395 38 solutions numerical problems 30 interest rate currency swaps 30

FINANCIAL MANAGEMENT 2eRajiv Srivastava - Dr. Anil Misra

Solutions to Numerical ProblemsChapter 30

30-1: Changing Fixed Rate Borrowing to Floating & Reducing CostIspat Industries Limited had raised funds through issue of fixed rate 5-year bonds with fixed interest rate of 12%. The issue was made two years ago. Since then the interest rates have declined and the low level of interest rate is likely to continue for some time. At present the yield on 3-year treasury bonds is 9%. The bankers of Ispat Industries have offered a swap to them at 50 bp over treasuries for MIBOR. The current MIBOR is 8.75%.

a) What savings in cost of funds can be made by the firm?b) Should the firm accept the swap? How would the swap work?c) What would be the risk for Ispat Industries if they enter the swap?

Solution: a) and b) The swap offered by bank to the firm requires payment of floating rate and receiving fixed rate for which the rate would be 9.50%. With MIBOR currently at 8.75% the savings would be 0.75% (75 bp). Ispat Industries must enter into a swap with the bank, where it pays floating MIBOR and receives fixed, as shown below:

If the firm accepts the swap under which it pays to the bank MIBOR and receives fixed, the cash inflows on the fixed leg would be 50 bp over treasury yield i.e. 9.50% and cash outflow on floating leg would be 8.75%. The cost of funds for the firm would then be:

Nature Basis Current CostPays to the bond holders Fixed 12% 12.00%Pays to the Bank under Swap Floating MIBOR 8.75%Receives from Bank under swap Fixed T + 50 bp 9.50%

11.25%The effective cost of the loan would then be 12% - 9.50% + MIBOR = MIBOR + 2.50%.With MIBOR currently at 8.75% the cost of funds would be 11.25% (8.75% + 2.50%)

The character of borrowing stands changed to fixed rate liability to floating rate liability.c) The risk involved in the swap would be the rise in the rate subsequent to the swap. As long as MIBOR does not go above 11.25% the firm would continue to benefit from the swap arrangement entered now.

30-2: Changing Floating Rate Borrowing to Fixed & Reducing CostCement Corporation Limited (CCL) had come out with the Foreign Currency Bonds at floating rate 3 years ago. The bonds had the maturity of 7 years and carried floating rate of interest at LIBOR + 2.5%. At the time of the issue CCL had anticipated decline in the interest rates. However in the last three years the rates have gone up. The trend of interest rates suggests further rise. Barclays Bank in London has offered swap at 75 bp over 4-year treasury yield for LIBOR. The yield on 4-year treasury is 8.25% and 6-m LIBOR is at 9.5%.

a) What swap should CCL enter into and what savings would it result?b) If CCL enters the swap what risk it carries?

Floating MIBOR (8.75%)

12%

Fixed T + 50 bp = 9.50%

Firm Bank

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Rajiv Srivastava & Anil Misra Financial Management, 2e

© Oxford University Press 2011



Solution:CCL must enter the swap with the Barclays Bank where it receives LIBOR and pays fixed T + 75 bp. At current yield on treasury and level of LIBOR the savings would be 50 bp. The swap arrangement is shown in the diagram below:

If CCL accepts the swap under which it receives from Barclays LIBOR and pays fixed, the cash outflows on the fixed leg would be 75 bp over treasury yield i.e. 9.00% while cash inflows would be at 9.50%. The cost of funds for the firm would then be:

Nature Basis Current CostPays to the bond holders Floating L+250 bp 12.00%Receives from the Bank under Swap Floating LIBOR 9.50%Pays to the Bank under swap Fixed T + 75 bp 9.00%

11.50%Cost without swap L + 2.5%Cost with Swap 11.50%Savings in cost at current levels 50 bp

b) As long as LIBOR remains more than 9% CCL would benefit from the swap.When LIBOR goes below 9.5% the swap deal would turn against CCL.

30-3: Reducing Cost of Borrowing Through SwapFirst Chemicals is AAA rated company engaged in manufacture of chemicals. It need funds of Rs 100 crore that can be raised either at floating rate of MIBOR + 50 bp or at fixed rate of 10.40%. At the same time Royal Oils, a AA rated firm too needs funds of the same magnitude and can raise them at MIBOR + 100 bp with floating rate borrowing or at 11.50% in the fixed ratemarket. The tenure of borrowing by both the firms is 7 years.First Chemical is inclined to raise funds on floating rate basis while Royal Oils is happy raising money on fixed rates.

Show how the swap can benefit both the firms and to what extent?If banks is involved as intermediary and wants 5 bp from each of the firm how would the cost of funds change?What function would bank discharge as intermediary?

Solution:The position of the two firms in the two markets is as below:

Fixed rate market Floating Rate marketFirst Chemicals 10.40% MIBOR + 50 bpRoyal Oils Ltd. 11.50% MIBOR + 100 bpAdvantage First Chemicals 110 bp 50 bp

Floating LIBOR (9.50%)

LIBOR + 2.50%

Fixed T + 75 bp = 9.00%

CCL BarclaysBank

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a) First Chemicals has advantage in borrowing from both the markets as compared to Royal Oils. This is because of the better rating First Chemicals has.

However, the advantage in the fixed rate market is 110 bp as compared to the advantage in the floating rate market at 50 bp. Therefore comparative advantage i.e. the difference of the two absolute advantages is 60 bp. The comparative advantage can be exploited by the two firms by arranging a swap between them. If the advantage of 60 bp is to be shared equally the cost of funds for each of them can come down by 30 bp.

Since First Chemicals has greater advantage in the fixed rate market it must raise borrowing at 10.40% fixed while Royal Oils must raise funds at floating rate at MIBOR +1.00%. Thereafter the two can enter into a swap where First Chemicals pays Royal Oils 11.20% fixed and receives in exchange M + 100 floating. This is shown in the diagram below:

After the swap the cost of funds would be 30 bp less for both the firms as shown:

First Chem Royal OilsPayment to the market 10.40% 10.40%Payment to counter party under swap M+1.00% 11.20%Receipt from counter party under swap 11.20% M+1.00%Cost of funds with swap M + 20bp 11.20%Cost of funds without swap M + 50bp 11.50%Benefit of swap 30 bp 30 bp

b) When swap is arranged by a bank the benefit has to be shared among three parties, the two borrowers and the bank. Assuming bank wants 10 bp as commission (5bp from each party) the benefit for the borrowers would stand reduced to 50 bp. The swap with bank as intermediary is shown below:

First Chem Royal Oils

11.20% 11.25%

M + 1.05% M +1.00%

10.40% M + 1.00%

First Chem

Bank Royal Oils

Fixed 11.20% Floating

10.40% M +1.00% M + 1.00%

First Chem

Royal Oils

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FINANCIAL MANAGEMENT 2e Rajiv Srivastava - Dr. Anil Misra


Payment to the market 10.40% 10.40%Payment to bank under swap M+1.05% 11.25%Receipt from bank under swap 11.20% M+1.00%Cost of funds with swap M + 25bp 11.25%Cost of funds without swap M + 50bp 11.50%Benefit of swap 25 bp 25 bp

c) The bank discharges many functions in a swap deal. Besides facilitating the deal between the two parties the most important function discharged by the bank is the elimination of counter-party risk. Under direct swap arrangement the two parties take risk on each other as one party may not be inclined to make payments depending upon the interest rate scenario. With bank acting in between such risks are eliminated.

30-4: Value of SwapIndian Petro Limited had entered into a swap with a bank under which it was paying 13% fixed for receiving LIBOR. The swap required annual payments of interest. The next cash flow is due 90 days from now for which the LIBOR was set at 11% nine months ago. Since the time of entering the swap arrangement the structure of interest rate has declined. Currently the 5-year swap is being quoted at 10% against LIBOR. 3-m LIBOR is 8%. What is the value of the swap.

Solution:Assumed principal amount Rs 100.00Fixed leg cash flow 13.00%Current swap rate 10.00%Following are the cash flows of the fixed leg:Value of the Fixed Leg

Time from now (yrs) 0.25 1.25 2.25 3.25 4.25 5.25Time from t=3 (yrs) 1 2 3 4 5Amount 13.00 13.00 13.00 13.00 13.00 113.00PV at t=3, at 10% 13.00 11.82 10.74 9.77 8.88 70.16 Present Value at current swap rate at t = 3 m Rs 124.37Present Value at current swap rate at t = 0 Rs 121.34

Value of the floating legLIBOR amount for next cash flow already set: 11.00%Current 3-m LIBOR 8.00%Present Value of floating rate cash flow Rs 108.82

(Interest + principal discounted at current 3-m LIBOR)Present Value of fixed leg - cash outflows -Rs 121.34Present Value of floating leg - cash inflows Rs 108.82Value of the swap -Rs 12.52

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30-5: Value of Currency Swap and CancellationAn Indian firm had entered a swap with a bank some time ago exchanging a rupee loan for US$. The exchange rate prevailing at that point of time was Rs. 45 per US $. The swap was agreed with the bank where Indian Steel received fixed 12% interest on Rs. 450 crore and paid floating on 6-m LIBOR on US $ 10 crore. The swap has 63 months to go with next exchange of interest falling due 3 months from now. In the meanwhile Indian Rupee has appreciated to Rs. 43.50 per $. The floating rate for US $ fixed for the next payment was at 11% being the 6-m LIBORprevailing 3 months ago. The current 3-m LIBOR is 9.5%. The current swap rate is 10% fixed for Rs. for US $ floating.

a) What is the value of the swap for Indian Steel today?b) If bank wants to cancel the swap today what amount should Indian Steel demand to agree for canceling the arrangement?c) What would be the value of swap if the exchange rate had remained constant?

Solution:Under the existing swap Indian Steel Limited was receiving 12% interest and paying 6-m LIBOR in US $. Since the interest rates have fallen subsequent to the swap arrangement the value of the cash flows has increased.

Value of the Fixed Leg Cash Flows:Principal Amount Rs 450.00 CroreInterest rate Fixed 11.00%Current exchange rate - Rs/$ 43.50Current Swap rate 10.00%

months from now

# of periods from t = 3 m

Cash flow Rs. crore

PV at 10%Rs. Crore

3 0 24.75 24.759 1 24.75 23.57

15 2 24.75 22.4521 3 24.75 21.3827 4 24.75 20.3633 5 24.75 19.3939 6 24.75 18.4745 7 24.75 17.5951 8 24.75 16.7557 9 24.75 15.9563 10 474.75 291.46

PV at t = 3 - Rs Crore 492.1239 PV at t = 0 - Rs Crore 480.1209 Equivalent $ at current exchange rate - Crore 11.0373

Value of floating leg

Exchange rate at the swap initiation - Rs/$ 45.00US $ Principal amount - Crore 10.00Next payment fixed at 10.50%Next payment due after 3 months3-m LIBOR 9.00%Amount of floating leg - US $ crore 10.525PV of floating leg - at 3-m LIBOR - US $ crore 10.2934

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Value of the swap (Receipts - Payments) - US $ Crore 0.7439 - Rs. Crore 32.3580

b) The present value of receipts of the firm exceed that of payments. If bank pays Indian Steel Limited Rs. 32.36 crore it may agree to cancel the swap.

c) The value of the swap for Indian Steel Limited is derived from two sources - 1) from decline in interest rate and 2) from appreciation of Indian Rupee. If the exchange rate had not moved from Rs 45 to Rs 43.50 the US $ equivalent of the fixed leg would have been US $ 10.6994 crore. (480.1209/45)

The value of the swap then would have been attributable entirely to decline in interest rate

US $ crorePresent Value of the fixed leg payments: 10.6694Present Value of floating leg receipts : 10.2934Value of the swap of the swap 0.3760Value of the swap Rs Crore

Attributable to decline in interest rate 16.9201Attributable to appreciation of Indian Rupee 15.4380

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395 38 solutions numerical problems 30 interest rate currency swaps 30

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