Question

FIELD: Exchange Rates and International Finance
The sales manager of a US company trades iPhones in three different markets, Europe (Eurozone), UK and the USA, has just received a total amount of $1million from the selling of 1,000 iPhones (each iPhone costs $1,000). He has a week available until the payment of firm’s suppliers and employees’ salaries. The current exchange rates between the currencies of the three markets (USD $, euro € and GBP £), are: ?¹_€⁄$=0.9110, ?²_€/£=1.1712 and ?³_{$ ⁄£}=1.2910.

a) If no transaction costs exist, could the manager take advantage of an arbitrage opportunity? Explain. [Mark 1.5]
b) When will there not be any room for profits? That is, there is no arbitrage opportunity. [Mark 0.5]
c) Suppose now that there is a cost each time currency is being traded, i.e., either bought or sold. Moreover, this transaction cost is equal to 1% of the value of currency that is traded. What will the manager’s decision be in this case? [Mark 1.0]

Note: Round your answers to the third decimal point.

Answer 1

	a)	EURO/DOLLAR	0.911
		1 Dollar=0.9110 EURO
		EURO/POUND Exchange Rate	1.1712
		1POUND =1.1712 EURO
		0.9110 EURO=0.9110/1.1712 POUND	0.777835	POUND
		DOLLAR/POUND Exchange Rate	1.291
		1POUND=1.291 DOLLAR
		0.777835 POUND=1.291*0.777835 Dollar	1.004184597
		Yes , There is arbitrage Opportunity
		Profit Per Dollar =(1.004185-1) dollar=	0.004184597	Dollar
		He can first Convert $1 million to EURO
		He will receive=1million*0.911	911000	EURO
		Then he converts EURO to POUND
		He will receive=1million*0.77835=	777834.6995	POUND
		Lastly he converts POUND to DOLLAR
		He will receive=1million*1.004185=	$1,004,184.60
		PROFIT=	$4,184.60
	b)	There will be no room for profit if
		0.777835Pounds *Exchange Rate(DOLLAR/POND)=1 DOLLAR
		Exchange RATE (DOLLAR/POUND)=1/0.77835	1.285620198
		DOLLAR/POUND Exchange Rate=1.2856
	c)	Transaction cost will offset the arbitrage profit
		For example, Transaction cost for the first transaction	$10,000	(1%*1million)
		This is more than the arbitrage profit
		Decision will be not to do arbitrage