INTERNATIONAL FINANCIAL MANAGEMENT

Prof. Parveen Sultana Kanth

RETURN ON INVESTMENT - IFM

PROBLEM

An American investor purchased securities in Indian market investing one million dollars, at the time of investing exchange rate is 50/50.5 Rs while one year latter the exchange rate is 53/54 Rs . what is the rate of return to American investor if he rate of Rs return on Indian security is 20% 25% & 50%.

If the rate is = 20% Amount invested in India = 10,00,000 * 50 = 50,000,000 (50

million)Return = 100,00,000 (1 million)After 1 year the amount to be repatriated = 60000000/54= 11,11,111.

Rate of return= 11,11,111/10,00,000 = 11.11% if the rate = 25% Amount invested is 10,00,000 * 50 = 5,00,00,

000 at 25% return rate of return in Indian rupees =

5,00,00,000 *25% = 1,25,00,000 at the closing rate = 6,25,00,000/54 = 11,57,407 Return = 157407/10,00,000 = 15.47%

If the rate is 50% in Indian Rs term Investment = 5,00,00,000 Return in Indian Rs = 5,00,00,000*50 =

2,50,00,000 Rs Total amount to be repatriated in Rs =

7,50,00,000/54 = 13,88,889$ Return on investment = 3,88,889/10,00,000 =

38.89%

PROBLEM :-2

Risk free return in India is 8%, an American investor wants to invest in Indian securities with beta of 2 with variance of 15%while exchange rate of rupees deprecation by 10% with variance of 20%. Market related return is 18% and correlation coefficient between return on security and exchange rate is 25% ,find out the expected rate of return and risk in investment

CAPM THEORY IS APPLIED

As per CAPM the expected return on securities = risk free interest rate +beta (market rate –risk free interest rate).

= .08 + 2 (.18 - .08) = 28%If 100 $ are invested in market then return is

128 $, then excluding exchange rate. variance of return = .15+.20+2* .25s square

root of (.15* .20) = .0.44 = 44% of risk

FOREIGN EXCHANGE MARKET

PROBLEM:-1 CROSS RATE

The Germany DM is selling for $ 0.62 & the buying rate for the French franc (FF) o.17$, what is the FF/DM cross rate ?

US$0.62 FF FF 3.65------------- x -------- = --------------- DM US$ 0.17 DM

PROBLEM:-2 CROSS RATE

The US$ Thai Bhat exchange rate is US$ 0.02339/Bhat, and the US$ Indian Rupees is US$0.02538/INR . Suppose that INR is not quoted against Thai Bhat . What is the Bhat/INR?

US$0.02538 US$ 0.02339 US$ 0.02538 Bhat ---------------- + --------------- = ------------- x --------- INR Baht US$ 0.02339 INR

Ans : Baht 1.085 ---------------- INR

THE SPOT PRICE = 0.025063,USD/INR , AND FORWARD RATE IS 0.02439, USD/INR FOR 6 MONTHS FORWARD , THE ANNUALIZED PREMIUM IS AS FOLLOWS SELLING AT PREMIUM

Forward premium spot rate- forward rate 360Or discount = ---------------------------- x ------- forward rate days

For 6 months forward , the annualized premium is as follows

0.025063 - 0.02439 360= -------------------------- x ------ = 5.5% 0.02439 180

Forward rupees is selling at a discount of 5.5%relative to the dollar for 6 months. In terms of indirect quote , the INR/$ spot exchange rate is INR 39.90/$ and forward rate is INR 41.00/$. For indirect quote, the forward premium or discount can be calculated as follows:

Forward premium Forward rate - spot rate 360 or discount = --------------------------- x ----- spot rate days 41.00 -39.90 360 = ---------------- x ------ 39.90 180 = 5.5%

Balance of payment, Cross Rate , Spot Rate Forward Rate, exchange rate theories

PROBLEM:-3An exporter has to surrender $ 100,000 to bank . Rate of dollar

against INR is 46/46.15, the bank charge a commission of .15%. If the transit time fixed by RBI is 20 day and the rate of interest charge by the bank is 10%.

Find out the net proceeds to be credited to exporters account?

Find out what is the amount to be paid by the person if he is an importer instead of exporter?

If Rs $ rate is 46/46.15 $/pound rate is 1.71/1.74 what is Rs pound rate.

If French franc $is 10.17/10.20 and Swiss franc $ rate is 1.73/1.75. find out French franc / Swiss franc rate?

If one Rs can buy 3.23 yen and if one Rs can buy .028 $ how many yens can 1$ buy?

In London a dealer quotes Dm/pound spot = 3.2550/3.2555,Yen pound spot = 180/181 . What do you expect yen/Dm rate in Frankfort?

Find out the net proceeds to be credited to exporters account?

Solution: since the exporter sells the dollar to bank bid price of 46 per $ to be taken . since it involves buying of $ by bank commission should be deducted from exchange rate.

Rate to be adopted is = 46 - (46 * .15%) =45.93

Total amount is 100,000* 45.93 = 45,93,000Interest charged is 10% for 20 days on the net

proceeds. = 45,93,000 * 10 *20/365 = 25,167 Rs

Net proceeds to be credited to the account of exporter = 45,93,000 - 25,167 = 45,67,833

Find out what is the amount to be paid by the person if he is an importer instead of exporter?

Solution: Since in this case the bank is selling the dollar to importer , it charges the ask rate of 46.15 and the commission is added instead of being deducted . Amount to be paid by the importer

= 46.15+(Rs 46.15*.15%) = 46.22 RsThe amount to be paid by the importer to bank = $

1,00,000* 46.22 = Rs 46,22,000.

If Rs $ rate is 46/46.15 $/pound rate is 1.71/1.74 what is Rs pound rate.

Rs/pound rate = Rs/$* $/pound (cross rate) = 46*1.71/46.15*1.74= 78.66/80.30

If French franc $is 10.17/10.20 and Swiss franc $ rate is 1.73/1.75. find out French franc / Swiss franc rate?

French franc /Swiss franc rate = French franc /$ * Swiss franc/$.

Swiss franc /$c rate = 1/1.75/1/1.73 = .5714/.5780French franc /Swiss franc =

10.17*.5714/10.20*.5780 = 5.81/5.90

If one Rs can buy 3.23 yen and if one Rs can buy .028 $ how many yens can 1$ buy?

= .028 $ = 3.23 yen 1 $ = ? $ = 3.23/.028 = 115.35 yen

In London a dealer quotes Dm/pound spot = 3.2550/3.2555,Yen pound spot = 180/181 . What do you expect yen/Dm rate in Frankfort?

Sol: Yen/Dm spot rate = yen /pound spot rate * pound /Dm spot rate.

Dm/pound spot rate = 3.2550/3.2555Pound /Dm spot rate = 1/3.2550/1/3.2555

= .3072/.3071Yen/Dm spot rate = 181* .3072/181*.3071 = 55.603/55.278 Frankfort get quote of yen/Dm spot

51.1530/51.2550 is there an arbitrage opportunity

Sol: Buy 1Dm in Frankfort by selling 51.2550 yen, sell 1 Dm and get 55.7278 yen there by making profit of 55.278 - 51.2550 = 4.023 yen

January , 24, 2014 a customer requested a bank to remit DG(Decigram) 250,000 to Holland as payment for Diamonds, However due to strike the bank can make payment only on Feb ,1,2014.

Inter bank rates are as follows:Jan 24,2014 Feb 1 2014

Mumbai $/Rs (100Rs) 3.10/3.15

3.07/3.12

London $/pound 1.7250/60

DG /pound 3.957/90

1.7175/85

3.9380/90

How much does the customer stand to gain or lose due to delay?

PROBLEM

Sol: Rs/Dg = Rs/$* $/Dg Rs/$ = 100/3.15/100/3.10= 31.75/32.26 = 100/3.12/100/3.07= 32.05/32.57$/Dg =$/pound*pound/Dg = 1.7250/3.9590/1.7260/3.9575

= .4357/.4361 = 1.7175/3.9390/1.7185/3.938

= .4360/.4364Rs /Dg = 31.75 * .4357/32.26 *.4361 =

13.83/14.07 = 32.05 *.4360/ 32.57 * .4364 =

13.97/14.21

The importer has lost (14.21 – 14.07) * 250,000 Dg = Rs 35000 due to delay remittance

PROBLEM

Consider the value of DEM relative to USD. The spot rate is DEM 1.82. the interest rates in the US and Germany are 5% and 3% respectively. Estimate the price on 4 month forward contract on DEM.

Solution:Spot rate of Dem (1USD= DEM) 1.82Interest rate US =5%Interest rate in Germany= 3%

SOLUTION

Et =Eo (1+rhc/1+rfc)t.Where et = expected forward rate for time t.Eo = spot rate rhc =rate of interest in home currency.Rfc =rate of interest in foreign currency.T= time period.1.82( 1+ 0.03/1+ 0.05) x 4//12 = 0.595

PROBLEM

USD/INR spot =48.75/80, 2 months swap =.12/.20. USD?JPY spot=125.50/126.10, 2 month swap =.20/.15. Find INR/JPY 2 month outright ?

Solution: USD/INR spot = 48.75/48.90 2 month = 48.87/ 49.90. USD/JPY spot = 125.50/ 126.10 2 month = 125.30/ 125.95 INR & JPY = 125.30/48.87 = 2.56. 125.97/ 49 = 2.57.JPY = 2.56/2.57 for 1 INR

PROBLEM

Give the following date, calculate the arbitrage possibilities

Spot rate : 42.0010=1$

Forward rate (6month)= 42.8020Rs/1$

Annualised interest rate on 6 month Rs:12%

Annualised interest rate on 6 month dollar:8%

SOLUTION The rule is that if the interest rate differential is

greater than the premium or discount ,place the money in the currency that has a higher rate of interest or vice versa

Negative interest rate differential = 12-8=4% Forward premium = forward rate –spot rate ------------------------------- X

100 spot rate 42.8020-42.001 12---------------------- x100 x -------- = 3.8141% 42.0010 6

Negative differential > forward premium . Hence, there is a possibility of arbitrage inflow in India.

Arbitrage possibility for an investment of $1000 by taking a loan @ 8% in US. An arbitrageur would invest in India at spot rate of RS 42.0010 @12% for six months and cover the principal +interest in six month forward rate

Principal:$1000= 42,001 Rs Interest on investment for six month = Rs 42001

x 12/100 x 6/12 = 2520.06So total amount at the end of six month+ principal

+interest = 2520.06+ 42001= 44,521.06

Converting the above in dollars at the forward rate = 44,521.06/42.8020= $1040.16

The arbitrageur will have to pay at the end of six month = $ 1000 + ($1000 x 8/100 x6/100) = $1000+ $40 =1040$

Hench the arbitrageur gain + ($1040.16-$1040) =$0.16 on borrowing $1000 for six month

PROBLEM: INTEREST RATE PARITY

An American firm purchases $4000 worth of perfume (ff 20,000) from a French francs. The following quotation and expectations exist for the FF.

Present spot rate $ 0.2000, US interest rate15%. 90 day forward rate 0.2200, French interest rate 10%

SR 90days = 0.2400. What is the premium or discount on the forward French francs ?

What is the interest differential between US and French ? Is there an incentive for covered interest arbitrage?

If there is CIA (covered interest arbitrage), how can an arbitrageur take advantage of the situation? Assume the arbitrageur is willing to borrow $4000 or FF 20,000 and there are no transaction costs.

If transaction costs are $50 , would an opportunity still exit for CIA?

SOLUTION

Forward premium on FF = FR-SR/SR X 100 .22-.20 ------------ X 100 X 4 =

40% .20 Interest rate different is 15-10=5% .Yes there is an incentive for CIA (outflow of

trends from US ) as interest differential in favour of France is -5% in flour of US 5%.

The arbitrageur can take advantage of the situation in the following manner.

Borrow $4000 for 90 days. So amount is t paid after 90 days

= 4000 (1+15% X1/4) =$4.150

Convert $4000into FF at current SR ie $1=5Ff

$4000 = FF 4000x5 =FF 20,000

$4000= FF 20,000

Invest 20,000 in France @10% p.a for 90 days

Amount received at the end of 90 days = FF 20,500

Sell investment proceed forward at rate FF1= $.22

Amount received in US $ after 90 days by selling FF 20500= $ (20500 x .22) = $4510

Amount received =4510$Amount paid =4150$ ------------Profit = 360$

As the profit of 360$ > transaction cost of 50 $ opportunity still exist for a CIA.

PROBLEM

Dm spot was quoted 0.40$ in New York, the price of the pound sterling was quoted $1.80.

1. what would you expect the price of the pound to be in Germany?

2. If the pound were quoted in Frankfort at Dm 4.40/pound what would you do to profit from the situation?

SOLUTION

1Dm =$ 0.40 ; 1 pound = $1.80 1/0.40Dm = 1/1.80pound 1 pound = 1.80/0.4 Dm = 4.5Dm = 4.5 Dm/pound.

Buy 1 pound for Dm 4.40 in Frankfort . With this pound sell in NY: for $1.80. with $1.80 , buy 4.5 Dm . Hench the arbitrager will profit 0.1 Dm for every 4.40 Dm

PROBLEM You have called your foreign exchange market and asked for

quotations on the spot , 1 month, 3 months, 6 months. The trader has responded with the following.

= $ 0.024.479/81 3/5 8/7 13/10

1. What does this mean in terms of dollars per euro2. If you wished to buy spot Euros how much would you pay in

dollars?3. If you wanted to purchase spot US$ how much would you

pay in euro?4. What is the premium or discount in the 1, 3, 6 months

forward rates in annual percentages? ( assume you are buying in Belgian francs)

5.

SOLUTION

Spot rate Bid price Ask price

Spot rate $0.2479 $0.2481

1 month $0.2482 $0.2486

3 months $0.2471 $0.2474

6 months $0.2466 $0.2471

2. $ 0.2481 Will Ask Price

3. US $ spot = 1/ 0.2481 = 4.034

Premium or discount rates in forward market (assuming that buying in Belgian francs)

0.2486 – 0.2481

1 month = ------------------------ X 12 X100 = 2.42%

forward 0.2481

premium

0.2474 – 0.2481 12

3 month = ------------------------ X 100 X ----- =1.13%

Forward 0.2481 3

Discount

6 month = 0.2471- 0.2481 12

Forward --------------------- X 100 X ----- = 0.8%

Discount 0.2481 6

PROBLEM

Spot rate = 44.0030 = $1 6 month FR = 45.0010 = $1 Annualised interest rate on 6 month rupee =

12% Annualised interest rate on 6 month dollar =

8%

Given the above data is there arbitrage possibility?

SOLUTION

6 month forward US $ is being quoted at a premium as follows

45.0010- 44.0030 12------------------------- X ------ X100 = 4.5361% 44.0030 6 Interest rate differential = 12-8 = 4%

Since interest rate differential is smaller than the premium , it would be beneficial to place money in US $ as 6 month interest rate is lower .

An arbitrageur would take the following steps:

1. Borrow Rs10,000 at 12% for 6 months

2. Convert this SR to obtain US$ 227.257 (10,000/44.0030)

3. Invest $ at 8% in money market for 6 months to receive

6 1= $ 227.257 8 X ----- X ----- + 1 12 100

4. Sell Us$ at 6 month forward to receive = 236.3473 X 45.0010 = Rs 10635.865

5. Return the rupee debt borrowed at12 % . The amount to be refunded is Rs 10,600

6 1=10,000 1+ 12 X ---- X ----- + 1 12 100 Profit = amount received – amount borrowed = 10,635.865 -10,600 = 35.865

PROBLEM

From the following data calculate the possibilities of gain /loss in arbitrage.

Spot rate FFr 6.00 = $1 , 6 month forward rate FFr 6.0020 = $1.

Annualised interest rate on 6 month s US$ = 5%

Annualised interest rate on 6 month Fr = 8% (It Direct Quote Method)

SOLUTION

Negative interest rate differential = 5 - 8 = -3% forward Premia (annualized ) = FR-SR/SR *100 *

12/6 = (6.0020 -6.0000 /6.0000) x100 x 12/6 = 0.67%

Here we find that the negative interest rate differential > forward Premia , Hench there will be arbitrage inflow in France

The arbitrage possibility will be shown below.1. Assume an arbitrageur borrows $1000 for 6 months.

Amount to be repaid at the end of 6 months will be = $1000 +$ 1000 x5/1000 x6/12 = $1025.

2. The arbitrage would then convert $ into FF at spot rate and invest the amount in France @8%. Converting $ into FF at the spot rate $100 –FF 6000.

Invest in France @8% = 6000 x 8/100 x 6/12 = 240 Total amount received is FF 6000 + FF240 = FF 6240.

convert Ff6240 into $ at the forward rate at the end of 6 month = FF 6240 /FF 6.0020 = $ 1039.65.

Amount received by the arbitrageur = $1039.65Amount paid = $ 1025.00 ----------------------- profit = $ 14.65

If the current Rs/$ rate is Rs 50, one year inflation rate is 10% for Rs and 2% for dollar. If 1 year later , the rate of exchange between $ & Rs in forward rate is 55, is there scope for arbitrage , if PPP is applicable?

Spot exchange rate between Rs/$ 50, if annual inflation rate is 10% in India and 3% in us what will be the rate of return to Indian investor if the return on us security is 10%if PPP is applicable?

In the above case if the percentage of return in India is 10%. What is the rate of return to American investor?

Problem:

Sol :1: S1A/B = S0A/B X (1+rA/1+rB)

S1 = Future Exchange Rate

rA = Interest rate of country A

rB = Interest rate of country B

As per PPP one year later rate will be = (50* 1.10)/1.02 = 53.92.Since the present forward rate is not in alignment he

can sell the $ forward Sol: 2: Indian investor can convertRs50 to one

dollar and invest the same in Us security. After one year he will get 1.10 $ .

One year later the= $=(50* 1.10)/1.03 =53.40 Rs. Sol:3: American investor can convert one dollar to

50Rs and invest the same in Indian market. After one year he will get Rs 50 * 1.10 = Rs55, if this is converted to dollar it will be 1.03$ . So the rate will be 3%for American investor.

PROBLEM

An Indian company ,AB ltd imports machinery worth ₤2.0 million and is to make the payment after 6 months. The current rate are

Spot rate = Rs 66.96/₤6 month forward rate = Rs 67.50 /₤ What should AB ltd do if they expect that in

six month time the pound will settle at Rs67.15/₤?

What are the option available to the company in case of an expected appreciation / depreciation in the rupees?

SOLUTION

Spot rate ₤1 = Rs 66.96 6 month forward rate ₤1 = 67.50 Expected spot rate after 6 month ₤1 = Rs 67.151) Since AB ltd has a liability in foreign currency

pound , they are importing a machinery worth ₤ 2.0 million . Both the market and the company expect the pound to appreciate.

2) Hench company should estimate the relative cost of hedging and if it is not high , the company should hedge its payments.

3) Incase of depreciation of pound the company need not do anything as it stands to gain . In case of appreciation of pound it should hedge its payments as the company will be exposed to exchange rate risk

PROBLEM

The following data is given:Spot rate FFrl = 66.60 Rs6 month forward rate FFrl = Rs 6.85FFr interest = 8.3%Rs interest = 10.5 % Analyze the different arbitrage possibilities

SOLUTION

Given the above data if one invest money in India , he gets = ( 1+ .105/2) =1.0525 after 6 months.

If one invest money in FFr , he gets 6.85/6.60 (1+0.83/2)= Rs10809

So there will be an arbitrage outflow from india.

PROBLEM Set out below is a table of cross rates.

Deutsch mark

Dollar French franc

Pound sterling

Frankfurt ? 2.2819 0.4712 4.0218

New York 0.4421 ? 0.2110 1.8000

Paris 2.0949 4.7393 ? 8.4301

London 4.0207 1.7775 8.4232 ?

For Frankfurt , New York and Paris all quotes for London all quotes are indirect. If all above quotes were available at the same time and assuming no transaction costs how might a trader take advantage of the situation

SOLUTION

Given the arbitrage opportunities with no transaction cost.

Arbitrage between Dm & pound : buy pound in Frankfort . For every Dm, one will get ₤4.0218. These can be sold in London to get Dm for which one will have to pay ₤ 4.0207. These can be sold in London to get Dm for which one will have to pay ₤ 4.0207.Thus there is a potential gain of 0.0011 pounds for every Dm.

Arbitrage between $ & ₤ : buy ₤ in New York and sell in London.

Arbitrage between FFr and ₤ : buy Paris and sell in London.

Arbitrage between $ & ₤ :buy $ in Frankfort and sell in New York . For every Dm one will get $2.2819. these can be sold in Frankfort and sell in New York . For every Dm one will get $2.2812. these can be sold in New York to get Dm for which one will have to pay ₤2.2619. thus there is a potential gain of $0.0193 for every Dm traded.

Arbitrage between Ff and Dm : buy in Paris and sell in Frankfort. For every FF one will get Dm 2.0949. these can be sold in Frankfort to get Ff for which one will have to pay Ff 0.9817. thus there is a potential gain of Ff 0.0128 for every Dm traded.

Similar arbitrage opportunities will exist across all the currency combinations.

PROBLEM A foreign exchange trader gives the following quotes

for the Belgian franc Spot , 1 month, 3month , 6 month to us based treasurer.

= $0.02368/70 4/5 8/7 14/12.1. Calculate the outright quotes for 1, 3, &6 months

forward?.2. If the treasurer wished to buy Belgium franc 3 month

s forward how much would the pay in dollars ?3. If he wished to purchase US$ 1 month forward how

much would he have to pay in Belgium franc? 4. Assuming that Belgian franc are being bought what is

the premium/ discount for the 1, 3, 6 months forward rate in annual percentage terms?

5. What do the above quotation imply in respect of the term structure of interest rates in the USA & Belgian?

SOLUTION

Bid Ask

Spot $ 0.02368 $0.02370

1 month $0.02372 $0.02375

3 month $ 0.02360 $0.02363

6 months $0.02354 $ 0.02358

2. To buy Belgian francs 3 month forward the treasurer has to pay $ 0.02363.

3.US $ 1 month forward = 1/0.02375= Belgian franc 42.10526.

For 1 month forward premium = (0.02372-0.02368)/0.02368 x 100 x 12=2..27%

p.a.For 3 month forward discount = (0.02360- 0.02368)/0.02368 X100 X12/3 = 1.35%

p.a.For 6 month forward discount= (0.02354- 0.02368)/0.02368 x100 x 12/6 = 1.185

p.a.4. Belgian interest rates are expected to rise and US

interest rate are expected to fall.

PROBLEM “Compaque” company has to make a US $ 1 million

payment in 3 months time . The dollars are available now . You decide to invest them for 3 months.

US$ deposit rate :9% p.a.UK deposit rate :10% p.a.Present spot rate is $ 1.90/pound.3 month forward rate is $ 1.88/₤. Where should the company invest for better returns? Assuming that the interest rates and the returns spot

exchange rate remain as above what forward rate would yield an equilibrium situation?

If the sterling deposit rate was 12% p.a. and all other rates remain as in the original question, where should you invest?

SOLUTION Alternative :11. invest US$ 1 million in Us @9% p.a. for 3 months. Interest earned = (

100,000 x.09 x 3/12) - $ 22,500. Alternative :2 1. sell the US $ 1 mn and buy pound from the spot market , we get =

1,000,000/1.90 = ₤ 526,315.789.2. Invest the available ₤ @10% for 3 months yield an interest =

526,315.789 x 10 /100 x 3/12 = 13,157.895. 3. principal + interest after 3 month = 526,315.789 + 13,157.895 = ₤

539,473.684. 4. selling the pound to buy US $ we get 539,473.684 x 1.88 = $

1,014,210.5265. Hench income = $1,014, 210.526- $1,000,000 = $14210.526. Hench

the company should invest in the US as it results in better return of US$ 8,290.

Assume the forward rate be ‘x’For an equilibrium situation amount at the end of 3 month s

should be equal . Hench amount invested in sterling covered by forward rate should be = $ 1,022,500.

Hench x = 1022,500/539473.684 = 1.895 Hench forward rate = $ 1.89 / ₤. Sell the US$ and buy ₤ from the spot market we get =

1,000,000/1.90 = ₤ 526,315.7891. invest the available ₤ @12% for 3 months yield an

interest = 526,315.789 x 12 /100 x 3/12 = 15,789.4732. Principal = interest after 3month = 526,315.789 =

15,789.473 = ₤ 542,105.262.3. Selling the pound to buy US$ we get = 542,105 .262

X1.88 = $ 1,019,157.893 Thus income (net) = 19,157.893.4. since interest earned by investing in US$ = 22,500.

Hench even if the sterling deposit rate become 12% p.a. investing US$ is still a more profitable alternative.

PROBLEM 21

A MNC gives the following outright quotations for the Singaporean dollars:

BID ASk

Spot rates 1.2440 1.2450

1 month 1.2455 2.2475

3month 1.2477 1.2484

6 month 1.2482 1.2498

Calculate forward quotes for the Singaporean dollar as an annual percentage premium or discount if you reside in US.

calculate the annual percentage premium or discount on the US dollar for each forward rate for a foreign exchange trader residing in singapore?

SOLUTION

We are buying USD.BID ASK Premium

on buying USD annualized

Spot rate 1.244 1.245

1 month 1.2455 1.2475 0.200803214

2.409638554

3 month 1.2477 1.2484 0.072144289

0.288577154

6 month 1.24 82 1.2498 0.112143544

0.224287087

Bid Ask % discount on buying USD annualized

Spot rate 0.80385852 0.803213

1 month 0.80289041 0.801603 -.0.002004008

-0.0240280

3 month 0.80147471 0.801025 - 0.000720923

-0.0028836

6 month 0.80115366 0.800128 -0.001120179

-.00022403

PROBLEM

The direct quote in Tokyo for Peso is given as ¥28.8358/MP Bid & ¥ 28.8725/MP Ask, in México city 0.04418/0.04488.

Calculate the bid –ask Spread as percentage of bid price from the Japanese and from the Mexican perspective.

would there exist an opportunity for profitable arbitrage? If yes describe the necessary transaction assuming a ¥ 1 million starting amount.

SOLUTION

Bid-Ask- spread as a % in yen (Japanese) = (28.8725- 28.8358)/ 28.8358 = 0.127%.

Bid –Ask-spread as % in MP (Mexican) = (0.04422-0.04418) / 0.04418 = -0.09%.

Opportunities for arbitrage:( in Mexico & in Tokyo) In Mexico= MP 0.04418/ ¥ Bid: MP 0.04422/ ¥. Or ¥22.6142/NP bid: ¥22.6346/MP ask

Direct terms Bid rate Ask rate

In Japan ¥ 28.8358/MP ¥28.8725/MP

In Mexico MP 0.04418/¥ MP 0.04422/¥

Purchase MP in Mexico at ¥ 22.6346/MP (ask) Assuming ¥ 1 million as the starting amount &

converting it to MP. so, MP received = 1m / 22.6346= 42625.7 MP.

In Tokyo, = ¥28.8358/MP bid and ¥28.8725/MP ask, convert MP into yen in Tokyo at ¥ 28.8358/MP bid.

Yen received = ¥1.229m Profit = ¥ 1.229m- ¥ 1m = ¥.229m Hence profit earned = ¥ 0.229m

PROBLEM

call option on euro is written with a strike price of $ 0.9400/e at premium of 0.9000$ per euro/E and with an expiration data 3 month s from now . The option is for E 100,000. calculate your profit or loss if the excise before maturity at the time when the euro is traded spot at:

$ 0.9000/e $ 0.9200/e $ 0.9400/e $ 0.9600/e $ 0.9800/e $ 1.0000/e $ 1.0200/e

SOL :CALL OPTION: FSP>SP =EXECUTE, PUT OPTION: FSP<SP = EXECUTE

Spot rate Strike price

Premium

Decision Profit = spot rate – (strike price +Premium)

$0.9000/e 0.9400/e

0.0090/e Execute option profit 0.049

$0.9200/e ,, ,, Execute option profit 0.029

$0.9400/e ,, ,, Execute option profit 0.009

$0.9600/e ,, ,, Not Execute 0.011

$0.9800/e ,, ,, Not Execute 0.031

$1.000/e ,, ,, Not Execute 0.051

$1.0200/e ,, ,, Not Execute 0.071

PROBLEM

Spot and 180 day forward exchange rates of several major currencies are given . For each pair calculate the percentage premium or discount expressed as annual rate.

Countries Quotation spot rate

180 days forward rate

European euro $ 0.8000/e $0.8160/e

British pound $ 1.562/₤ $1.5300/₤

Japanese yen ¥120.00/$ ¥118.00/$

Swiss franc SF 1.6000/$ SF 1.6200/$

Hong kong dollar HK $ 8.000/$ HK $7.8000/$

SOLUTION Forward premium/ discount = = FR-SR/SR X100 X360/number of days. European Euro = 0.8160- 0.8000/0.8000 X 360/180X100 Premium = 4% British Pound =1.5300-1.562/1.562 X 360/180 x 100 Discount = -4.08% Japanese yen = 118.00-120.00/120.00 x360/180 x 100 Discount = -3.33%. Swiss franc = 1.6200- 1.6000/1.6000 x 360/180 x 100 Premium = 2.5% Honk kong dollar = 7.8000-8.000/8.000 x 360/180 x 100 Discount= -5%

ASSIGNMENT PROBLEMS

PROBLEM:1

Given the following date calculate the arbitrage possibilities

Spot rate 1 $ = Rs 42.0010.6 month forward rate 1$ = Rs 42.8020Annualised interest rate on 6 month Rs:12 %Annualised interest rate on 6 month USD:8% Is arbitrage is possible.

PROBLEM:2

Given the following data:Spot rate = 46.0010 Rs =1$6 month forward rate Rs 46.8020 =1$Annualised interest rate on 6 month Rs = 12%Annualised interest rate on 6 month $ =8%Initial investment is 10,000$Calculate the arbitrage possibilities.

PROBLEM:3

USD/INR spot rate = 53.75/90. 2 month swap =.12/.20

USD/JPY spot rate = 110.50/125.45 . 2 month swap =.20/.15

Find INR/JPY , 2 month outright

PROBLEM: 4 The current CHF/USD spot =0.6675. the following

90 day call option on CHF is available. Strike price Premium0.60 0.075 0.65 0.030.68 0.010.70 0.0050.75 0.002Your view is that CHF is going to make strong up move during the next 90 days your risk appetite is moderate . What strategy is suitable for you/ explain with the pay off table

EXOSURE :TRANSLATION ,

TRANSACTION, OPERTING

PROBLEM: Farm product is the Canadian affiliate of a US

manufacturing company .its balance sheet in thousand of Canadian $ for dollars for January, the January 1 20x2, exchange rate was C $ 1.6/$.

Farm product balance sheet (thousand of C$)

Assets Liabilities and networth

Cash =C$ 100000Account receivable = 220000Inventory = 320000Net plant and equipment = 200000 --------------- Total 8,40,000

Current liabilities =C $ 60,000Long term debt = 160,000Capital stock =620000 ---------------- total 8,40,000

Determine farm product accounting exposure on January 1 2012, using the current rate method/ monetary /non monetary method.

Calculate farm product contribution to its parent accounting loss if the exchange rate on December 3 20x2 was C$ 1.8 per $. Assume all accounts remain as they were at the beginning of the year.

SOLUTION Current /non current method

C$ Exchange rate

Conversion to US$ on jan 1 20x2

Assets1. Account

receivable2. cash3. Inventory4. Plant &

equipmentLiabilities5. Current

liabilities6. Long term

debt7. Capital stock

CTA

100,000220,000320,000200,000

60,000

160,000

620,000========840,000

1.81.81.81.8

1.8

1.8

1.6

(100000/1.8)= 55,555.55= 122,222.22= 1,77,777.77= 1,11,111.11--------------------= 4,66,666.66-------------------= 33,333.33= 88,888.88= 3,87,500.00= (43,055.55)--------------------4,66,666.66

As per current rate method Accounting exposure on Jan 1 20x2 is as followsExposed asset = US$ 4,66,666.66.Exposed liabilities = US $ 1,22, 222.22.Accounting exposure = 3,44,444.45Accounting loss as show as in CTA (Cumulative Translation Adjustment) account is =US $ 43,055.55

Cumulative Translation Adjustment :- Cumulative Translation Adjustments are an integral part of the financial statements for firms with international market exposure.

An entry in the comprehensive income section of a translated balance sheet summarizing the gains/losses resulting from varying exchange rates over the years. A CTA entry is required under the Financial Accounting Standards Board (FASB) No.52 rule as a means of helping investors differentiate between actual operating gains/losses and those generated via translation.

(Opening Functional Balance x (Current month-end rate - Previous month-end rate)] + [Sum(Transactions in month) x (Current month-end rate - current average rate)]) x [-1]

Monetary/non monetary method

C$ Exchange rate Cinversion to US $ on jan 1 20x2

• Cash• Account

receivable• Inventory• Plant &

equipment• =========

==• Current

liabilities• Long term debt• Capital stockCTA

100,000220,000

320,000200,000

=========60,000160,000620,000

1.81.8

1.61.6

1.81.81.6

55,555.55122,222.22200,000.00125,000==========5,02,777.77

33,333.3388,888.8838,7500.(6,944.44)

AS PER THE MONETARY/ NON MONETARY METHOD

Accounting exposure on jan /1/20x2Exposure assets= US $ 1,77,777.77Exposure liabilities =US $ 1,22,222.21Accounting exposure = 55555.57Accounting lose as on CTA a/c =US $ 6,944.44

PROBLEM

ABC house ltd manufactures orange marmalade in England .it is the wholly owned subsidiary of XYZ Inc. of USA the financial currency for ABC is the pound sterling which currently sells at $1.5000/£. The reporting currency for XYZ is the US $ . Non- consolidated financial statement for both ABC and XYZ are as follows ( in thousand )

ASSETS XYZ ABC LIBILITES XYZ ABC

• CASH• ACCOUNT

RECEIVABLE• INVENTORY• NET PLANT &

EQUIPMENT

• INVESTMENT

$ 800010,0008,00010,000

4,500

₤ 2000400020006000

----

• CURRENT LIABILTIES

• 5 YEAR TERM LOAN

• CAPITAL STOCK• RETAINED

EARNING

$ 22,000----

9,000

9,500

£ 4,0004,000

2,000

4,000

Prepare a consolidation balance sheet for XYZ ltd.What is ABC LTD accounting exposure in dollars ? Use the current rate method of calculation.Before n business activates take place the pound sterling deprecation 9% in value relative to the dollars what is the new spot rate?What is XYZ accounting loss or gain if any by the current rate method / Monterey non monetary method

SOLUTION

Balance sheet for ABC ltd in dollar

Assets ABC Rate

$ Liabilities ABC Rate $

CASH ₤2000 1.5 3000 CURRENT LIABILTIES

£ 4000 1.5 6000

ACCOUNT RECEIVABLE

4000 1.5 6000 5 YEAR TERM LOAN

4000 1.5 6000

INVENTORY 2000 1.5 3000 CAPITAL STOCK

2000 1.5 3000

NET PLANT & EQUIPMENT

6000 1.5 9000 RETAINED EARNING

4000 1.5 6000

14000 21000

14000 21000

CONSOLIDATION BALANCE SHEET FOR XYZ AND ITS SUBSIDIARY ABC LTD

Assets Amount Liabilties Amount CASH $11000

(8000+3000)Current liabilities

$ 28000 (22000+6000)

ACCOUNT RECEIVABLE

16000 (10000+6000)

5 year term loan

6000 (0+ 6000)

INVENTORY 11000 (8000+3000)

Capital stock 12000 (9000+3000)

NET PLANT & EQUIPMENT

19000(10000+9000)

Retained earning

15500 (9500+6000)

INVESTMENT 4500Total 61500 Total 61500

B. USING THE CURRENT RATE METHOD

Assets Amount

Cash $ 3000

Accounts receivable $ 6000

Inventory $ 3000

Net plant & equipment

$ 9000

total $ 21000Liabilities tterm loan Amount

Current liabilities $ 6000

5 yrs term loan 6000

Capital stock 2000

Retained earning 4000

total 18000

CONTI…………….

Accounting Exposure (21000-18000) = $3000.

New position of the firm after deprecation Assets Current rate method

m/nm amount

Cash $ 2730 (3000*9%)-3000

$ 2730

Account receivable

$ 5460 (6000*9%)-6000

$ 5460

Inventory $ 2730 (3000*9%)-3000

$ 3000

Net plant equipment

$ 8190 (9000*9%)-9000

$ 9000

Total $ 19110 $ 20190

Liabilities & net worth

Current liabilities $ 5460 $ 5460

5 yrs term loan $ 5460 $ 5460

Capital stock $ 3000 $ 3000

Retained earning $ 6000 $ 6000

CTA (810) 270

total $19110 $ 20190

Loss by current method =$ 810Gain monetary/non monetary method =270$

PROBLEM

New Haven a dealer based in Europe is owned by an MNC inc. of the united states. Given below is new haven’s balance sheet at the current exchange rate of $1.50/ euro.

Value in euro At value at $ 1.5/euro

Assets

Cash & short term securities

$ 50,000 $ 75,000

Account receivable $ 30,000 $ 45,000

Inventory $ 20,000 $ 30,000

Plant equipment $ 600,000 $ 900,000

Total assets $700,000 $10,50,000

Liabilities Value in euro Value at $1.5/e

Account payable $ 150,000 $ 225,000

Short term debt $ 60,000 $ 90,000

Long term debt $ 410,000 $ 615,000

Net worth $ 80,000 $ 120,000

Total liabilities and net worth

$7,00,000 $ 10,50,000

For the current /non current method the temporal method and the all current rate method calculate .

a. The company’s exposed assets exposed liabilities and net exposed assets under each accounting translation method

b. Suppose the euro depreciate by25% identify the impact of 25% depreciation of the euro on new haven’s consolidation balance sheet under each accounting translation method.

SOLUTION Value in euro

Value at 1.50 (in $)

Assets;• Cash and short

term securities• Account receivable• Inventory• Plant and

equipment Total assets

Liabilities• Account receivable• Short term debt• Long term debt• Net worthTotal liabilities & net worth

50,000

30,00020,000600,000700,000

15000060,00041000080,000700,000

75000

4500030000900,0001050000

2,2500090,000615,000120,0001050,000

Deprecation = 25%initial euro = 1.5$ that is 1 $ = .67 euro, Deprecation of 25% implies 1 $ = 1.25 x .67 euro =.83 which is same as 1 euro = 1.2 $.All current method: Expose assets: 8,40,000$ Expose liabilities : 744,000$ Net exposed assets: 96,000$Current /non current method: Expose assets : 120,000$ Expose liabilities: 252000$ Net exposed asset: =132,000$Temporal method: Exposed assets: 120,000$ Exposed liabilities: 744,000$ Net exposed assets: = -624,000$

Balance sheet

In euro Ex. rate

C /non C ($)

Ex. rate

Temporal ($)

Ex. rate

Cur. Rate ($)

Assets:• Cash &

short term securities.

• Account receivable

• Inventory• Plant &

equipmentTotal asset

Liabilities• Account

payable• Short term

securities• Long term

securities• Net worthTotal liabilities

Translation exposure

50,000

30,000

20,000600,00

700,000

150,000

60,000

410,00080,000700,000

1.2

1.2

1.21.5

1.2

1.2

1.51.5

(50,000x1.2)60,000

36000

24000900,000

1020,000

180000

72000

615000120000987000

33000

1.2

1.2

1.21.5

1.2

1.2

1.21.5

60,000

36000

24000900,000

1020,000

180,000

72,000

492,000120,000864000

156000

1.2

1.2

1.21.2

1.2

1.2

1.21.5

60,000

36000

24000720,000

840,000

180000

72000

492000120000864000

-24000

PROBLEM

An MNC has account receivable of $ 1.8 billion and account payable of $940 million . It also has borrowed $ 700 million . The current spot rate is $ 1.81138/£

What is the MNC dollar transaction exposure in dollar terms? In pound term?

Suppose the pound appreciates to $ 2.1122 /₤ what is the MNC gain or loss in pound terms , on its dollar transaction exposure?

SOLUTION

In dollar term:Functional currency = dollar (i.e. foreign currency so the method used would be current rate method)Net exposure = exposure asset – exposure liabilities.Current methodExposure assets = $ 1800 mnExposure liabilities = $ 940+ $700= $ 1640Translation exposure = 1800-1640 = $ 160 mn

In pound term Translation exposure = 1800- 1640 = $ 160 mnCurrent rate = 1.8138/£ so translation exposure = 160/1.8138 = ₤ 88.21mnb. The pound appreciation to $ 2.1122/£Net exposure = ₤ 160 mn Current rate = $ 2.1122/£ so translation exposure = 160/2.1122 = ₤ 75.75

So this is a loss of (£ 88.21 – £ 75.75) = £12.46 mn

PROBLEM

A foreign company expect to receive Mexico $ 15 million entertainment fees from Mexico in 90 days . The current spot rate is $0.2320/M$ and the 90 day forward rate is 0.2240/M$. What I the company’s peso transaction

exposure associated with this fee? What is the expected US $ value of the fee if

the spot rate expected in 90 days in $0.2305. also calculate the hedged dollar value of the fee?

SOLUTION

Mex $ received if the fee to be paid today = $ million

15 x .2320 = US $ 3.48 million Mex $ received by the foreign company if the fee

is to be paid in 90 days = 15 x .2240 = US $ 3.36 million

Transaction exposure = 3.36 - 3.48 = -0.12 million

B. The expected US$ fee = 15 x .2305 = Us $ 34,57,500

The hedged dollar value of the fee is = 3480,000 – 3457000 = $ 23,000.

PROBLEM AV ltd is the Indian affiliate of affiliate of a

US sports manufacture . AV ltd manufacture items which are sold primarily in the united states and Europe .AV balance sheet in thousand of rupees as of march 31 is as follows: Assets Liabilities

Cash $ 6000Account receivable $ 4500Inventory $ 4500Net plant equipment $ 10,000Total $ 25000

Account payable $ 3500Short term bank loan $ 1500Long term loan $ 4000Capital stock $ 10,000Retained earning $ 6000

Exchange rate for translating the balance sheet into US $ are: RS 35/$ : historic exchange rate , at which

plant and equipment long term loan and common stock were acquired or issued.

RS 40/$ : march 31 exchange rate this was also the rate at which inventory was acquired.

RS 42/$ April 1 exchange rate , after devaluation of 20%.

Assuming no change in balance sheet a/c between march 31 and April 1 calculate accounting gain /loss by the current rate method and by monetary / non monetary method explain accounting loss in term of change in the value of exposed accounts

SOLUTION

Exchange rate: RS 35/$ historical rate for the others RS 40/$ for inventory march 31 – historical rate for

inventory. RS 42/$ for April 1 – current rate as on April 1

Rs Ex. Change rate

Conversion to $ on Nov 31

Ex. Change rate

Conversion to $ on April 1

• Cash • A/c

Receivable

• Inventory• Plant &

equipment

• Total

• Account payable

• short term loan

• Long term loan

• Capital stock

• retained earning

• CTA • Total

60004500

450010,000

25000

3500

1500

4000

10,000

6000

4040

4040

40

40

40

35

35

$ 150$112.50

$112.50$250.00

$625.00

$87.50

$37.50

$100.00

$285.71

$171.43

(57.14)$625.00

4242

4242

42

42

42

35

35

$ 142.50$107.14

$107.14$238.10

$595.24

$83.33

$35.71

$95.24

$285.71

$171.043

(76.19)$595.24

ACCOUNTING LOSS BY CURRENT RATE METHOD IS $ 57.14 ON MARCH 31

March 31 April 1

Exposed assets $ 625.00 $ 595.24

Exposed liabilities $ 225.00 $ 214.28

Net exposed $ 400.00 $ 380.96

Monetary /non monetary method

Rs Ex. Change rate

Conversion to $ on Nov 31

Ex. Change rate

Conversion to $ on April 1

• Cash • A/c

Receivable• Inventory• Plant &

equipment• Total

• Account payable

• short term loan

• Long term loan

• Capital stock

• retained earning

• CTA • Total

60004500

450010,000

25000

3500

1500

4000

10,000

6000

4040

3535

40

40

40

35

35

$ 150$112.50

$128.50$285.71

$676.78

$87.50

$37.50

$100.00

$285.71

$171.43

(5.36)$676.78

4242

3535

42

42

42

35

35

$ 142.50$107.14

$128.57$285.71

$664.29

$83.33

$35.71

$95.24

$285.71

$171.043

(7.13)$664.29

MONETARY / NON MONETARY METHOD

Accounting loss by monetary / non monetaryIs = $ 5.36 on march 31,= $ 7.13 on April 1

March 31 April 1

Exposed assets $ 262.50 $ 250.00

Exposed liabilities

$ 225.00 $ 214.28

Net exposed $ (37.5) $ (35.72)

THE END