#5 PM Mon 6 Feb FIN 250 HW 4 Second semester 22-23 Question #31 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/E. 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 State Boom Probability 70% Recession 30% P+ S PSP) $1,000,000 $1.40/-> 714,300 0.7143/5 $500,000 $1.602-> 312,500 0.625/5 You are the British venture capitalist and you want to invest in the American company. P is the pound value of your equity stake in the US firm P is the dollar value of your equity stake in the US firm Step 1: Compute average pound value of equity stake (P) and average exchange rate (S) P-70(714,300)+30(312,500)-593,760 S-70(0.7143/5)+30(0.625/5)-0.688/5 Step 2: Compute variance and covariance Var (S) 70(0.7143-0.688)^2+30(0.625-0.688) "2-00167 Cov (P,S)-70(714,300-593,760) (0.7143-0.688)+30(312,500-593,760) (0.625-0.688)- 7,535 Step 3: Compute exposure coefficient, b. b-CPS) Var(5) 7535 00167 $4,511,976 b. Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. Var(P)=bVar(S)+ Var(e) b'Var(S)-(4,511,976) (.00167)-33,997,738,800 40%