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Problem 6.1 - 6.5 The Latin American Big Mac Index: Historical
This textbook has used the Economist magazine's Big Mac Index for many years and many editions. Below are the Big Mac pric
actual exchange rates for select Latin American countries as printed in previous editions. Use the data to complete the calculatio
implied PPP value of the currency versus the U.S. dollar and the calculation as to whether that currency is undervalued (-%) or o
(+%) versus the U.S. dollar.
April 1997 (1) (2) (3)
Big Mac Actual Big Mac
Price in local exchange rate Prices in
Country currency (April 7, 1997) dollars
United States (dollar) 2.42 ---- 2.42
Argentina (peso) 2.50 1.00 2.50
Brazil (reais) 2.97 1.06 2.80
Chile (peso) 1,200 417 2.88
Mexico (peso) 14.90 7.90 1.89
y editions. Below are the Big Mac prices and
Use the data to complete the calculation of the
that currency is undervalued (-%) or overvalued
(4) (5)
Implied Local currency
PPP of the under (-) / over (+)
dollar valuation
1.00
1.03 3.3%
1.23 15.8%
496 18.9%
6.16 -22.1%
Problem 6.6 Argentine Peso and PPP
The Argentine peso was fixed through a currency board at Ps1.00/$ throughout the 1990s. In January 2002 the Argentine
peso was floated. On January 29, 2003 it was trading at Ps3.20/$. During that one year period Argentina's inflation rate was
20% on an annualized basis. Inflation in the United States during that same period was 2.2% annualized.
Assumptions
Spot exchange rate, fixed peg, early January 2002 (Ps/$)
Spot exchange rate, January 29, 2003 (Ps/$)
US inflation for year (per annum)
Argentine inflation for year (per annum)
a. What should have been the exchange rate in January 2003 if PPP held?
Beginning spot rate (Ps/$)
Argentine inflation
US inflation
PPP exchange rate
b. By what percentage was the peso overvalued?
Actual exchange rate (Ps/$)
PPP exchange rate (Ps/$)
Percentage overvaluation (positive) or undervaluation (negative)
c. What were the probable causes of undervaluation?
The rapid decline in the value of the Argentine peso was a result of not only inflation,
but also a severe crisis in the balance of payments (see Chapter 4).
ry 2002 the Argentine
ntina's inflation rate was
lized.
Value
1.0000
3.2000
2.20%
20.00%
1.00
20.00%
2.20%
1.17
3.20
1.17
-63.307%
Problem 6.7 Akira Numata -- CIA Japan
Akira Numata, a foreign exchange trader at Credit Suisse (Tokyo), is exploring covered interest arbitrage possibilities. He wants
a covered interest arbitrage between U.S. dollars and Japanese yen. He faced the following exchange rate and interest rate quote
Assumptions
Arbitrage funds available
Spot rate (¥/$)
180-day forward rate (¥/$)
180-day U.S. dollar interest rate
180-day Japanese yen interest rate
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or expected change i
interest yielding currency. If the difference in interest rates is less than the forward premium (or expected change in the spot ra
Difference in interest rates ( i ¥ - i $)
Forward premium on the yen
CIA profit potential
This tells Toshi Numata that he should borrow yen and invest in the higher yielding currency, the U.S. dollar, to lock-in a cover
$ 5,000,000 → →
↑
↑
↑
↑
↑
Spot (¥/$)
118.60
↑
↑
↑
593,000,000.00 → →
Japanese yen
START
Akira Numata generates a CIA profit by investing in the higher interest rate currency, the dollar, and simultaneously selling the
premium which does not completely negate the interest differential.
yo), is exploring covered interest arbitrage possibilities. He wants to invest $5,000,000 or its yen equivalent, in
yen. He faced the following exchange rate and interest rate quotes.
Value Yen Equivalent
$5,000,000 593,000,000
118.60
117.80
4.800%
3.400%
reater than the forward premium/discount, or expected change in the spot rate for UIA, invest in the higher
ess than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
-1.400%
1.358%
-0.042%
n the higher yielding currency, the U.S. dollar, to lock-in a covered interest arbitrage (CIA) profit.
U.S. dollar interest rate (180 days)
4.800%
1.0240 → → $ 5,120,000
↓
↓
↓
↓
↓
---------------> 180 days ----------------> Forward-180 (¥/$)
117.80
↓
↓
603,136,000
1.0170 → → 603,081,000
55,000
3.400%
Japanese yen interest rate (180 days) END
interest rate currency, the dollar, and simultaneously selling the dollar proceeds forward into yen at a forward
tial.
Problem 6.8 Akira Numata -- UIA Japan
Akira Numata, Credit Suisse (Tokyo), observes that the ¥/$ spot rate has been holding steady, and both dollar and yen interest r
week. Akira wonders if he should try an uncovered interest arbitrage (UIA) and thereby save the cost of forward cover. Many of
models -- are predicting the spot rate to remain close to ¥118.00/$ for the coming 180 days. Using the same data as in the previo
Assumptions
Arbitrage funds available
Spot rate (¥/$)
180-day forward rate (¥/$)
Expected spot rate in 180 days (¥/$)
180-day U.S. dollar interest rate
180-day Japanese yen interest rate
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or expected change i
interest yielding currency. If the difference in interest rates is less than the forward premium (or expected change in the spot ra
Difference in interest rates ( i ¥ - i $)
Expected gain (loss) on the spot rate
UIA profit potential
This tells Akira Numata that he should borrow yen and invest in the higher yielding currency, the U.S. dollar, to potentially gain
$5,000,000 → →
↑
↑
↑
↑
↑
Spot (¥/$)
118.60
↑
↑
↑
593,000,000.00 → →
Japanese yen
START
a) Akira Numata generates an uncovered interest arbitrage (UIA) profit of ¥1,079,000 if his expectations about the future spot r
b) The risk Akira is taking is that the actual spot rate at the end of the period can theoretically be anything, better or worse for h
"wiggle room," as they say. A small movement will cost him a lot of money. If the spot rate ends up any stronger than about 117
(Verify by inputting ¥117.70/$ in the expected spot rate cell under assumptions.)
t rate has been holding steady, and both dollar and yen interest rates have remained relatively fixed over the past
trage (UIA) and thereby save the cost of forward cover. Many of Akira's research associates -- and their computer
0/$ for the coming 180 days. Using the same data as in the previous problem, analyze the UIA potential.
Value Yen Equivalent
$5,000,000 593,000,000
118.60
117.80
118.00
4.800%
3.400%
reater than the forward premium/discount, or expected change in the spot rate for UIA, invest in the higher
ess than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
-1.400%
1.017%
-0.383%
n the higher yielding currency, the U.S. dollar, to potentially gain on an uncovered basis (UIA).
U.S. dollar interest rate (180 days)
4.800%
1.0240 → → $5,120,000
↓
↓
↓
↓
Expected Spot Rate
---------------> 180 days ----------------> in 180 days (¥/$)
118.00
↓
↓
604,160,000
1.0170 → → 603,081,000
1,079,000
3.400%
Japanese yen interest rate (180 days) END
A) profit of ¥1,079,000 if his expectations about the future spot rate, the one in effect in 180 days, prove correct.
of the period can theoretically be anything, better or worse for his speculative position. He in fact has very little
ot of money. If the spot rate ends up any stronger than about 117.79/$ (a smaller number), he will lose money.
der assumptions.)
Problem 6.10 XTerra exports and pass through
Assume that the export price of a Nissan XTerra from Osaka, Japan is ¥3,250,000. The exchange rate is ¥115.20/$.
The forecast rate of inflation in the United States is 2.2% per year and is 0.0% per year in Japan. Use this data to
answer the following questions on exchange rate pass through.
Steps
Initial spot exchange rate (¥/$)
Initial price of a Nissan Xterra (¥)
Expected US dollar inflation rate for the coming year
Expected Japanese yen inflation rate for the coming year
Desired rate of pass through by Nissan
a. What was the export price for the XTerra at the beginning of the year?
Year-beginning price of an XTerra (¥)
Spot exchange rate (¥/$)
Year-beginning price of a XTerra ($)
b. What is the expected spot rate at the end of the year assuming PPP?
Initial spot rate (¥/$)
Expected US$ inflation
Expected Japanese yen inflation
Expected spot rate at end of year assuming PPP (¥/$)
c. Assuming complete pass through, what will the price be in US$ in one year?
Price of XTerra at beginning of year (¥)
Japanese yen inflation over the year
Price of XTerra at end of year (¥)
Expected spot rate one year from now assuming PPP (¥/$)
Price of XTerra at end of year in ($)
d. Assuming partial pass through, what will the price be in US$ in one year?
Price of XTerra at end of year (¥)
Amount of expected exchange rate change, in percent (from PPP)
Proportion of exchange rate change passed through by Nissan
Proportional percentage change
Effective exchange rate used by Nissan to price in US$ for end of year
Price of XTerra at end of year ($)
xchange rate is ¥115.20/$.
Japan. Use this data to
Value
115.20
3,250,000
2.200%
0.000%
75.000%
3,250,000
115.20
$ 28,211.81
115.20
2.20%
0.00%
112.72
3,250,000
0.000%
3,250,000
112.72
$ 28,832.47
3,250,000
2.200%
75.000%
1.650%
113.330
$ 28,677.30
Problem 7.6 Russian Ruble
The Russian ruble ( R) traded at R6.25/$ on August 7, 1998. By September 10, 1998, its value had fallen
to R20.00/$. What was the percentage change in its value?
Assumptions Rate Values
Spot rate, August 7, 1998 (Rub/$) S1 6.25
Spot rate, September 10, 1998 (Rub/$) S2 20.00
Calculation of percentage change:
Percentage change in the peso versus the dollar -68.75%
Percent change = ( S1 - S2 ) ÷ ( S2 )
Problem 8.1 Peregrine Funds -- Jakarta
Samuel Samosir trades currencies for Peregrine Funds in Jakarta. He focuses nearly all of his time and attention on the U.S. dollar/Singap
cross-rate. The current spot rate is $0.6000/S$. After considerable study, he has concluded that the Singapore dollar will appreciate versu
in the coming 90 days, probably to about $0.7000/S$. He has the following optons on the Singapore dollar to choose from:
Option choices on the Singapore dollar:
Strike price (US$/Singapore dollar)
Premium (US$/Singapore dollar)
Assumptions
Current spot rate (US$/Singapore dollar)
Days to maturity
Expected spot rate in 90 days (US$/Singapore dollar)
a) Should Samuel buy a put on Singapore dollars or a call on Singapore dollars?
Since Samuel expects the Singapore dollar to appreciate versus the US dollar, he should buy a call on Singapore dollars. This gives him t
Singapore dollars at a future date at $0.65 each, and then immediately resell them in the open market at $0.70 each for a profit. (If his exp
future spot rate proves correct.)
b) What is Samuel's breakeven price on the option purchased in part a)?
Note this does not include any interest cost on the premium.
c) What is Samuel's gross profit and net profit (including premium) if the ending spot rate is $0.70/S$?
Spot rate
Less strike price
Less premium
Profit
d) What is Samuel's gross profit and net profit (including premium) if the ending spot rate is $0.80/S$?
Spot rate
Less strike price
Less premium
Profit
on on the U.S. dollar/Singapore dollar ($/S$)
dollar will appreciate versus the U.S. dollar
choose from:
Call on S$ Put on S$
$0.6500 $0.6500
$0.00046 $0.00003
Values
$0.6000
90
$0.7000
ore dollars. This gives him the right to BUY
each for a profit. (If his expectation of the
Per S$
Strike price $0.65000
Plus premium $0.00046
Breakeven $0.65046
Gross profit Net profit
(US$/S$) (US$/S$)
$0.70000 $0.70000
($0.65000) ($0.65000)
($0.00046)
$0.05000 $0.04954
Gross profit Net profit
(US$/S$) (US$/S$)
$0.80000 $0.80000
($0.65000) ($0.65000)
($0.00046)
$0.15000 $0.14954
Problem 8.2 Paulo's Puts
Paulo writes a put option on Japanese yen with a strike price of $0.008000/¥ (¥125.00/$) at a premium of 0.0080¢ per yen and with an e
option is for ¥12,500,000. What is Paulo's profit or loss at maturity if the ending spot rates are ¥110/$, ¥115/$, ¥120/$, ¥125/$, ¥130/$, ¥
a) b) c) d)
Assumptions Values Values Values Values
Notional principal (¥) 12,500,000 12,500,000 12,500,000 12,500,000
Maturity (days) 180 180 180 180
Strike price (US$/¥) $0.008000 $0.008000 $0.008000 $0.008000
Premium (US$/¥) $0.000080 $0.000080 $0.000080 $0.000080
Ending spot rate (¥/US$) 110.00 115.00 120.00 125.00
in US$/¥ $0.009091 $0.008696 $0.008333 $0.008000
Gross profit on option $0.000000 $0.000000 $0.000000 $0.000000
Less premium ($0.000080) ($0.000080) ($0.000080) ($0.000080)
Net profit (US$/¥) ($0.000080) ($0.000080) ($0.000080) ($0.000080)
Net profit, total ($1,000.00) ($1,000.00) ($1,000.00) ($1,000.00)
080¢ per yen and with an expiration date six month from now. The
, ¥120/$, ¥125/$, ¥130/$, ¥135/$, and ¥140/$.
e) f) g)
Values Values Values
12,500,000 12,500,000 12,500,000
180 180 180
$0.008000 $0.008000 $0.008000
$0.000080 $0.000080 $0.000080
130.00 135.00 140.00
$0.007692 $0.007407 $0.007143
$0.000308 $0.000593 $0.000857
($0.000080) ($0.000080) ($0.000080)
$0.000228 $0.000513 $0.000777
$2,846.15 $6,407.41 $9,714.29
Problem 8.5 Madera Capital
Katya Berezovsky works is a currency speculator for madera Capital of Los Angeles. Her latest speculative
position is to profit from her expectation that the U.S. dollar will rise significantly against the Japanese yen.
The current spot rate is ¥120.00/$. She must choose between the following 90-day options on the Japanese yen:
Assumptions Values
Current spot rate (Japanese yen/US$) 120.00
in US$/yen $0.00833
Maturity of option (days) 90
Expected ending spot rate in 90 days (yen/$) 140.00
in US$/yen $0.00714
Call on yen Put on yen
Strike price (yen/US$) 125.00 125.00
in US$/yen $0.00800 $0.00800
Premium (US$/yen) $0.00046 $0.00003
a) Should she buy a call on yen or a put on yen?
Katya should buy a put on yen to profit from the rise of the dollar (the fall of the yen).
b) What is Katy'as break even price on her option of choice in part a)?
Katya buys a put on yen. Pays premium today.
In 90 days, exercises the put, receiving US$.
in yen/$
Strike price $0.00800 125.00
Less premium -$0.00003
Breakeven $0.00797 125.47
c) What is Katya's gross profit and net profit if the end spot rate is 140 yen/$?
Gross profit Net profit
(US$/yen) (US$/yen)
Strike price $0.00800 $0.00800
Less spot rate -$0.00714 -$0.00714
Less premium -$0.00003
Profit $0.00086 $0.00083
Problem 8.8 Call Profits
Assume a call option on euros is written with a strike price of $1.2500/€ at a premium of 3.80¢ per euro ($0.0380/€) and with an expirati
option is for €100,000. Calculate your profit or loss should you exercise before maturity at a time when the euro is traded spot at .....
Note: the option premium is 3.8 cents per euro, not 38 cents per euro.
a) b) c) d)
Assumptions Values Values Values Values
Notional principal (euros) € 100,000.00 € 100,000.00 € 100,000.00 € 100,000.00
Maturity (days) 90 90 90 90
Strike price (US$/euro) $1.2500 $1.2500 $1.2500 $1.2500
Premium (US$/euro) $0.0380 $0.0380 $0.0380 $0.0380
Ending spot rate (US$/euro) $1.1000 $1.1500 $1.2000 $1.2500
Gross profit on option $0.0000 $0.0000 $0.0000 $0.0000
Less premium ($0.0380) ($0.0380) ($0.0380) ($0.0380)
Net profit (US$/euro) ($0.0380) ($0.0380) ($0.0380) ($0.0380)
Net profit, total ($3,800.00) ($3,800.00) ($3,800.00) ($3,800.00)
380/€) and with an expiration date three months from now. The
ro is traded spot at .....
e) f) g)
Values Values Values
€ 100,000.00 € 100,000.00 € 100,000.00
90 90 90
$1.2500 $1.2500 $1.2500
$0.0380 $0.0380 $0.0380
$1.3000 $1.3500 $1.4000
$0.0500 $0.1000 $0.1500
($0.0380) ($0.0380) ($0.0380)
$0.0120 $0.0620 $0.1120
$1,200.00 $6,200.00 $11,200.00
Problem 8.10 Downing Street
Sydney Reeks is a currency trader for Downing Street, a private investment house in London. Downing Street’s clients are a collection of
wealthy private investors who, with a minimum stake of £250,000 each, wish to speculate on the movement of currencies. The investors
expect annual returns in excess of 25%. Although officed in London, all accounts and expectations are based in U.S. dollars.
Sydney is convinced that the British pound will slide significantly -- possibly to $1.3200/£ -- in the coming 30 to 60 days. The current
spot rate is $1.4260/£. Andy wishes to buy a put on pounds which will yield the 25% return expected by his investors. Which of the
following put options would you recommend he purchase. Prove your choice is the preferable combination of strike price, maturity, and
up-front premium expense.
Assumptions Values
Current spot rate (US$/£) $1.4260
Expected endings spot rate in 30 to 60 days (US$/£) $1.3200
Potential investment principal per person (£) £250,000.00
Put options on pounds Put #1 Put #2
Strike price (US$/£) $1.36 $1.34
Maturity (days) 30 30
Premium (US$/£) $0.00081 $0.00021
Put options on pounds Put #4 Put #5
Strike price (US$/£) $1.36 $1.34
Maturity (days) 60 60
Premium (US$/£) $0.00333 $0.00150
Issues for Sydney to consider:
1. Because his expectation is for "30 to 60 days" he should confine his choices to the 60 day options to be sure and capture
the timing of the exchange rate change. (We have no explicit idea of why he believes this specific timing.)
2. The choice of which strike price is an interesting debate.
* The lower the strike price (1.34 or 1.32), the cheaper the option price.
* The reason they are cheaper is that, statistically speaking, they are increasingly less likely to end up in the money.
* The choice, given that all the options are relatively "cheap," is to pick the strike price which will yield the required return.
* The $1.32 strike price is too far 'down,' given that Sydney only expects the pound to fall to about $1.32.
Put #4 Put #5
Net profit Net profit
Strike price $1.36000 $1.34000
Less expected spot rate (1.32000) (1.32000)
Less premium (0.00333) (0.00150)
Profit $0.03667 $0.01850
If Sydney invested an individual's principal purely
in this specific option, they would purchase an
option of the following notional principal ( £): £75,075,075.08 £166,666,666.67
Expected profit, in total (profit rate x notional): $2,753,003.00 $3,083,333.33
Initial investment at current spot rate $356,500.00 $356,500.00
Return on Investment (ROI) 772% 865%
Risk: They could lose it all (full premium)
Street’s clients are a collection of
ment of currencies. The investors
based in U.S. dollars.
coming 30 to 60 days. The current
y his investors. Which of the
tion of strike price, maturity, and
Put #3
$1.32
30
$0.00004
Put #6
$1.32
60
$0.00060
o be sure and capture
nd up in the money.
ill yield the required return.
Put #6
Net profit
$1.32000
(1.32000)
(0.00060)
($0.00060)
£416,666,666.67
-$250,000.00
$356,500.00
-70%
Problem 10.1 Kona Macadamia Nuts
Kona Macadamia Nuts, based in Hilo, Hawaii, exports Macadamia nuts worldwide. The Japanese market is its biggest
export market, with average annual sales invoiced in yen to Japanese customers of ¥1,200,000,000. At the present exchange
rate of ¥125/$ this is equivalent to $9,600,000. Sales are relatively equally distributed during the year. They show up as a
¥250,00,000 account receivable on Kona’ balance sheet. Credit terms to each customer allow for 60 days before payment is
due. Monthly cash collections are typically ¥100,000,000. Kona Macadamia Nuts would like to hedge its yen receipts, but it
has too many customers and transactions to make it practical to sell each receivable forward. It does not want to use options
because they are considered to be too expensive for this particular purpose. Therefore, they have decided to use a
“matching” hedge by borrowing yen.
a. How much should Kona borrow in yen?
Kona receives cash collections of one hundred million yen per month. This is the source of repayment of any
balance sheet hedge. If Kona wants to be covered for one year at a time, it would need to borrow one year's
cash flow plus interest, and convert the borrowed yen to US dollar at once. A sample calculation would be:
Sample Values
One month's cash flow 100,000,000
Months per year 12
One year's cash flow 1,200,000,000
Plus interest 4.000%
Principal and interest 1,248,000,000
Spot exchange rate 125.00
US dollars $9,984,000
Realistically, Kona would probably want to be covered for the long term. In that case, the 1.2 billion yen loan
could be structured so that it could be renewed annually with interest reset annually. This would only cover the
foreign exchange and interest rate risk for a year at a time, but would probably be acceptable to a bank lender.
Also unknown are the expected sales for year 2 and beyond.
b. What should be the terms of payment on the loan?
The loan should be repaid out of the monthly cash flow, with payments on principal only. The interest payment one
year hence has already been covered by borrowing both principal and interest up-front.
Note: Kona should not borrow 250 million yen to cover only its balance sheet exposure. Such a loan would cover
only the accounting exposure, and not the cash flow exposure (operating exposure).
anese market is its biggest
00,000. At the present exchange
g the year. They show up as a
w for 60 days before payment is
e to hedge its yen receipts, but it
It does not want to use options
have decided to use a
ource of repayment of any
need to borrow one year's
ple calculation would be:
Units
Yen
Yen
per annum
Yen
Yen/US$
US$
ase, the 1.2 billion yen loan
ally. This would only cover the
acceptable to a bank lender.
al only. The interest payment one
osure. Such a loan would cover
Problem 10.4 Pucini's Risk-Sharing
Pucini Leather, based in New York City, imports leather coats from Boselli Leather Goods, a reliable and longtime
supplier, based in Buenos Aires, Argentina. Payment is in Argentine pesos. When the peso lost its parity with the
U.S. dollar in January 2002 it collapsed in value to Ps 4.0/$ by October 2002. The outlook was for a further decline
in the peso’s value. Since both Pucini and Boselli wanted to continue their longtime relationship they agreed on a
risk-sharing arrangement. As long as the spot rate on the date of an invoice is between Ps3.5/$ and Ps4.5/$ Pucini
will pay based on the spot rate. If the exchange rate falls outside this range they will share the difference equally with
Boselli Leather Goods. The risk-sharing agreement will last for six months, at which time the exchange rate limits
will be reevaluated. Pucini Fashionwear contracts to import leather coats from Boselli for Ps8,000,000 or $2,000,000
at the current spot rate of Ps4.0/$ during the next six months.
a. If the exchange rate changes immediately to Ps6.00/$, what will be the dollar cost of 6 months of imports to
Pucini?
Bottom Top
The allowable range of exchange rates is (Ps/$) 3.50 4.50
Outside of this range the trading partners will share the extra risk equally.
New exchange rate (Ps/$) 6.00
Allowable exchange rate (Ps/$) 4.50
Difference to be shared (Ps/$) 1.50
Pucinii's share 0.75
Boselli's share 0.75
Therefore, Pucini will use the following effective exchange rate after risk-sharing:
Top of range 4.50
Pucini's share 0.75
Effective total of risk-sharing 5.25
Assuming that 6 months of imports will still be (Ps) 8,000,000
Effective exchange rate for Pucini (Ps/$) 5.25
Pucini's cost in US dollars $1,523,809.52
However, the lower cost of importing might lead to higher Pucini sales and therefore a higher import
total than Ps 8 million.
b. At Ps6.00/$, what will be the peso export sales in Boselli to Pucini?
The export sales of Boselli would remain at Ps 8 million, unless the lower dollar cost encourages Pucini
to import more from Boselli.
Problem 10.6 Trident Europe: Case 4
Trident Europe (Exhibit 10.3) decides not to change its domestic price of €12.80 per unit within Europe, but to raise its export price (in e
from €12.80 per unit to €15.36 per unit, thus preserving its original dollar equivalent price of $15.36 per unit. Volume in both markets r
the same because no buyer perceives that the price has changed.
Balance Sheet Information, End of Fiscal 2005
Assets Liabilities and net worth
Cash € 1,600,000 Accounts payable € 800,000
Accounts receivable 3,200,000 Short-term bank loan 1,600,000
Inventory 2,400,000 Long-term debt 1,600,000
Net plant and equipment 4,800,000 Common stock 1,800,000
Retained earnings 6,200,000
Sum € 12,000,000 Sum € 12,000,000
Important Ratios to be Maintained and Other Data
Accounts receivable, as percent of sales 25.00%
Inventory, as percent of annual direct costs 25.00%
Cost of capital (annual discount rate) 20.00%
Income tax rate 34.00%
Base Case Case 1 Case 2
Assumptions
Exchange rate, $/€ 1.2000 1.0000 1.0000
Sales volume (units) 1,000,000 1,000,000 2,000,000
Export sales volume (case 4)
Sales price per unit € 12.80 € 12.80 € 12.80
Export sales price per unit (case 4)
Direct cost per unit € 9.60 € 9.60 € 9.60
Annual Cash Flows before Adjustments
Sales revenue € 12,800,000 € 12,800,000 € 25,600,000
Direct cost of goods sold 9,600,000 9,600,000 19,200,000
Cash operating expenses (fixed) 890,000 890,000 890,000
Depreciation 600,000 600,000 600,000
Pretax profit € 1,710,000 € 1,710,000 € 4,910,000
Income tax expense 581,400 581,400 1,669,400
Profit after tax € 1,128,600 € 1,128,600 € 3,240,600
Add back depreciation 600,000 600,000 600,000
Cash flow from operations, in euros € 1,728,600 € 1,728,600 € 3,840,600
Cash flow from operations, in dollars $ 2,074,320 $ 1,728,600 $ 3,840,600
Adjustments to Working Capital for 2006 - 2010 Caused by Changes in Conditions
Accounts receivable € 3,200,000 € 3,200,000 € 6,400,000
Inventory 2,400,000 2,400,000 4,800,000
Sum € 5,600,000 € 5,600,000 € 11,200,000
Change from base conditions in 2006 € - € - € 5,600,000
Year Year-End Cash Flows
1 (2006) $ 2,074,320 $ 1,728,600 $ (1,759,400)
2 (2007) $ 2,074,320 $ 1,728,600 $ 3,840,600
3 (2008) $ 2,074,320 $ 1,728,600 $ 3,840,600
4 (2009) $ 2,074,320 $ 1,728,600 $ 3,840,600
5 (2010) $ 2,074,320 $ 1,728,600 $ 9,440,600
Year Change in Year-End Cash Flows from Base Conditions
1 (2006) na $ (345,720) $ (3,833,720)
2 (2007) na $ (345,720) $ 1,766,280
3 (2008) na $ (345,720) $ 1,766,280
4 (2009) na $ (345,720) $ 1,766,280
5 (2010) na $ (345,720) $ 7,366,280
Present Value of Incremental Year-End Cash Flows
na $ (1,033,914) $ 2,866,106
hin Europe, but to raise its export price (in euros)
$15.36 per unit. Volume in both markets remains
Case 3 Case 4
1.0000 1.0000
1,000,000 500,000
500,000
€ 15.36 € 12.80
€ 15.36
€ 9.60 € 9.60
€ 15,360,000 € 14,080,000
9,600,000 9,600,000
890,000 890,000
600,000 600,000
€ 4,270,000 € 2,990,000
1,451,800 1,016,600
€ 2,818,200 € 1,973,400
600,000 600,000
€ 3,418,200 € 2,573,400
$ 3,418,200 $ 2,573,400
Changes in Conditions
€ 3,840,000 € 3,520,000
2,400,000 2,400,000
€ 6,240,000 € 5,920,000
€ 640,000 € 320,000
nd Cash Flows
$ 2,778,200 $ 2,253,400
$ 3,418,200 $ 2,573,400
$ 3,418,200 $ 2,573,400
$ 3,418,200 $ 2,573,400
$ 4,058,200 $ 2,893,400
sh Flows from Base Conditions
$ 703,880 $ 179,080
$ 1,343,880 $ 499,080
$ 1,343,880 $ 499,080
$ 1,343,880 $ 499,080
$ 1,983,880 $ 819,080
mental Year-End Cash Flows
$ 3,742,892 $ 1,354,489
Problem 15.2 Botany Bay Corporation
Botany Bay Corporation of Australia seeks to borrow US$30,000,000 in the Eurodollar market. Funding is needed for two years.
Investigation leads to three possibilities. Compare the alternatives and make a recommendation.
#1. Botany Bay could borrow the US$30,000,000 for two years at a fixed 5% rate of interest
#2. Botany Bay could borrow the US$30,000,000 at LIBOR + 1.5%. LIBOR is currently 3.5%, and the rate would be reset every six
months
#3. Botany Bay could borrow the US$30,000,000 for one year only at 4.5%. At the end of the first year Adelaide Corporation would
have to negotiate for a new one-year loan.
Assumptions Values
Principal borrowing need $ 30,000,000
Maturity needed, in years 2.00
Fixed rate, 2 years 5.000%
Floating rate, six-month LIBOR + spread
Current six-month LIBOR 3.500%
Spread 1.500%
Fixed rate, 1 year, then re-fund 4.500%
First 6-months Second 6-months Third 6-months
#1: Fixed rate, 2 years
Interest cost per year $ 1,500,000
Certainty over access to capital Certain Certain Certain
Certainty over cost of capital Certain Certain Certain
#2: Floating rate, six-month LIBOR + spread
Interest cost per year $ 750,000 $ 750,000 $ 750,000
Certainty over access to capital Certain Certain Certain
Certainty over cost of capital Certain Uncertain Uncertain
#3: Fixed rate, 1 year, then re-fund
Interest cost per year $ 1,350,000 ???
Certainty over access to capital Certain Certain Uncertain
Certainty over cost of capital Certain Certain Uncertain
Only alternative #1 has a certain access and cost of capital for the full 2 year period.
Alternative #2 has certain access to capital for both years, but the interest costs in the final 3 of 4 periods is uncertain.
Alternatvie #3, possessing a lower interest cost in year 1, has no guaranteed access to capital in the second year.
Depending on the company's business needs and tolerance for interest rate risk, it could choose between #1 and #2.
is needed for two years.
rate would be reset every six
Adelaide Corporation would
Fourth 6-months
$ 1,500,000
Certain
Certain
$ 750,000
Certain
Uncertain
???
Uncertain
Uncertain
of 4 periods is uncertain.
in the second year.
ose between #1 and #2.
Problem 15.6 Cañon Chemicals
Amanda Suvari, the treasurer of Cañon Chemicals believes interest rates are going to rise, so she wants to swap her future floating
rate interest payments for fixed rates. At present she is paying LIBOR + 2% per annum on $5,000,000 of debt for the next two
years, with payments due semiannually. LIBOR is currently 4.00% per annum. Ms. Suvari has just made an interest payment
today, so the next payment is due six months from today.
Ms. Suvari finds that she can swap her current floating rate payments for fixed payments of 7.00% per annum.
(Cañon’s weighted average cost of capital is 12%, which Ms. Suvari calculates to be 6% per six month period,
compounded semiannually).
a. If LIBOR rises at the rate of 50 basis points per six month period, starting tomorrow, how much does Ms. Suvari
save or cost her company by making this swap?
b. If LIBOR falls at the rate of 25 basis points per six month period, starting tomorrow, how much does Ms. Suvari
save or cost her company by making this swap?
Assumptions Values
Notional principal $ 5,000,000
LIBOR, per annum 4.000%
Spread paid over LIBOR, per annum 2.000%
Swap rate, to pay fixed, per annum 7.000%
First Second Third
Interest & Swap Payments 6-months 6-months 6-months
a. LIBOR increases 50 basis pts/6 months 0.500%
Expected LIBOR 4.500% 5.000% 5.500%
Current loan agreement:
Expected LIBOR (for 6 months) -2.250% -2.500% -2.750%
Spread (for 6 months) -1.000% -1.000% -1.000%
Expected interest payment -3.250% -3.500% -3.750%
Swap Agreement:
Pay fixed (for 6-months) -3.500% -3.500% -3.500%
Receive floating (LIBOR for 6 months) 2.250% 2.500% 2.750%
Net interest (loan + swap) -4.500% -4.500% -4.500%
Swap savings?
Net interest after swap $ (225,000) $ (225,000) $ (225,000)
Loan agreement interest (162,500) (175,000) (187,500)
Swap savings (swap cost) $ (62,500) $ (50,000) $ (37,500)
b. LIBOR decreases 25 basis pts/6 months -0.250%
Expected LIBOR 3.750% 3.500% 3.250%
Current loan agreement:
Expected LIBOR (for 6 months) -1.875% -1.750% -1.625%
Spread (for 6 months) -1.000% -1.000% -1.000%
Expected interest payment -2.875% -2.750% -2.625%
Swap Agreement:
Pay fixed (for 6-months) -3.500% -3.500% -3.500%
Receive floating (LIBOR for 6 months) 1.875% 1.750% 1.625%
Net interest (loan + swap) -4.500% -4.500% -4.500%
Swap savings?
Net interest after swap $ (225,000) $ (225,000) $ (225,000)
Loan agreement interest (143,750) (137,500) (131,250)
Swap savings (swap cost) $ (81,250) $ (87,500) $ (93,750)
In both cases Canon is suffering higher total interest costs as a result of the swap.
nts to swap her future floating
00 of debt for the next two
made an interest payment
nts of 7.00% per annum.
er six month period,
ow much does Ms. Suvari
ow much does Ms. Suvari
Fourth
6-months
6.000%
-3.000%
-1.000%
-4.000%
-3.500%
3.000%
-4.500%
$ (225,000)
(200,000)
$ (25,000)
3.000%
-1.500%
-1.000%
-2.500%
-3.500%
1.500%
-4.500%
$ (225,000)
(125,000)
$ (100,000)
Problem 15.7 Xavier and Zulu
Xavier Manufacturing and Zulu Products both seek funding at the lowest possible cost. Xavier would
prefer the flexibility of floating rate borrowing, while Zulu wants the security of fixed rate borrowing.
Xavier is the more credit-worthy company. They face the following rate structure. Xavier, with the better
credit rating, has lower borrowing costs in both types of borrowing.
Xavier wants floating rate debt, so it could borrow at LIBOR+1%. However it could borrow
fixed at 8% and swap for floating rate debt. Zulu wants fixed rate, so it could borrow fixed at
12%. However it could borrow floating at LIBOR+2% and swap for fixed rate debt. What should
Assumptions Xavier Zulu
Credit rating AAA BBB
Prefers to borrow Floating Fixed
Fixed-rate cost of borrowing 8.000% 12.000%
Floating-rate cost of borrowing:
LIBOR (value is unimportant) 5.000% 5.000%
Spread 1.000% 2.000%
Total floating-rate 6.000% 7.000%
Comparative Advantage in Borrowing Values
Xavier's absolute advantage:
in fixed rate borrowering 4.000%
in floating-rate borrowing 1.000%
Comparative advantage in fixed rate 3.000%
One Possibility Xavier Zulu
Xavier borrows fixed -8.000% ---
Zulu borrows floating --- -7.000%
Xavier pays Zulu floating (LIBOR) -5.000% 5.000%
Zulu pays Xavier fixed 8.500% -8.500%
Net interest after swap -4.500% -10.500%
Savings (own borrowing versus net swap):
If Xavier borrowed floating 6.000%
If Xavier borrows fixed & swaps with Zulu 4.500%
1.500%
If Zulu borrowes fixed 12.000%
If Zulu borrows floating & swaps with Xavier 10.500%
1.500%
The 3.0% comparative advantage enjoyed by Xavier represents the opportunity set for
improvement for both parties. This could be a 1.5% savings for each (as in the example shown)
or any other combination which distributes the 3.0% between the two parties.
The 3.0% comparative advantage enjoyed by Xavier represents the opportunity set for
improvement for both parties. This could be a 1.5% savings for each (as in the example shown)
or any other combination which distributes the 3.0% between the two parties.
Problem 15.8 Trident's Cross Currency Swap: Sfr for US$
Trident Corporation entered into a three-year cross currency interest rate swap in the chapter to receive U.S. dollars and pay Swiss francs
however, decided to unwind the swap after one year – thereby having two years left on the settlement costs of unwinding the swap after o
Repeat the calculations for unwinding, but assume that the following rates now apply:
Assumptions Values Swap Rates 3- year bid
Notional principal $ 10,000,000 US dollar 5.56%
Spot exchange rate, SFr./$ 1.5000 Swiss franc -- SFr. 1.93%
Spot exchange rate, $/euro 1.1200
a) Interest & Swap Payments Year 0 Year 1 Year 2
Receive fixed rate dollars at this rate: 5.56% 5.56%
On a notional principal of: $ 10,000,000
Trident will receive cash flows: → $ 556,000 → $ 556,000
↑
Exchange rate, time of swap (SFr./$) 1.5000
↓
Trident will pay cash flows: → SFr. 301,500 → SFr. 301,500
On a notional principal of: SFr. 15,000,000
Pay fixed rate Swiss francs at this rate: 2.01% 2.01%
b) Unwinding the swap after one-year Year 1 Year 2
Remaining dollar cash inflows $ 556,000
PV factor at now current fixed $ interest 5.20% 0.9506
PV of remaining dollar cash inflows $ 528,517
Cumulative PV of dollar cash infllows $ 10,066,750
Remaining Swiss franc cash outflows SFr. 301,500
PV factor at now current fixed SF interest 2.20% 0.9785
PV of remaining SF cash outflows SFr. 295,010
Cumulative PV of SF cash outflows SFr. 14,944,827
New current spot rate, SFr./$ 1.5560
Cumulative PF of SF cash outflows in $ $ 9,604,645
Settlement:
Cash inflow $ 10,066,750
Cash outflow (9,604,645)
Net cash settlement of unwinding $ 462,105 This is a cash receipt by Trident from the swap dealer.
dollars and pay Swiss francs. Trident,
f unwinding the swap after one year.
3-year ask
5.59%
2.01%
Year 3
5.56%
→ $ 10,556,000
→ SFr. 15,301,500
2.01%
Year 3
$ 10,556,000
0.9036
$ 9,538,232
SFr. 15,301,500
0.9574
SFr. 14,649,818
nt from the swap dealer.
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