Question

Consider a U.S.-based company that exports goods to Germany. The U.S. company expects to receive a payment of €1,000,000 for the exports in one year. The U.S. company wants to hedge against a possible decline in the value of the euro that would lead to a drop in the dollar value of the euro receipt in one year. The current spot exchange rate is $1.20/€ and the one-year forward rate is $1.25/€. The annual interest rate is 5% in the U.S. and 3% in Germany.

a. How to do the hedge using a forward contract? Compute the guaranteed dollar proceeds in one year using the forward hedge.

b. How to do the hedge using money market instruments? Compute the guaranteed dollar proceeds in one year using money market hedge.

c. If the U.S. company decides to hedge using put option on euros, what would be the gross and net dollar proceeds in one year? Assume that the $-€ spot exchange rate is $1.18/€ in one year. Also suppose that the one-year put option has an exercise price of $1.26/€ and a premium of $0.05/€.

Answer 1

Answer :

The US company will receive a payment of  € 1000,000 in one year.

Current Spot exchange rate = $1.20 /  €

One year forward rate = $1.25 /  €

Annual US int. rate = 5%

Annual Germany int. rate = 3%

a).

Using forward hedge dollar proceeds will be = One-year forward rate $ / €   * Amount Rcv in  €

= 1000,000 * 1.25 = 1250,000 USD

Therfore, Guaranteed dollar proceeds in one year Using forward hedge =  1250,000 USD.

b).

Money Market Hedge

The US Company will receive a payment of  € 1000,000 in one year.

The company will receive payments in Euro So they will borrow in the Euro first. And the same amount will convert in USD and Invested.

01. Present Value of € 1000,000 Euro = Amount / (1 + Int Rate in Euro)

= 1000,000 / ( 1+ 3%) = € 970873.786

02. Now € 970873.786 Euro will convert in USD at spot rate of today.

So Value of € 970873.786 in USD = Amount in Euro * Spot rate $ / €

= 970873.786 * 1.20 = $ 1165048.54

03. Now this  $ 1165048.54 amount will invest in US market for One Year.

Future Value after one Year = Amount * ( 1+ US Int Rate)

= 1165048.54 * ( 1 + 5%) = 1223,300.97

Therefore, Guaranteed dollar proceeds in one year Using Money Market hedge = 1223,300.97 USD

c).

Hedge against Put Option

Current Spot Exchange rate = $ 1.18 /  €

Exercise Price after 01 Year = $ 1.26 / €

Premium = $ 0.05 / €

Premium paid today = Amount in EURO  * Put Premium per EURO = 1000,000 * 0.05 = $ 50000

Time Value of Money of Put Premium today = Total Premium * ( 1 + US Int Rate) = 50000 * ( 1 + 5%)

= $ 52500

As Exercise Price Higher than Spot Exchange(at the time of Booking put option) Put option will not exercise.

So Gross Dollar Proceed from Put Option = Spot Exchange rate * Amount in EURO

= 1.18 * 1000,000 =  1180,000 USD

Net Dollar Proceed = Gross Dolar - Put Premium paid in Future Value =  = 1.18 * 1000,000 - 52500 = 1127,500 USD

Therefore, Gross and Net Dollar Proceed in one year are 1180,000 USD &   1127,500  USD.