Question

a. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting €0.855/$1.00 Credit Suisse is offering SF1.1825/$1.00. UBS’s current direct quoting €/SF currently @ € 0.754/SF

i. (4pts) Prove and explain whether at these quoted rates there a chance for triangular arbitrage (Hint: Use the no arbitrage cross exchange rate here).

ii. (8pts) Show and explain how you can make a triangular arbitrage profit by trading at these prices. (Ignore bid-ask spreads for this problem.) Assume you have $5,000,000 with which to conduct the arbitrage. If your answer in a is that there is no chance of arbitrage profits please say so.

b. (8 pts) Assume the following information: You have $400,000 to invest: Current spot rate of Sudanese dinar (SDD) = $.00570 90-day forward rate of the dinar = $.00569 90-day interest rate in the U.S. = 4.0% 90-day interest rate in Sudan = 4.2% Show and explain how given the information above you will conduct covered interest arbitrage, what amount will you have after 90 days.

c. (14 pts) Lakonisho Equipment has an investment opportunity in Europe. The project costs €10.5 million and it is expected to produce cash flows of €1.7 million, €2.4 million, and €3.3 million, for years 1, 2 and 3 respectively. The current spot exchange rate is $1.36/€; the current risk-free rate in the United States is 2.3%, compared to that in Europe of 1.8%. The appropriate discount rate for the project is estimated to be 13%, the U.S. cost of capital for the company. In addition, the subsidiary can be sold at the end of the 3 years for an estimated €7.5 million. What is the NPV of the project? What is the IRR of the project? Should Lakonisho Invest in this project?

Answer 1

a-i)

Triangluar arbitrage is possible if the cross exchange rate of €/SF is different from quoted exchnage rate of €/SF.

Cross exchange rate (€/SF) = 0.8550/1.1825 = 0.7230

Quoted exchange rate  (€/SF) = 0.7540

Therefore, triangular arbitrage is possible.

a-ii)

Step 1: Sell $5000,000 to Credit Suisse @ SF1.1825/$ and receive = SF 5912,500

Step 2: Sell the SF 5912,500 to UBS @ €0.754/SF, and receive € = 5912,500*0.754 = € 4458,025

Step 3: Sell the € 4458,025 to Deutsche Bank @ € 0.855/$1.00 and receive $ = 4458,025/0.855 = $5,214,064.33, resulting in a net profir of $ 214,064.33

b)

At T=0:

• Step 1: Convert $400,000 into SDD at current exchange rate of $0.0057 and receive SDD = 400,000/0.0057 = 70,175,438.60
• Step 2: Invest SDD 70,175,438.60 for 90-days period at the rate of 4.20%
• Step 3: Enter forward contract to covert the FV of SDD 70,175,438.60 investment in 90-days time

At T=90 days:

• Step 1: Receive SDD 70,175,438.60 *(1 + 4.20%) = SDD 73,122,807.02
• Step 2: Convert SDD 73,122,807.02 to $ at $0.00569 = 73,122,807.02*0.00569= $416,068.77, which the amount you will have after 90-days.

NOTE: SINCE THE RATES ARE NOT SPECIFIED TO BE ANNUAL RATES, THEY HAVE BEEN ASSUMED TO BE 90-DAYS EFFECTIVE RATE.

c)

Year	Exchange Rate	Cash Flow (€)	Cash Flow ($)	PVF @ 13%	PV ($)
0	1.3600	-10.5	-14.28	1.0000	-      14.28
1	1.3600*(1.023/1.018) = 1.3667	1.70	2.32	0.8850	2.06
2	1.3667*(1.023/1.018) = 1.3734	2.40	3.30	0.7831	2.58
3	1.3734*(1.023/1.018) = 1.3801	10.80	14.91	0.6931	10.33
				NPV ($)	0.69million

IRR($) calculation:

Step 1: calculate NPV using two discount rates (I have taken 15% and 16%)

Year	Cash Flow ($)	PVF @ 15%	PV ($)		Year	Cash Flow ($)	PVF @ 16%	PV ($)
0	-14.28	1.0000	-      14.28		0	-14.28	1.0000	-14.28
1	2.32	0.8696	2.02		1	2.32	0.8621	2.00
2	3.30	0.7561	2.49		2	3.30	0.7432	2.45
3	14.91	0.6575	9.80		3	14.91	0.6407	9.55
		NPV	0.0333				NPV	-0.2782

Step 2: Calculate IRR using following formula:

IRR = Rate 1 + [ (NPV at Rate 1 x (rate 2 - rate 1) ) / (NPV at rate 1 - NPV at rate 2)]

= 0.15 +[(0.0333*(0.16-0.15))/ (0.0333-(-0.2782))] = 15.11%

Since the NPV of the project is positive and IRR> discount rate, the company should invest in the project.