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# Arbitrage and Value of Money Problem

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Suppose your firm receives a \$5 million order on the last day of the year. You fill the order with \$2million worth of inventory. Customer picks up entire order the same day and pays \$1million upfront in cash; you also issue a bill for the customer to pay the remaining balance of \$4million within 30 days. Suppose your firm's tax rate is 0%(ignore taxes). Determine possible consequences of this transaction for each of the following:
a)Revenues
b)Earnings
c)Receivables
d)Inventory
e)Cash

Problem 2
Your firm has identified 3 potential investments. The projects and their cash flows are shown here:

Project Cash flow Today Cash flow in one year
A -10 20
B 5 5
C 20 -10

Suppose all cash flows are certain and risk-free interest rate is 10%
a)What is NPV of each project
b)If the firm can chose only 1, which should it choose?
c)If the firm can choose any 2, which should it choose?

Problem 3

Suppose Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans.

a)what arbitrage opportunity is available?
b)which bank would experience a surge in the demand for loans?which bank would get a surge in deposits?
c)What would you expect to happen to the interest rates the two banks are offering?

Problem 4

The promised cash flows of three securities are listed below. If the cash flows are risk-free and risk-free interest rate is 5%, determine the no-arbitrage price of each security before the first cash flow is paid

Security Cash Flow today Cash flow in 1 Year
A 500 500
B 0 1000
C 1000 0

#### Solution Summary

The solution explains some questions relating to Arbitrage and Value of Money

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## Covered interest arbitrage problems

2. Exchange rate pass through. Assume that the export price of a Nissan Maxima from Osaka Japan is ¥3,000,000. The exchange rate is ¥122/\$. The forecast rate of inflation in the United States is 2% per year and tis 0% per year in Japan.

a. What is the export price of the Nissan at the beginning of the year expressed in US dollars?
b. Assuming purchasing power parity holds, what should the exchange rate be at the end of the year?
c. Assuming 100% pass through of exchange rate changes, what should be the dollar price of a Nissan at the end of the Year?
d. Assuming 70% pass through of exchange rate changes what should be the price of a Nissan at the end of the Year?

4. International fisher effect, Assume that one year interest rates ate 3% in the United States and 5% in the Euro Zone. The spot rate between the euro and the dollar is â?¬1.02/\$. Assuming the international fisher effect holds, what should the â?¬/\$ rate be one year in the future?

5. Covered interest arbitrage- Denmark A. James Change a foreign exchange trader at JP Morgan Chase, can invest \$5 million or the foreign currency equivalent of the bank's short term funds in a covered interest arbitrage with Denmark. He has the following quotes:

sport exchange rate DKr7.5000/\$
three month forward rate DKr7.5372/\$
three month dollar interest 3% per year(.0.75% for 90 days)
three month krone interest 5% per year (1.25% for 90 days)

can James Cang make a covered interest arbitrage profit?

7. Covered interest arbitrage- Japan I, Yukiko Miyaki a foreign exchange trader at Credit Swiss first boston want to invest \$800,000 or its yen equivalent in a covered interest arbitrage between US dollars and Japanese yen she has the following quotes:

Spot Exchange rate ¥124/\$
Six month forward exchange rate ¥123/\$
Six month dollar interest rate 3.00% per year 1.50% for 180 days)
Six month yen interest rate 1.00% per year .0.50% for 180 days)

The bank does not calculate transaction costs on any individual transaction because these costs are part of the overall operating budjet of the arbitrage department . Explain and diagram the specific steps Yukiko must take to make a covered interest arbitrage profit.

10. Mary Smith- Mary smith is a foreign exchange dealer for a bank in New York she has \$1,000,000 or its swiss franc equivalent for a short term money market investment and wonders if she should invest in US dollars for three months or make a covered interest arbitrage investment in Swiss franc she faces the following rates:
Spot exchange rate SF.6000/\$
Three month forward rate SF1.5800/\$
Three month US interest rate 8.00% p.a. (2.00% per quarter)
Thee month swiss franc interest rate 6.00%p.a. (1.50% per quarter0

Where do you recommend Ms Smyth invest? Why?

14. Covered interest arbitrage against the Norwegian Krone A Foreign exchange trader sees the following prices on his computer screen
Spot rate NKr8.8181/\$
3 month forward rate NKr8.9169/\$
US 3 month treasury bill rate 2.60% p.a
Norweigan 3 month treasury bill rate 4.00% p.a.

Could a trader profit by placing \$500,000 of principle in a covered interest arbitrage operation in Norway?

15. Frankfurt and New York Money and foreign exchange markets in Frankfurt and new york are very efficient the following information is available:

Frankfort New York
Spot exchange rates \$0.90000/â?¬ \$0.9000/â?¬
One year T-bill rate 6.50% 3.20%
Expected inflation rate unkown 2.00%

a. what do the financial markets suggest for inflation in Europe next year
b. Estimate today's one year forward exchange rate between the dollar and the euro

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