Dell is selling 20,000 units in Europe at an average price of €1,700 per unit. B

Question

Dell is selling 20,000 units in Europe at an average price of €1,700 per unit. Both the spot and forward exchange rates are $1.20/€. The cost of each unit in dollars is $1,500 per unit. The elasticity of demand for Dell computers in Europe is = 1.5.

1. Now consider a depreciation of Euro (relative to US dollar) from $1.2/€ to $1.08/€ and assume zeo passthrough. What is Dell's dollar profit exposure and how to hedge it using forward?

a. $45 million, buy $45million forward

b. €45 million, sell €45million forward

c. $34 million, buy $20 million forward

d. €34 million, sell €34 million forward

2. What is the delta for Dell's profit assuming zero passthrough?

a. 0

b. 2.35

c3.78

d.3.65

3. Reconsider a depreciation of Euro ( relative to US dollar) from $1.20/€ to $1.08/€. Now assume passthrough = 0.5. What is Dell's total profit in $?

a. $11,869,440

b. $8,038,860

c. $12,028,410

d. $6,397,440

4. What are respectively the delta and exposure for Dell's dollar profit passthrough =0.5?

a. delta = 1.981; exposure = €17,829,000 million

b. delta = 1.137; exposure = €10,233,000 million

c. delta = 2.566; exposure = €23,094,000 million

d. delta = 5.741; exposure = €51,660,000 million

Explanation / Answer

1) revenue =20,000 units at €1,700 = € 34 M

cost = 20,000 units at €1,500 = € 30 M

profit = € 4 M

reduction in exchange rate = (1.2-1.08)/1.2 = 10%

reduction in profit = 10% = 0.1 * € 4 M = € 0.4 M

To hedge, sell Euro 34 M forward.

2) since the profit is in dollars and is after forex conversion, the delta is zero, i.e., no change in profit.

3) passthrough = 0.5, half the price increase passed on to consumers, their demand will decrease.

new price = old price + passthrough * increase in cost = Euro (1700+ 0.5 * (-10%) * 1500) = Euro 1625

new cost = (1+increase in cost) * old cost = (1-10%)*1500 = Euro 1350

change in demand = - price change * elasticity = (1700-1625)/1700 * 1.5 = 6.62%

new demand = 1.0662 * 20000 = 21324

New profit = (new price - new cost) * new demand = 21324 * (1625-1350) = Euro 275 * 21324= euro 5.8641 M

= euro 5.8641 M * $1.08/Euro = $6.33M

4 ) New revenue = new price * new demand = Euro 1625 * 21324 = Euro 34.6515 M = exposure

Delta = change in profit% / change in exchange rate% = [(5.8641-4)/4]/[(1.2-1.08)/1.2)] = 0.466/.1 = 4.66

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