Swap Rates US dollar Swiss franc -- SFr. Year 1 5.56% $10,000,000 1.5000 $556,000 $556,000 $10,556,000 3- year bid 5.56% 1.93% Year 2 5.56% 3-year ask 5.59% 2.01% Year 3 5.56%
b) Unwinding the swap after one-year Remaining dollar cash inflows PV factor at now current fixed $ interest PV of remaining dollar cash inflows Cumulative PV of dollar cash infllows Remaining Swiss franc cash outflows PV factor at now current fixed SF interest PV of remaining SF cash outflows Cumulative PV of SF cash outflows New current spot rate, SFr./$ Cumulative PF of SF cash outflows in $ Settlement: Cash inflow Cash outflow Net cash settlement of unwinding 2.20% $10,650,457
Year 1
Year 2 $556,000 0.9785 $544,031
Year 3 $10,556,000 0.9574 $10,106,426
5.20% SFr. 14,112,787 1.5560 $9,069,915
SFr. 301,500 0.9506 SFr. 286,597
SFr. 15,301,500 0.9036 SFr. 13,826,190
$10,650,457 (9,069,915) $1,580,542
This is a cash receipt by Carlton from the swap dealer.
Problem 14.9 Carlton's Cross Currency Swap: Receive Euros & Pay Yen
Calculate gains or losses from swap position. Assumptions Notional principal Spot exchange rate, Yen/euro Values 5,000,000 104.00 Swap Rates Euros -- Japanese yen 3- year bid 3.24% 0.56% 3-year ask 3.28% 0.59%
a) Interest & Swap Payments Receive fixed rate euros at this rate: On a notional principal of: Carlton will receive cash flows: Exchange rate, time of swap (/) Carlton will pay cash flows: On a notional principal of (yen): Pay fixed rate Japanese yen at this rate:
Year 0
Year 1 3.24%
Year 2 3.24% 162,000
Year 3 3.24% 5,162,000
5,000,000 104.00 520,000,000 0.59% 0.59% 0.59% 3,068,000 3,068,000 523,068,000 162,000
b) Unwinding the swap after one-year Remaining euro cash inflows PV factor at now current fixed interest PV of remaining cash inflows Cumulative PV of cash infllows Remaining cash outflows PV factor at now current fixed interest PV of remaining cash outflows Cumulative PV of cash outflows New current spot rate, / Cumulative PV of cash outflows in Settlement: Cash inflow Cash outflow Net cash settlement of unwinding
Year 1
Year 2 162,000 0.9653 156,371
Year 3 5,162,000 0.9317 4,809,484
3.60% 4,965,855
0.80% 517,841,931 114.00 4,542,473
SFr. 3,068,000 0.9921 SFr. 3,043,651
SFr. 523,068,000 0.9842 SFr. 514,798,280
4,965,855 (4,542,473) 423,382
This is a cash receipt by Carlton from the swap dealer.
Problem 14.10 Delphi's 7-Year Cross Currency Swap
Calculate gains or losses from swap position. Assumptions Notional principal Spot exchange rate, $/ Values $50,000,000 1.16 Swap Rates US dollar Euros 7- year bid 5.86% 4.01% 7-year ask 5.89% 4.05%
a) Interest & Swap Payments Receive fixed rate dollars at rate: Notional principal of: Receive cash inflows of: Spot exchange rate, $/ Pay cash outflows of: Notional principal of: Pay fixed rate euros at rate:
Year 0 5.86% $50,000,000
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
$2,930,000 1.16 1,745,690 43,103,448 4.05%
$2,930,000
$2,930,000
$2,930,000
$2,930,000
$2,930,000
$52,930,000
1,745,690
1,745,690
1,745,690
1,745,690
1,745,690
44,849,138
b) Unwindingthe Swap
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
If the swap is unwound three years later, there are four years of cash flows remaining: Remaining dollar cash inflows PV factor at now current fixed $ interest PV of remaining dollar cash inflows Cumulative PV of $ cash infllows $2,930,000 0.9579 $2,806,513 $2,930,000 0.9175 $2,688,231 $2,930,000 0.8788 $2,574,934 $52,930,000 0.8418 $44,555,354
4.40% $52,625,033
Remaining euro cash outflows PV factor at now current fixed interest PV of remaining euro cash outflows Cumulative PV of cash outflows Spot exchange rate at unwinding ($/) Cumulative PV of cash outflows, $ Settlement: Cash inflow Cash outflow Net cash settlement of unwinding
5.35% 41,132,542 1.02 $41,955,193
1,745,690 0.9492 1,657,038
1,745,690 0.9010 1,572,889
1,745,690 0.8553 1,493,012
44,849,138 0.8118 36,409,603
$52,625,033 (41,955,193) $10,669,840
This is a net cash payment to Delphi from the swap dealer.