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SAP (a German company) bought Qualtrics for $8 billion in 2018. The deal was to close...

SAP (a German company) bought Qualtrics for $8 billion in 2018. The deal was to close in 12 months. The current exchange rate between USD and Euro was $1.185 at the time of the deal. The exchange rate forecast was for Euro to depreciate against the USD, but the exact decline is not known. SAP decided to hedge with derivatives and purchased enough options for USD. The call option with strike price of $1.18 per Euro is selling for the price of $0.005 USD. The put option with strike price of $1.18 is selling for $0.01. Which option should SAP use? What is the profit/loss from the hedge if the exchange rate turns out to be $1.165 in 12 months? What about if the rate is $1.19?

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SAP should use call option which will give SAP a right but not an obligation to purchase USD at the strike price of the call option. for this right of purchasing USD at the strike price of the call option, SAP has to pay the premium of $0.005. If at the maturity of the call option, spot rate will not be favorable for SAP then it will exercise the option and purchase USD at strike rate of the option. If spot rate will be favorable for SAP then it will let the option expire worthless and purchase the USD from spot market.

profit from the hedge if the exchange rate turns out to be $1.165 in 12 months

Value in Euros of USD payment at the time of the deal = $8 billion/$1.185 = 6.75 billion

Profit = value in euro*(Strike price - spot price after 12 months - premium paid) = 6.75*($1.18 - $1.165 - $0.005) = 6.75*$0.01 = 0.0675 billion euros or 67.5 million euros

If SAP purchased the USD from spot market then it has to pay $8 billion/$1.165 = 6.87 billion euros. now after exercising the option it will get $8 billion at $8/1.18 = 6.78 billion Euros.

if the rate is $1.19

If the rate is $1.19 after 12 months than SAP will let the option expire because it is worthless for them and purchase the USD at lower rate from spot market.

If they purchase USD at strike rate then they have to pay $8/1.18 = 6.78 billion Euros and now they purchase from spot market then they have to pay $8/1.19 = 6.72 billion Euros.

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