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4252 Homework 2

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Solution of Problem 1

BUSFIN 4252 International Finance

Problem Set 2 – Solutions

BUSFIN 4252 – International Finance

a) Airbus expects to receive €30m in 1 year, so they will enter a 1-year forward contract to sell €30m for dollars at the given forward rate.

To get the fair forward rate, apply the covered interest rate parity: 𝐹($/€)=𝑆($/€)1+𝑖$.

Inserting the given numbers, we obtain 𝐹($/€) = $1.05/€ ∗ 1.06 = $1.06/€. 1.05

b) After entering the forward at time 0, Boeing receives €30m*$1.06/€ = $31.8m for the €30m at time 1.

c) We need to figure out what kind of forward contract we could enter today to get us out of the original forward contract. In the original forward contract, we sell €30m in 1 year (originally, now: in 11 months) at a forward rate of $1.06/€. So we want to enter a forward through which we can buy €30m in 11 months. The fair forward rate for this contract is

𝐹′($/€) = $1.08/€ ∗ 1.0611/12 = $1.0894/€. 1.0511/12

The current value of the original forward contract is the same as the value of the original and the new one together, as the initial value of a forward is 0. Taking the cash-flows of both forwards together means that we sell €30m in 11 months at $1.06/€, getting $31.8m, and buy €30m in 11 months at $1.0894/€, paying $32.6827m. Therefore the cash-flow of both contracts together in 11 months is $31.8m - $32.6827m = -$0.8827m. Discounting this cash-flow at the interest rate of 6% yields the current value of the original forward contract as -$0.8827m/1.0611/12 = -$0.8368m.

d) In the case of the money market hedge, Boeing borrows the present value of its euro receivable, which is €30m/1.055=€28,436,018.96, as Boeing’s interest rate for borrowing euros is 50bps above the inter-bank rate of 5%. Converting these euros to dollars on the spot market makes €28,436,018.96*$1.05/€ = $29,857,819.91. Boeing deposits these dollars at an interest rate of 5.5% (6% minus 50bps) to receive $29,857,819.91*1.055 = $31.5m in 1 year.

As they would get $31.8m through the forward hedge, they forward prefer the forward hedge.

e) Boeing would be indifferent between the forward hedge and the money market hedge if both strategies had the same outcome. The forward rate at which the forward hedge delivers $31.5 is $1.05/€, as €30m*$1.05/€ = $31.5m. Therefore, Boeing is indifferent between both methods if the forward rate is $1.05/€.

1+𝑖€

Problem Set 2 BUSFIN 4252 Solutions International Finance

Solution of Problem 2

Let us first summarize the three different scenarios in the following table:

a) To quantify the company’s exposure, we decide to calculate the 𝛽 (see also the slides on “Economic Exposure”) as an appropriate sensitivity measure. The calculations are as follows:

𝑃̅ = 13 ∗ 3,850m + 12 ∗ 3,850m + 16 ∗ 3,391.5m = 3773.5833m [¥]

𝑆 ̅ = 13 ∗ 1 0 0 + 12 ∗ 1 1 0 + 16 ∗ 8 5 = 1 0 2 . 5 [ ¥ / $ ]

𝑉𝑎𝑟(𝑆) = 13 (100 − 102.5)2 + 12 (110 − 102.5)2 + 16 (85 − 102.5)2 = 81.25

𝐶𝑜𝑣(𝑃, 𝑆) = 13 ∗ (3,850m − 3773.5833m)(100 − 102.5)

+ 12 (3,850m − 3773.5833m)(110 − 102.5)

State

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