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058

Case 058Interest rate derivativesCore

A company with a Rs 300 crore floating loan at benchmark plus 1.5% buys a three-year 8% cap for 0.9% upfront. What does it pay each year if the benchmark runs at 7%, 9% or 10%?

1The situation

Neelgagan Logistics has a Rs 300 crore term loan that resets each year at the benchmark rate plus 1.5%. Its board wants protection against the benchmark rising, but does not want to swap to a fixed rate and lose the saving if rates fall. The treasurer buys a three-year interest rate capAn option that pays the buyer whenever a floating benchmark fixes above an agreed strike rate, on an agreed notional, for an agreed period. struck at 8% on the benchmark, on Rs 300 crore, for a one-off premium of 0.9% of notional, Rs 2.7 crore, paid today.

2Your task

Show the all-in annual cost, spreading the premium evenly over three years, if the benchmark fixes at 7%, 9% or 10%, and state the ceiling the cap creates.

Quick check

Before working it: with the benchmark at 10%, what does Neelgagan pay all-in?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

At 7% the loan costs 8.8%, at 9% and at 10% it costs 9.8%, which is the ceiling. Below the 8% strike the cap pays nothing and the company pays benchmark plus 1.5% plus 0.3% a year of spread premium. Above it the cap refunds everything over 8%, so the cost is 8% plus 1.5% plus 0.3%. In rupees that is Rs 26.4 crore at 7% and Rs 29.4 crore at either 9% or 10%, against Rs 34.5 crore unhedged at 10%.

Step 1What does the cap do, and what does it not do?

Think of a prepaid electricity plan where you pay the market tariff each month but the supplier refunds anything above Rs 8 a unit, in exchange for a joining fee. Your bill still falls when the tariff falls; it just cannot rise past the ceiling. The cap is that refund: each year the benchmark fixes above 8%, the seller pays Neelgagan the excess on Rs 300 crore, and in years it fixes below 8% the cap pays nothing and the company simply pays less interest. It does not touch the 1.5% margin, which the bank charges whatever the benchmark does, and it does not refund its own premium.

BenchmarkUnhedged rateCap paysPremium per yearAll-in rateRs crore all-in
7%8.5%0.0%0.3%8.8%26.4
9%10.5%1.0%0.3%9.8%29.4
10%11.5%2.0%0.3%9.8%29.4
Annual cost on Rs 300 crore. The 0.9% premium is spread as 0.3% a year without interest. Below 8% the cap pays nothing and the company pays 0.3% more than an unhedged borrower; at 9% and 10% the cost stops at 9.8%.
Step 2Where does the 9.8% ceiling come from?

Add the three pieces that still have to be paid when the cap is working. The capped benchmark, 8%, plus the lender's margin, 1.5%, plus the premium spread over three years, 0.3%, is 9.8%, and no benchmark level can push the cost above it. At 10% the cap pays 2% of Rs 300 crore, Rs 6 crore, which is exactly the gap between the Rs 34.5 crore unhedged bill and the Rs 29.4 crore all-in. At 9% it pays Rs 3 crore. At 7% it pays nothing, and the company has paid Rs 0.9 crore that year for protection it did not use, which is what insurance costs in the years the house does not burn.

The cap turns a rising cost line into a ceiling, for a fee of 0.3% a year7%8%9%10%11%12%5%6%7%8%9%10%11%Benchmark rate7%: 8.8% capped, 8.5% open9%: 9.8% capped10%: 9.8% capped10%: 11.5% open9%: 10.5% opencap strike 8%unhedged: benchmark + 1.5%with cap: + 1.5% + 0.3% fee, ceiling 9.8%
The unhedged cost rises one for one with the benchmark while the capped cost runs 0.3% above it until the 8% strike and then stays flat at 9.8%, so at 9% and 10% the company saves 0.7% and 1.7% of Rs 300 crore respectively.
Step 3Why a cap rather than a swap, and what is the honest cost comparison?

A swap to fixed would have removed the premium and the ceiling both, replacing them with one fixed rate; if that fixed rate were, say, 7.8%, the company would pay 9.3% all-in in every year, better than the cap at 9% and 10%, worse at 7%. The cap costs 0.3% a year more than doing nothing in every calm year, and that is the price of keeping the saving when rates fall; a borrower who is confident rates will rise should swap, and one who wants a ceiling but expects to benefit from falls should cap. Say the simplification out loud: spreading Rs 2.7 crore evenly ignores the interest on money paid three years early, so the true annual cost is a little above 0.3%, and the cap's payout timing, usually at each reset, has been treated as if it matched the loan's interest dates exactly.

A treasurer's closing line names the residual risks: the cap is written on the benchmark, so if the bank re-prices the 1.5% margin the cap does not help; the cap seller must be good for the payout in the year it matters; and if the loan is repaid early the cap is left over, with whatever value the market gives it then.

Where candidates lose it

Candidates cap the whole loan rate at 8% and report 8% at every high benchmark, forgetting that the 1.5% margin sits on top. The cap is on the benchmark; the lender's spread is untouched.

The second miss is leaving the premium out, which makes the cap look free in the 7% year. Spread it, say how you spread it, and admit that spreading evenly is a simplification.

What the interviewer asks next

  • What would a collar look like here: sell a 6% floor to pay for the cap. What does the company give up?
  • The cap is on a one-year benchmark but the loan resets quarterly. What basis risk does that create?
  • If the benchmark fixes at 8.5% in year one and 6% in years two and three, what has the cap earned against its cost?
← Case 057A client places USD 1 million for one month in a dual currency deposit paying 7% instead of 4.5%, spot 84.00, and the bank may repay in rupees at 84.50. Decompose it, price the extra yield, and show the client's position at 83.00 and 86.00.Case 059 →Five counterparties with exposures of Rs 40, 25, 60, 15 and 30 crore, default probabilities of 0.5%, 2%, 0.8%, 6% and 1.5%, and 60% loss given default except the fifth at 45%. Compute and rank expected loss, and say which limit you would cut first.

Company names and figures are illustrative.

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