Bank of England eal and nominal forward rates

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MOCK EXAM QUESTION SOLUTIONS
Emma Black: Semester One
Section A (40 marks)
a) The Law of One Price states that identical goods and services should trade at the same price in all locations. Briefly discuss why this is the case. Suppose you are the manager of a large multinational corporation that trades internationally in the sale of oil. Let PUSD and PEUR be the price of oil in the US and Europe respectively. If S0(USD/EUR) = 4, then what will be the price of oil in Europe if LOOP holds and it trades in the US for $50 a barrel? Explains the barriers to why this may not hold

(10 marks)
Solution:
Source: Lecture 2 - Law of One Price
The Law of One Price states that identical goods and services should trade at the same price in all locations due to the presence of an exploitable arbitrage opportunity if this were not to hold.
Consider a car selling in Germany for €20,000. If the Euro to GBP exchange rate was 2:1 then the car should theoretically sell in the UK for half the price at £10,000. Lets say that the car was trading in the UK for £12,000. What would this mean? This would indicate that the car was more expensive to buy in the UK that in Germany. Buyers should therefore buy the car in Germany rather than the UK and save £2,000. This action would place price pressure onto the UK price, as a fall in the demand in the UK would lower the selling price if we assume that supply would be held constant. Simultaneously, the extra demand for buying the car in Germany would see the German price slightly adjust up-over. This would continue until there was no exploitable opportunity still present and the two prices equated. To find out what price oil should trade at in Europe for the LOOP to hold in the question, we can use the formulae:

PUSD = PEURSo(USD/EUR)
PEUR = PUSD / S0(USD/EUR)
We use the second formula and we find oil should trade at:
PEUR = 50 / 4 (USD/EUR) = €12.50 per barrel
We can check using the first formula:
PUSD = 12.50 x 4 USD/EUR) = $50 per barrel
The barriers to why LOOP may not hold can be summarized as:


Border Effect
o Taxes, tariffs and transportation costs mean it is difficult for us to ship the car





back to the UK for the price differential to still make it worthwhile. Law fails intertemporally
o Prices for the same car in Germany can be different at different times. Incomplete information
o We don’t know the car is cheaper in Germany and so therefore the price differential persists.
Balassa-Samuelson Effect
o This effect argues that the LOOP is not applicable to all goods internationally as not all goods are tradable. Labour in one country could be cheaper relative to another and so the same good or service can cost more or less dependent on where it is being delivered.

b) Consider that you are faced with the following mutual choice for investing £100,000. Project

Initial Cost

A
B

-100,000
-100,000

Cash Flow
Year 1
20,000
35,000

Cash Flow
Year 2
44,000
45,000

Cash Flow
Year 3
68,000
55,000

Because the two projects vary in terms of their risk, you require a return of 8% for Project A and 6% for Project B. Calculate the NPV and Profitability Index for the two projects. Decide which you would like to invest in and briefly explain why. If the two investments will be made abroad, briefly explain any additional risks you should consider.

(10 marks)
Solution:
Source: Lecture 2 - Capital Budgeting
The NPV’s for the two projects are calculated as:
𝑁𝑃𝑉! = −100,000 +

20,000 44,000 68,000
+
+
= 10,222.02
1.08
1.08!
1.08!

𝑁𝑃𝑉! = −100,000 +

35,000 45,000 55,000
+
+
= 19,247.77
1.06
1.06!
1.06!

The PI for Project A is equal to:
𝑃𝑉  𝐶𝑎𝑠ℎ  𝐹𝑙𝑜𝑤𝑠 =

20,000 44,000 68,000
+
+
= 110,222.02
1.08
1.08!
1.08!
𝑃𝐼! =

110,222.02
= 1.10
100,000.00

The PI for Project A is equal to:
𝑃𝑉  𝐶𝑎𝑠ℎ  𝐹𝑙𝑜𝑤𝑠 =

35,000 45,000 55,000
+
+
= 119,247.77
1.06
1.06!
1.06!

𝑃𝐼! =

119,247.77
= 1.19
100,000.00

The NPV...
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