SUGGESTED SOLUTIONS TO CHAPTER 3 PROBLEMS 1. During the currency crisis of September 1992, the Bank of England borrowed DM 33 billion from the Bundesbank when a pound was worth DM 2.78 or $1.912. It sold these DM in the foreign exchange market for pounds in a futile attempt to prevent a devaluation of the pound. It repaid these DM at the post-crisis rate of DM 2.50:£1. By then, the dollar:pound exchange rate was $1.782:£1.
a. By what percentage had the pound sterling devalued in the interim against the Deutsche mark? Against the dollar?
Answer.During this period, the pound depreciated by 10.1% against the pound
b. What was the cost of intervention to the Bank of England in pounds? In dollars?
Answer. The Bank of England borrowed DM 33 billion and must repay DM 33 billion. When it borrowed these DM, the DM was worth £0.3597, valuing the loan at £11.87 billion (DM 33 billion x 0.3597). After devaluation, the DM was worth £0.4000. Hence, the Bank of England's cost of repaying the DM loan was £13.20 billion (DM 33 billion x 0.4), a rise of £1.33 billion. Thus, the cost to the Bank of England of this DM borrowing and intervention was £1.33 billion.
In dollar terms, intervention cost the Bank of England $825 million. This estimate is based on the difference of $0.025 between the DM's initial value of $0.6878 (1.912/2.78) and its ending value of $0.7128 (1/2.50) times the DM 33 billion borrowed and spent defending the pound. Specifically, the cost calculation is $0.025 x 33,000,000,000 = $825 million.
2. Suppose the central rates within the ERM for the French franc and DM are FF 6.90403:ECU 1 and DM 2.05853:ECU 1, respectively.
a. What is the cross-exchange rate between the franc and the mark?
Answer. Since things equal to the same thing are equal to each other, we have FF 6.90403 = DM 2.05853. Hence, FF1 = DM 2.05853/6.90403 = DM 0.298164. Equivalently, DM 1 = FF 6.90403/2.05853 = FF 3.35386.
b. Under the original 2.25% margin on either side of the central rate, what were the approximate upper and lower intervention limits for France and Germany?
Answer.Given the answer to part a, the French franc could rise to approximately DM 0.298164 x 1.0225 = DM 0.304872 or fall as far as DM 0.298164 x 0.9775 = DM 0.291455. Similarly, the upper limit for the DM is FF 3.42933 and the lower limit is FF 3.27840.
c. Under the revised 15% margin on either side of the central rate, what are the current approximate upper and lower intervention limits for France and Germany?
Answer. Given the answer to part a, the French franc could rise to approximately DM 0.298164 x 1.15 = DM 0.342888 or fall as far as DM 2.98164 x 0.85 = DM 0.253439. Similarly, the upper limit for the DM is FF 3.85694 and the lower limit is FF 2.85078.
3. A Dutch company exporting to France had FF 3 million due in 90 days. Suppose that the current exchange rate was FF 1 = Dfl 0.3291.
a. Under the exchange rate mechanism, and assuming central rates of FF 6.45863/ECU and Dfl 2.16979/ECU, what was the central cross-exchange rate between the two currencies?
Answer. Given central rates of DFl 2.16979:ECU and FF 6.45863:ECU for the Dutch guilder and French franc, respectively, the central cross rate between the two currencies is DFl 1 = FF 2.97662 (6.45863/2.16979). Equivalently, FF 1 = DFl 0.335952 (2.16979/6.45863).
b. Based on the answer to part a, what was the most the Dutch company could lose on its French franc receivable, assuming that France and the Netherlands stuck to the ERM with a 15% band on either side of their central cross rate?
Answer.At worst, the French franc can fall by 15% relative to its central guilder cross rate, to a cross-exchange rate of FF 1 = DFl 0.285559 (0.335952 x 0.85). Since the current exchange rate is FF 1 = DFl 0.3291, the most the Dutch company can lose on its FF 3 million receivable is 3,000,000 x (0.3291 - 0.285559) = DFl 130,622.
c. Redo part b, assuming the band was narrowed to 2.25%.
Answer. If the band were narrowed to 2.25%, then the minimum value for the French franc would be DFl 0.328393 and the maximum loss that the Dutch company could sustain would be 3,000,000 x (0.3291 - 0.328393) = DFl 2,121.
d. Redo part b, assuming you know nothing about the current cross-exchange rate.
Answer. Knowing nothing about the current cross-exchange rate, the worst that could happen is that the cross rate would be at its upper bound of DFl 0.386345 (0.335952 x 1.15) and it falls to its lower bound of 0.285559 (established in the answer to part b). In this case, the maximum possible loss is 3,000,000 x (0.386345 - 0. 285559) = DFl 302,357.
4. Panama adopted the U.S. dollar as its official paper money in 1904. There is currently about $400 million to $500 million in U.S. dollars circulating in Panama. If interest rates on U.S. Treasury securities are 7%, what is the value of the seigniorage that Panama is forgoing by using the U.S. dollar instead of its own-issue money?
Answer. Instead of using U.S. dollars as its currency in circulation, the Panamanian government could substitute its own currency and invest the $400 million to $500 million in U.S. Treasury securities. This policy would earn the Panamanian government $28 million to $35 million annually at the current 7% interest rate. Thus, the Panamanian government is foregoing seigniorage worth $28 million to $35 million annually. The present value of this seigniorage equals the amount of U.S. dollars in circulation, or $400 million ($28 million/.07) to $500 million ($35 million/.07).
5. By some estimates, $185 billion to $260 billion in currency is held outside the United States.
a. What is the value to the United States of the seigniorage associated with these overseas dollars ? Assume that dollar interest rates are about 6%.
Answer. The annual value of seigniorage equals the foregone interest on the currency held outside the United States. Based on the numbers presented in the question, this annual value varies between $11.1 billion (0.06 x $185 billion) and $15.6 billion (0.06 x $260 billion). If this money stays overseas permanently, then the value of seigniorage is just equal to the amount of dollars held outside the United States, or $185 billion to $260 billion. In other words, the United States receives goods and services worth this amount of money from foreigners and paid for them with pieces of green paper that are never redeemed for U.S. goods and services.
b. Who in the United States realizes this seigniorage?
Answer. The U.S. government realizes this seigniorage. Who in the United States benefits from this seigniorage is an issue in political economy and depends what the government does with the money: cuts taxes, spends it (which raises the further question of on whom), uses it to reduce the deficit, etc.