FD 2

FORWARD CONTRACTS
1. On January 2, a bank sells a 2 × 5 FRA. The contracted forward rate is 5.34%. The principal
amount is INR 1 million. On the settlement date, the spot MIBOR rates are:
Maturity Rate
1 month 4.85%
2 months 4.92%
3 months 4.95%
4 months 5.01%
5 months 5.04%
6 months 5.08%
The reference rate for the loan in the market is MIBOR + 50 basis points.
What amount would the bank pay or receive on the settlement date?
Solution:
Since it is a 2 x 5 FRA contracted on Jan 2, the settlement date will be March 2, and the
agreement will be for a 3-month period ending on June 1.
Agreed rate = 5.34%

3-month MIBOR on settlement date = 4.95%
Loan rate in market = MIBOR + 50 bps
= 4.95 + 0.05 = 𝟓. 𝟒𝟓%
Since the loan rate is higher than the agreed rate, the bank will need to make payments on the
settlement date.
𝑃[𝑟 − 𝑓](𝐷⁄𝐵)
Settlement amount =
𝐷
[1 + 𝑟 (𝐵 )]
1,000,000[5.45% − 5.34%][92⁄360]
=
92
[1 + 5.45% (360)]
=INR 277.25
The bank will need to pay INR 277.25.

2. An Indian gold merchant enters into a contract to buy 200 ounces of gold from an Australian
gold mining company at a price of USD 910 per ounce, and the payment would be made after
three months from the date of the contract. The current exchange rate is USD 1 = INR 42.8754.
The interest rate in the USA is 5%, and the interest rate in India is 8%. The merchant decides to
hedge the risk of exchange rate by entering into a forward contract. What would be the
forward rate? How much amount in Indian rupees would the merchant pay three months
later?
Solution:
Since the interest rate in the USA is 5%, and in India it is 8%, and the spot exchange rate is
USD1 = INR42.874,
𝑟
𝑒0 (1 + 4𝐼 )
3-month forward rate = 𝑟
(1 + 𝑈𝑆4 )
0.08
42.8754 (1 + )
= 4
0.05
(1 + 4 )
= INR 43.193
The amount to be paid = quantity of gold * price per ounce in USD * forward rate
= 200 × 910 × 43.193 = INR 7,861,125
3. Suppose the gold merchant enters into a forward contract to buy gold from an Australian gold
mining company 6 months later at USD 930 per ounce. At the end of three months from the
date this contract was entered into, the forward price of a forward contract to sell gold three
months hence is USD 920 per ounce. Does the gold merchant gain or lose on the original
forward contract? Suppose it is expected that the price of gold is likely to decrease further in
the next three months, what should the gold merchant do?
Solution:
The original forward contract is to buy gold at USD 930 per ounce after six months.
Three months later, the forward price is USD 920 per ounce. Since the gold price has decreased,
the gold merchant is losing. However, there is no realized loss, since the original forward
contract maturity is three months later, and gain or loss will depend on how gold prices move
over the next three months. If prices are expected to decrease further, the gold merchant
should enter into a forward contract to sell gold at USD 920 so that his losses are limited to USD
10 per ounce.
4. Suppose that on April 1, 2008, you entered into a forward contract to buy 100,000 U.S. dollars
at USD 1 = INR 42.2478, for delivery on July 1, 2008. The spot rate on April 1, 2008, is USD 1 =
INR 42.1145. On July 1, 2008, the spot rate is USD 1 = INR 42.3245 and the forward rate for
delivery (three months later) is USD 1 = INR 42.4223. Did you profit or lose on this
transaction? What is the amount of profit or loss made?
Solution:
The forward contract is to buy USD 100,000 at INR 42.2478 on July 1.
On July 1, the spot rate is 42.3245.
Since the forward rate is below the spot rate on July 1, you profited from the transaction.
Profit = 100,000(42.3245 – 42.2478) = INR 𝟕, 𝟔𝟕𝟎
5. A market maker quotes 3 × 5 FRAs at 7.5 (bid) and 7.64 (asked). You buy an FRA with a
principal amount of INR 1 million. On the settlement date, the following spot rates are
observed:
Maturity Rate
2 months 8.45%
3 months 8.38%
4 months 8.32%
5 months 8.26%
Assume that the banks use the convention of 360 days in a year to compute the settlement
amount and the number of days per month is 30 days.
When will the payments be made? Will you receive a payment on the settlement day or will
you have to make a payment? What will be the settlement amount?
Solution:
It is a 3 x 5 FRA or settlement takes place three months later, the loan period being 2 months.
The appropriate market rate is 8.45% for a two-month maturity. Since you buy FRA, you will buy
at an ask rate of 7.64%, which is the agreed rate.
Payment will be made on the settlement date, which is three months from the current date.
Since the agreed rate of 7.64% is lower than the market rate of 8.45%, you would receive
payment.
60
1 million (8.45 − 7.64)% (360)
Settlement amount =
60
(1 + 8.45% (360))
= 𝐈𝐍𝐑𝟏𝟑𝟑𝟏. 𝟐𝟓
6. Shriram Cosmetics has exported cosmetics to Dang Imports in Vietnam for Vietnam dong
(VND) 100 million on March 14, and Dang Imports will pay the amount on May 28. The
exchange rate on March 14 is INR 1 = VND 372.4578. Since Shriram Cosmetics is concerned
about currency risk, it enters into a non-deliverable forward contract with Citibank for a
notional amount of VND 100 million. According to the forward contract, the forward rate is
fixed at INR 1 = VND 374.4964, with expiry on May 28. If the actual spot rate on May 28 is INR
1 = VND 373.3894, what will be the settlement on May 28?
Solution:
Forward rate = INR 1

INR 1 = VND 374.4964
Spot rate on May 28 = VND 373.3894
Amount = VND 100,000,000
100,000,000
Amount of INR under forward rate =
374.4984
100,000,000
Amount of INR under spot rate =
373.3894
= 267,816.90
Since the amount under the forward rate is lower than the amount under the spot rate, Shriram
Cosmetics has lost under the forward contract, and will pay the difference of 267.816.90 –
267,025.30 = INR 791.60 to the bank.
7. Mohan Textiles has imported cotton from Ng Exports in Cambodia for Cambodian riel (KHR)
40 million on May 20, and Mohan Textiles will pay the amount on July 20. The exchange rate
on May 20 is INR 1 = KHR 86.3844. Since Mohan Textiles is concerned about currency risk, it
enters into a non-deliverable forward contract with the IDBI Bank for a notional amount of
KHR 40 million. According to the forward contract, the forward rate is fixed at INR 1 = KHR
86.4356, with expiry on July 20. If the actual spot rate on July 20 is INR 1 = KHR 87.3542, what
will be the settlement on July 20?
Solution:
Mohan needs to pay HR 40 million on July 20.
Forward rate = INR 1

Forward rate = KHR 86.4356
Spot rate = INR 1
Spot rate = KHR 87.3542
Amount of INR under forward rate = INR 462772.30
Amount of INR under spot rate = INR 457905.90
Since Mohan needs to pay INR 462772.30 under the forward contract, he will use the spot rate and pay
INR 457905.90 to Ng Exports and INR 4,866.40 to the bank.

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FORWARD CONTRACTS

Agreed rate = 5.34%

The bank will need to pay INR 277.25.

The forward contract is to buy USD 100,000 at INR 42.2478 on July 1.

On July 1, the spot rate is 42.3245.

Profit = 100,000(42.3245 – 42.2478) = INR 𝟕, 𝟔𝟕𝟎

Forward rate = INR 1

Mohan needs to pay HR 40 million on July 20.

Forward rate = INR 1

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