Question

Problem 25-5 Suppose a US investor wishes to invest in a British firm currently selling for £33 per share. The investor has $66,000 to invest, and the current exchange rate is $2/. Suppose now the investor also sells forward $33,000 at a forward exchange rate of $205/5 Calculate the dollar-denominated returns for each scenario (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Price per Share (E) Rate of Return (%) at Given Exchange Rate 51.80V 52.00/ 52 20/ Exchange Rate: E 31 E f

Answer 1

1. Exchange $66000 for $2 per pound and get 33000 pounds
2. Buy 33000/33 = 1000 shares at the price of 33 pounds each
3. Enter into a forward contract of exchanging 33000 pounds for $2.05 per pound

Now if the price is

Share price	Cost Price	Profit per share (negative value means a loss)	Total profit on 1000 shares
£        31.00	£        33.00	-£        2.00	-£2000
£        36.00	£        33.00	£        3.00	£3000
£        41.00	£ 33.00	£        8.00	£8000

Now these need to be converted to $ for each exchange rate scenario:

Profit on shares	$            1.80/£	$            2.00/£	$            2.20/£
-£           2,000.00	-200 x 1.8 = $ -3,600.00	-2000 x 2 = $ -4,000.00	-2000 x 2.2 = $ -4,400.00
£            3,000.00	3000 x 1.8 = $   5,400.00	3000 x 2 = $   6,000.00	3000 x 2.2 = $   6,600.00
£            8,000.00	8000 x 1.8 = $ 14,400.00	8000 x 2 = $ 16,000.00	8000 x 2.2 = $ 17,600.00

Now coming to the forward contract. Here the contracted rate is $2.05 per  £ so if the actual exchange rate is lower then the investor profits because he can exchange at a higher rate but if the rate in the market is higher, then he will lose because he will have to fulfill the contract at the contracted rate while had he not entered into the contract, he could get a higher rate in the market

Contracted amount	$            1.80/£	$            2.00/£	$            2.20/£
£           33,000.00	33000 x (2.05 -1.8) = $8,250.00	33000 x (2.05 -2) = $1,650.00	33000 x (2.05-2.20) = -$4,950.00

So total profit would be:

Share price	$            1.80	$            2.00	$            2.20
£        31.00	$ -3,600.00 + 8250 = $4650	$ -4,000.00+1650 = -$2350	$ -4,400.00-4950=-$9350
£        36.00	$   5,400.00+ 8250 = $13650	$   6,000.00+1650 = $7650	$   6,600.00-4950=$1650
£        41.00	$ 14,400.00+ 8250 = $22650	$ 16,000.00+1650 = $17650	$ 17,600.00-4950=$12650

Initial investment was $66000 so the return is :

4650/66000 x 100 = 7.05%	-2350/66000 x 100 = -3.56%	-9350/66000 x 100 = -14.17%
13650/66000 x 100 = 20.68%	7650/66000 x 100 = 11.59%	1650/66000 x 100 = 2.50%
22650/66000 x 100 = 34.32%	17650/66000 x 100 = 26.74%	12650/66000 x 100 =19.17%