If you establish a hedge six months before your cash market transaction and then prices move unfavorably, your futures market position will start to earn you cash in the short
Step 2: Change the amount in home currency ($ into £)
Pv = 350,000 / (1.04)5/12 = $344,328
Step 2: Change the amount in home currency ($ into £)
1£ = 1.9210$ $ 344,328 = £? , 344,328 / 1.9210 = £ 179,243
Hint: Here we use rate 1.9210 because we are taking loan and bank will charge higher of the spot rates.
Step 3: calculate FV for investable amount in the home currency at lending rate. 4.2%
𝐹𝑉 = PV(1 + i)𝑛 , FV = 179,243(1.042)5/12 = £ 182,343 3. Forwards
First calculate 5 month future rate.
3 months forward: 1.9120
1 year forward: 1.8945
---
Decrease in rates 0.0175
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Average rate per month = 0.0175 / 9 = .0019
5 months forward = 1.9120 – 2(0.0019) = 1.9082
Conversion in £ with rate 1.9082 $ 350,000 / 1.9082 = £ 183,419
Hint: Here we use minus sign 1.9120
–
2(0.0019) because rates are decreasing. If the rates were increased we should use the + sign in this equation.It means forward will give a sum of £ 183,419 which is better than amount of money market hedge that gives £ 182,343. Therefore forward is better choice than money market hedge.
4. Futures
CME $ / £ Currency futures (£ 62,500) , contract size
Spot rate: 1.9156 – 1.9210
Future rates: September 1.9065 December 1.8985 5 month period ends October 31st
Position long call
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First calculate 5 month future rate on Basis risk.
Basis risk = spot rate – future rate
Basis risk = 1.9210 – 1.8985 = 0.0225 (rate is decreasing in future time) Basis risk per month = 0.0225 / 7 = 0.0032 ( 7 months is total period June to Dec.) Expected future price = 1.9210 – 5(.0032) = 1.905 (used minus sign as rates decreased) Conversion of amount in home currency $ 350,00 / 1.905 = £183,727
Contract size = £62,500
No. of contracts = 183,727 / 62,500 = 2.93 means 2 or 3 contracts.
Here we take 2 contracts: 62,500 x 2 = £ 125,000 Convert in dollars 125,000 x 1.9050 = $ 238,125
Unhedged amount = $ 350,000 – 238,125 = $ 111,875 (amount covered by forwards) Convert unhedged amount in £ = $ 111,875 / 1.9082 = £ 58629
Total amount received through this choice =
Amount received in futures = £ 125,000 + Amount in forwards = £ 58,629
Total £ 183,629
Decision: £ 183,629 is amount received through futures and £ 183,419 is amount received using the choice of forwards calculate in previous situation. When there is a nominal or no difference in these two choice we will opt the forwards, as it more customized and bears less restrictions.
5. options
CME currency options prices, $ / £ options £ 31,250 (cents per pound)
Strike price Call Put
September December September December
1.8800 4.70 5.90 1.60 2.95
1.9000 3.53 4.70 2.36 4.34
1.9200 2.28 3.56 3.40 6.55
Hint: while selecting the rates always use that rates which are in the benefit of the bank. Bank will charge higher rates when we borrow and will give the lower rates when we lend or invest in the bank.
Contract size: £31,250
Exercise price: 1.8800 $ / £ ( we use this price as it is lower than 1.9082 calculated) Position: long call (because we need to buy)
Contract used: December ( as the contracts mature in October) Amount in £ = 350,000 / 1.8800 = £ 186,170
No. of contracts = 186,170 / 31,250 = 5.95 contracts ( we take 5 contracts) Amount covered in options = 31,250 x 5 = £156,250
Convert in dollars = 156,250 x 1.8800 = $ 293,750
Unhedged amount = 350,000 – 293,750 = $ 56,250 ( covered in forwards)
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Unhedged amount in £ = $ 56,250 / 1.9082 = £ 29,478 (forward rate used) Cost of options (premium) = 156,250 x .059 = $ 9219
Convert option premium in £ $ 9219 / 1.9156 = £ 4812 (used spot rate) Now see it on time line: (future value) = 𝐹𝑉 = PV(1 + i)𝑛
𝐹𝑉 = PV(1 + i)𝑛 = 𝐹𝑉 = 4812.46(1 + .042)5/12 = £ 4896 Net value received from options:
Amount covered in 5 contracts = £ 156,250 + Amount covered in forwards = £ 29,478 - Cost of options (premium) = £ 4896
= Net amount receive in option = £ 180,832
Decision: amount received through options is £ 180,832 which is lower than all other choices, therefore forward is the best option in all cases.
EXAMPLE 7:
Casasophia co, base in a European country that uses euro €, constructs and maintains advanced energy efficient commercial properties around the world. It has just completed a major project in the USA and is due to receive the final payment of us$ 20 million in four months.
Casasophia Co. is planning to commence a major construction and maintenance project in mazabia, a small African country, in six months time. This government owned project is expected to last for three years during which time Casasophia Co. will complete the construction of state of the art energy efficient properties and provide training to a local mazabian company in maintaining the properties. The carbon neutral status of the building project has attracted some grand funding from the European Union and these fund will be provided to the mazabian government in mazabian Shillings (MShs).
Casasophia co. intends to finance the project using the US# 20 million it is due to receive and borrow the rest through a € loan. It is intended that the US $ receipts will be converted into € and invested in short dated treasury bills until they are required. These funds plus the loan will be converted in t MShs on the date required, at the spot rate at that time.
Mazabia‘s government requires Casasophia co. to deposit the MShs 2.64 billion it needs for the project with mazabian central bank, at the commencement of the project. In return, Casasophia co. will receive a fixed sum of MShs 1.5 billion after tax at the end of each year.
Neither of these amounts is subject to inflationary increases. The relevant risk adjusted discount rate for the project is assumed to be 12%. Following are the financial information available.
Exchange Rates: $ / € MShs / €
Spot : 1.3585 – 1.3618 MShs 116 – MShs 128
4 months forward: 1.3588 – 1.3623 Not available Futures:
CME $ / £ Currency futures (€ 125,000) , $ / € contract size Future rates: 2 months expiry 1.3633
5 months expiry 1.3698
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Options:
Contract size: € 125,000, exercise price quotation US$ per €, cents per Euro Calls, Puts.
exercise price Call Put
2 month expiry 5 month expiry 2 month expiry 5 month expiry
1.36 2.35 2.80 2.47 2.98
1.38 1.88 2.23 4.23 4.64
Casasophia co. local government base rate: 2.20%
Mazabian government base rate: 10.80%
Yield on short dated Euro treasury bills 1.80%
Assume 360 days a year.
Mazabia‘s current annual inflation rate is 9.7% and is expected to remain at this level for the next six years. However, after that, there is considerable uncertainty about the future and the annual level of inflation and it could be anywhere between 5% and 15% for the next few years.
The country where Casasophia co is based is expected to have a stable level of inflation at 1.2% per year for the foreseeable future. A local bank in mazabia has offered Casasophia co the opportunity to swap the annual income of MShs 1.5 billion receivable in each of the next three years for Euro, at the estimated annual MShs / € forward rates based on the current government base rates.
Required:
a. Advise Casasophia co on, and recommend an appropriate hedging strategy for the US$
income it is due to receive in four months. Include all relevant calculations.
b. Provide a reasoned estimate of the additional amount of loan finance Casasophia so needs to obtain to undertake the project in Mazabia in six months.
c. Given that Casasophia co agrees to the local bank‘s offer of the swap, calculate the net present value of the project in six month‘s time in €. Discuss whether the swap would be beneficial to Casasophia co.
Solution:
Query (a) Recommend the hedging strategy.
We need to decide whether to hedge or not. If we need to hedge what is the best choice out the four available choices.
1. Hedge or not
2. Money market hedge 3. Forwards
4. Futures 5. Options
We need to decide whether to hedge or not. If we need to hedge what is the best choice out the four available choices.
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1. Hedge or not
An amount of $ 20,000,000 is receivable in four months time. So we need to hedge for this amount.
2. Money market hedge
We are not given the borrowing and lending rates, so we cannot use this money market hedge option.
3. Forwards
As opposed to previous examples, here forward rates for future are given. So we not need to calculate these rates and use the higher rate to convert the dollar amount in Euro. Rates given are:-
Exchange Rates: $ / € MShs / €
Spot : 1.3585 – 1.3618 MShs 116 – MShs 128
4 months forward: 1.3588 – 1.3623 Not available Convert $ amount in € = 20,000,000 / 1.3623 = € 14,681,054
4. Futures
CME $ / £ Currency futures (€ 125,000) , $ / € contract size
Spot rate: 1.3585 – 1.3618
Future rates: 2 months expiry 1.3633 5 months expiry 1.3698
Period: 4 months
Contract period used: 5 months future 1.3698
Position: Long call
First calculate 5 month future rate on Basis risk.
Basis risk = spot rate – future rate
Basis risk = 1.3618 – 1.3698 = 0.008 (rate is increasing in future time) Basis risk per month = 0.008 / 5 = 0.0016
Expected future price = 1.3618 + 4(.0016) = 1.3682 (used plus sign as rates increased) Conversion of amount in home currency $ 20,000,00 / 1.3682 = €14,617,746
Contract size = €125,000
No. of contracts = 183,734 / 125,000 = 116.96 contracts.
Here we take 116 contracts: 125,000 x 116 = € 14,500,000 amount covered Convert in dollars € 14,500,000 x 1.3682 = $ 19,838,900
Unhedged amount = $ 20,000,000 – 19,838,900 = $ 161,100 (covered by forwards) Convert unhedged amount in € = $ 161,100 / 1.3623 = €118,255 (forward rate used) Total amount received through this choice =
Amount received in futures = € 14,500,000 + Amount in forwards = € 118,255
Total € 14,618,255
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Decision: € 14,618,255 is amount received through futures and € 14,681,054 is amount received using the choice of forwards calculated in previous situation. When there is a nominal or no difference in these two choices we will opt the forwards, as it is more customized and bears fewer restrictions and also low risk of marked to market settlement losses.
5. Options
Contract size: € 125,000, exercise price quotation US$ per €, cents per Euro
exercise price Call Put
2 month expiry 5 month expiry 2 month expiry 5 month expiry
1.36 2.35 2.80 2.47 2.98
1.38 1.88 2.23 4.23 4.64
Contract size: €125,000
Exercise price: 1.3600 $ / € ( we use this price as it is lower than 1.3682 calculated) Position: long call (because we need to buy)
Contract used: 5 months
Amount in € = 20,000,000 / 1.3600 = € 14,705,882
No. of contracts = € 14,705,882/ 125,000 = 117.64 contracts Amount covered in options = 125,000 x 117 = €14,625,000
Convert in dollars = 14,625,000 x 1.3600 = $ 19,890,000
Unhedged amount = 20,000,000 –19,890,000 = $110,000 ( covered in forwards) Unhedged amount in € = $ 110,000 / 1.3623 = € 80,746 (forward rate used)
Cost of options (premium) = 14,625,000 x .028 = $ 409,500
Convert option premium in € $ 409,500 / 1.3585 = €301,435 (lower of spot rate used) Now see it on time line: (future value) = 𝐹𝑉 = PV(1 + i)𝑛
𝐹𝑉 = PV(1 + i)𝑛 = 𝐹𝑉 = 301,435(1 + .022)4/12 = € 303,630 Net value received from options:
Amount covered in 5 contracts = € 14,625,000 + Amount covered in forwards = € 80,746 - Cost of options (premium) = € 303,630
= Net amount receive in option = € 14,402,116
Decision: amount received through options is € 14,402,116.which is lower than all other choices, therefore forward is the best option in all cases.
Query (b)
Provide a reasoned estimate of the additional amount of loan finance Casasophia so needs to obtain to undertake the project in Mazabia in six months.
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Solution:
Mazabian government requires Casasophia to deposit MShs 2.64 Billion as security.
We receive € 14,681,054 from forwards at the end of month 4. These should be invested for 2 months in a bank. The risk free lending rate on treasury bills is 1.80%.
First see what will be value of this amount after 2 months investment.
𝐹𝑉 = PV(1 + i)𝑛 = 𝐹𝑉 = 14,681,054(1 + .018)4/12 = € 14,724,770
Convert into MShs at spot rate 116/€ (here we use purchasing power parity theory)
𝐸𝑥𝑐𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑎𝑓𝑡𝑒𝑟 𝟏 𝒚𝒆𝒂𝒓 = PV (1+𝑖𝑑)𝑛
This short amount will be borrowed from bank. A local bank in mazabia has offered
Casasophia co the opportunity to swap the annual income of MShs 1.5 billion receivable in each of the next three years for Euro, at the estimated annual MShs / € forward rates based on the current government base rates. 10.80%.
Query (c)
Given that Casasophia co agrees to the local bank‘s offer of the swap, calculate the net present value of the project in six month‘s time in €. Discuss whether the swap would be beneficial to Casasophia co.
We need to calculate the value of the funds of 1.5 billion to be received every year with the future rates of MShs to Euro.
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𝐸𝑥𝑐𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑎𝑓𝑡𝑒𝑟 𝟏 𝒚𝒆𝒂𝒓 = PV (1+𝑖𝑑)𝑛
(1+𝑖𝑓)𝑛 = 144.60(1.108)
(1.022) = MShs 156.77 𝐸𝑥𝑐𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 𝑎𝑓𝑡𝑒𝑟 𝟏 𝒚𝒆𝒂𝒓 = PV (1+𝑖𝑑)𝑛
(1+𝑖𝑓)𝑛 = 156.77(1.108)
(1.022) = MShs 169.96 Convert these amounts in Euro €
Year 1 Year 2 Year 3
MShs to € 1500 / 144.60 = 10.37 1500 / 156.77 = 9.57 1500 / 169.96 = 8.83
PVF(1/(1+i)n .893 .797 .712
PV 9.25 7.63 6.30
PV of cash flows = 9.25+7.63+6.30 = € 23.1m
PV of cash out flows = € 21.8 m
Net present value (NPV) = € 1.3 m
Decision: NPV is positive, therefore project is favorable and they should go for it.
EXAMPLE: 8
Tertial company of UK has recently commenced exports to Buldonia, a developing country. A payment of 100 million pesos is due from a customer in Buldonia in three month‘s time. The Buldonia government sometimes restricts the movement of funds from the country, but has indicated that payment to Tertial has a good chance of receiving approval. No forward market or derivatives market exist for the Buldonian peso. The Buldonian peso is currently liked to the US Dollar.
Exchange rates:
Spot rate B. Peso / $ 126.4 – 128.2
Spot rate $ / £ 1.775 – 1.782
3 month forward rate B Peso / £ not available 3 month forward rate $ / £ 1.781 – 1.789
Tertial can borrow at 6% per annum or invest at 4% per annum in the UK, can borrow at 7%
and invest at 4.5% in the USA, and at 14% and 10% respectively in Buldonia.
Inflation rates: UK 3%, USA 4%, Buldonia 14%
Tertial‘s Buldonian customer has indicated that it might be willing to make a lead payment in return for a 1.5% discount on the sale price.
Required:
Discuss the advantages and disadvantages of the alternative currency hedges that are available to Tertial. Calculate the expected outcome of each hedge and recommend which hedge should be selected.
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Solution:
We have three choices available to hedge the amount.
1. Discounting
2. Money market hedge 3. Forwards
1. Allow a discount of 1.5% and receive the amount.
Customer is willing to pay a lead payment at a discount of 1.5%. (payment today) For three months discount = 1.5% x 3/12 = 0.375
Net amount received will be : 100 – 0.375 = 99.625 m BP. (Buldonia Peso)
Convert in US$: 99.625 / 128.2 = 0.7771 m US$
Convert in £: 0.7771 / 1.782 = 0.4360 m £ (PV)
£ 0.4360 m will be net amount received today, if we allow a discount of 5% to customer.
We can calculate FV using £ investment rate, 4% per annum (net received through discount) 𝐹𝑉 = PV(1 + i)𝑛 , FV = 0.4360(1 + .04)3/12 = 0.4402m £
2. Money Market Hedge
Annual interest rates available to ABC co.
Borrowing Lending
UK 6% 4%
USA 7% 4.5%
Buldonia 14% 10%