Solution a ES 25120 110100090 105 EP 25180015401300 1080 1430 VarS 25120 105 2

Solution a es 25120 110100090 105 ep 25180015401300

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Solution: (a) E(S) = .25(1.20 +1.10+1.00+0.90) = $1.05/€ E(P) = .25(1,800+1,540+1,300 +1,080) = $1,430 Var(S) = .25[(1.20-1.05) 2 +(1.10-1.05) 2 +(1.00-1.05) 2 +(0.90-1.05) 2 ] = .0125 Cov(P,S) = .25[(1,800-1,430)(1.20-1.05) + (1,540-1,430)(1.10-1.05) (1,300-1,430)(1.00-1.05) + (1,080-1,430)(0.90-1.05)] = 30 b = Cov(P,S)/Var(S) = 30/0.0125 = €2,400. (b) Var(P) = .25[(1,800-1,430) 2 +(1,540-1,430) 2 +(1,300-1,430) 2 +(1,080-1,430) 2 ] = 72,100($) 2 . (c) Var(P) - b 2 Var(S) = 72,100 - (2,400) 2 (0.0125) = 100($) 2 .
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This means that most of the volatility of the dollar value of the French asset can be removed by hedging exchange risk. The hedging can be achieved by selling €2,400 forward. 3. Suppose you are a British venture capitalist holding a major stake in an e-commerce start-up in Silicon Valley. As a British resident, you are concerned with the pound value of your U.S. equity position. Assume that if the American economy booms in the future, your equity stake will be worth $1,000,000, and the exchange rate will be $1.40/£. If the American economy experiences a recession, on the other hand, your American equity stake will be worth $500,000, and the exchange rate will be $1.60/£. You assess that the American economy will experience a boom with a 70 percent probability and a recession with a 30 percent probability. (a) Estimate your exposure to the exchange risk. (b) Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. (c) How would you hedge this exposure? If you hedge, what is the variance of the pound value of the hedged position?
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Suggested Solution to Economic Exposure of Albion Computers PLC a) The projected annual cash flow can be computed as follows: ______________________________________________________ Sales (40,000 units at £1,080/unit) £43,200,000 Variable costs (40,000 units at £697/unit) £27,880,000 Fixed overhead costs 4,000,000 Depreciation allowances 1,000,000 Net profit before tax £15,315,000 Income tax (50%) 7,657,500 Profit after tax 7,657,500 Add back depreciation 1,000,000 Operating cash flow in pounds £8,657,500 Operating cash flow in dollars $12,986,250 ______________________________________________________ b) ______________________________________________________ Benchmark Current Variables Case Case ______________________________________________________ Exchange rate ($/£) 1.60 1.50 Unit variable cost (£) 650 697 Unit sales price (£) 1,000 1,080 Sales volume (units) 50,000 40,000 Annual cash flow (£) 7,250,000 8,657,500 Annual cash flow ($) 11,600,000 12,986,250 Four-year present value ($) 33,118,000 37,076,946 Operating gains/losses ($) 3,958,946 ______________________________________________________
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c) In this case, Albion actually can expect to realize exchange gains, rather than losses. This is mainly due to the fact that while the selling price appreciates by 8% in the U.K. market, the variable cost of imported input increased by about 6.25%. Albion may choose not to do anything.
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