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End-of-Chapter Question Solutions
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CHAPTER 6: TRANSACTION EXPOSURE
6-1.
Tektronix, Inc.: Account Receivable (page 179 in text)
a)
What are the costs of each alternative of hedging a i2,000,000 account receivable due in six months?
Remain uncovered. The receivable would be settled at whatever the spot exchange rate is at the end of the 180
day period. If, for example, the ending spot rate was the same as the spot rate now, the expected value of the A/R
in U.S. dollars would be:
i2,000,000 x $1.0538/ i ' $ 2,107,600.
This is highly uncertain, however.
Forward hedge. Jerry Davies might sell the i2,000,000 forward 180-days at the current forward rate of $1.0687/i,
resulting in a certain U.S. dollar cash settlement of:
i2,000,000 x $1.0687/ i ' $ 2,137,400.
Money market hedge. A money market hedge would require Tektronix to put the A/R up as collateral against a
euro-denominated loan. The receivable’s settlement at the end of 180 days would in turn settle the principal and
interest due on the loan, while allowing Tek to receive the loan principal up front in cash.
First we calculate what the loan principal would be given that Tek would have to pay 3.125% per annum interest.
i2,000,000
180
1 % .03125 x
360
' i 1,969,230.77.
This principal, received by Tek up front from using the A/R as collateral, would be exchanged for U.S. dollars at
the current spot rate of $1.0538/i, resulting in dollar proceeds of:
i1,969,230.77 x $1.0538/ i ' $ 2,075,175.38.
This dollar proceed would have to be now carried forward 180 days for comparison purposes with the uncovered
and forward hedge alternatives (all hedge values need to be compared in the same currency at the same point in
time). The time value of money for Tektronix could be either of two alternatives: 1) the 6-month U.S. dollar interest
rate of 6.00% per annum, or 2) the Tektronix weighted average cost of capital of 12.00%.
Using the 6.00% rate to carry the money market hedge proceeds forward 180 days results in:
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$ 2,075,175.38 x 1% .0600 x
180
360
' $2,137,430.65 .
If the Tektronix cost of capital of 12% is used to carry the cash proceeds 180 days forward, the value is
substantially greater:
$ 2,075,175.38 x 1% .1200 x
180
360
' $2,199,685.90 .
Option hedge. Given that Tektronix has a long position in euros it would need the right to sell the euros received
in 180 days – a put option. Tek currently has two different strike prices it can consider, $1.00/i (premium of
$0.007/i) and $1.12/i (premium of $0.061/i).
Strike price of $1.00/i. The premium cost of purchasing this put option is $0.007/i, totaling:
i2,000,000 x $0.007/i ' $ 14,000.
This premium would have to be carried forward 180 days at Tek’s cost of capital of 12% for relevant financial
analysis. If the spot rate at the end of 180 days was less than $1.00/i, Tektronix would exercise its option to
exchange all i2,000,000 at the strike rate of $1.00/i, for net proceeds of:
( i2,000,000 x $1.00/i) & $ 14,000 x 1% .12 x
180
360
' $ 1,985,160.00.
This $1,985,160 represents the minimum proceeds under the put option hedge. If the spot exchange rate at the end
of 180 days was above $1.00/i, the option would be allowed to expire out-of-the-money and the euros would be
exchanged for U.S. dollars on the open market.
Strike price of $1.12/i. The premium cost of purchasing this put option is $0.061/i, totaling:
i2,000,000 x $0.061/i ' $ 122,000.
This premium would have to be carried forward 180 days at Tek’s cost of capital of 12% for relevant financial
analysis. If the spot rate at the end of 180 days was less than $1.12/i, Tektronix would exercise its option to
exchange all i2,000,000 at the strike rate of $1.12/i, for net proceeds of:
( i2,000,000 x $1.12/i) & $ 122,000 x 1% .12 x
180
360
' $ 2,110,680.00.
End-of-Chapter Question Solutions
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This $2,110,680 represents the minimum proceeds under the put option hedge. If the spot exchange rate at the end
of 180 days was above $1.12/i, the option would be allowed to expire out-of-the-money and the euros would be
exchanged for U.S. dollars on the open market.
b)
Diagram of alternatives. The money market hedge diagramed here is that carried forward at Tek’s WACC. Only
the $1.00/i strike price put option is shown for simplicity of presentation.
US$ Value
of A/R
GRAPHIC NOT AVAILABLE IN PDF FILE FORM
Uncovered A/R in i
Put Option Hedge
($1.00/i strike)
$2,199,685.90
Money Market Hedge
(@ WACC)
$2,137,400.00
Forward Hedge
$1,985,160.00
$/i
0
1.000
1.0687
1.0998
1.1073
The calculation of the breakeven point exchange rates is detailed in section g) below.
c)
Summary of hedging alternatives, including the expected dollar amount and degree of certainty.
Hedge
Remain uncovered
Forward contract
Money market hedge (@ 6%)
Money market hedge (@ 12%)
Put option hedge ($1.00/i strike)
Put option hedge ($1.12/i strike)
U.S. dollar amount
?
$2,137,400.00
$2,137,430.65
$2,199,685.90
$1,985,160.00
$2,110,680.00
Certainty?
Uncertain
Certain
Certain
Certain
Minimum
Minimum
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d)
If Jerry Davies wishes to “play it safe” he should choose the money market hedge according to the calculations
above, because it yields the highest U.S. dollar value and is certain.
e)
If Jerry Davies is willing to take a reasonable risk, and has a directional view that the euro may be appreciating
versus the U.S. dollar, Jerry should consider the put option hedges. It would give him the opportunity to benefit
from his directional view, and still provide relatively adequate protection against unpredicted movements of the
exchange rate on the downside. The choice between the two strike prices depends on what Tek considers the
minimum acceptable dollar receivable.
f)
If Jerry Davies is willing to take a reasonable risk, and has a directional view that the euro may be depreciating
versus the U.S. dollar, he should lock in his dollar proceeds immediately with the money market hedge or forward
contract to avoid any loss in the receivable’s dollar value.
g)
The breakeven points are fairly obvious when looking at the diagram in part c) above.
1. Forward versus money market hedge (@ WACC) breakeven:
$2,075,175.38 x (1+x) = $2,137,400.00
Solving for x:
(1 %x) '
$ 2,137,400.00
' 1.03 for 6 months, or 6% per annum.
$2,075,175.38
If Tek can reinvest its cash proceeds from the money market loan at a rate greater than 6.0% per annum, then
Jerry Davies should choose the money market alternative.
2. Put option at $1.00/i strike price versus the money market hedge carried forward at the WACC.
Money market proceeds @ WACC
Less put option minimum proceeds
Difference in proceeds
$2,199,685.90
- 1,985,160.00
$ 214,525.90
Difference in proceeds per euro:
$ 214,525.90
' $0.1073/ i.
i 2,000,000
In order for the put option proceeds to breakeven with the money market proceeds the spot exchange at the
end of the period needs to increase from the put option strike price of $1.00/i by the difference in proceeds
of $0.1073/i to:
$1.000 / i % $0.1073 / i ' $1.1073/ i.
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3.
Money market versus uncovered. The money market proceeds carried forward at the WACC total
$2,199,685.90. On a per euro basis, this is:
$2,199,685.90
' $1.0998 / i.
i 2,000,000
If Tek remains uncovered, its proceeds will breakeven with the money market hedge at $1.0998/i.
6-2.
Tektronix, Inc.: Account Payable (page 180 in text)
a)
Do nothing. The account payable is then settled at whatever the spot exchange rate turns out to be at the end of
period. For example, if the spot exchange rate at the end of the period is the same as the forward rate ($0.009186/¥),
the account payable would cost Tektronix:
¥ 80,000,000 x $0.009186/ ¥ ' $734,880 .
If the ending spot rate was equal to the current spot rate of $0.008930/¥, the account payable would amount to:
¥ 80,000,000 x $0.008930/ ¥ ' $714,400 .
In either case, the final cost in U.S. dollar terms of the A/P is uncertain at the beginning of the period and
potentially unlimited in size.
Buy Japanese yen forward. The account payable could be hedged by buying the required amount of Japanese
yen forward at the forward rate of $0.009186/¥.
¥ 80,000,000 x $0.009186/ ¥ ' $734,880.00.
This dollar cost, $734,880, is certain and known to Tektronix at the beginning of the transaction exposure period.
Money market hedge. Since this is an account payable, a money market hedge would require Tektronix to invest
a specific amount of money at the beginning of the period which is then invested in a Japanese yen-denominated
interest-bearing account for the 180-day period. We first determine the amount of investment needed up front by
discounting the A/P by the interest bearing rate of interest which Tektronix will receive on the investment for the
180-day period:
¥ 80,000,000
180
1 % .0025 x
360
'
¥ 80,000,000
' ¥ 79,900,124.84 .
1.00125
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(Note: A common student mistake at this point is to interpret the Japanese yen interest rate as 2.50% rather than
0.250%.)
These Japanese yen, when exchanged into U.S. dollars at the current spot rate of $.008930/¥ indicates an initial
investment by Tektronix in the money market hedge of :
¥ 79,900,124.84 x $0.008930/ ¥ ' $713,508.11 .
For comparison purposes, this dollar amount needs to be carried forward 180-days to compare with the uncovered
and forward cover alternatives. The rate used to carry the dollar value forward can be either the 6-month U.S.
dollar interest rate of 6.000% per annum, or 2) the Tektronix weighted average cost of capital of 12.00% per annum.
If carried forward 180 days at the 6.000% dollar interest rate:
$713,508.11 x 1%
.0600 x
180
360
' $734,913.36.
If carried forward 180 days at the 12.00% Tektronix cost of capital rate:
$713,508.11 x 1%
.1200 x
180
360
' $756,318.60.
Option hedge. Because Tektronix has a short position – the need to acquire Japanese yen at a future date – to
hedge the position Jerry Davies needs to buy a call option on Japanese yen. A six-month call option on yen with
a strike price of 0.9090 (U.S. cents/¥ ) costs $0.00037/¥ up front.
¥ 80,000,000 x $0.00037/ ¥ ' $29,600.00 .
This premium is paid regardless of whether the call option is ever exercised. If the spot exchange rate at the end
of the period rises above 0.9090, Jerry Davies would exercise his option to buy ¥80,000,000 at the strike price of
$0.009090/¥. The premium, because it is paid up-front, must be carried forward 180 days at Tek’s cost of capital
of 12%:
$29,600.00 x 1 %
.12 x
180
360
' $31,376.00 .
The net proceeds of the option premium, if exercised (which is the worst case scenario), would be the following:
Cost of exercising the option: ¥80,000,000 x $0.009090/¥
$727,200.00
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Plus cost of call option (premium expense)
Total cost of call option (maximum)
b)
31,376.00
$758,576.00
Hedging Summary
Uncovered
Forward cover
Money market hedge (@ 6%)
Money market hedge (@ 12%)
Call option hedge (.9090 strike)
U.S. dollar amount
?
$734,880.00
$734,913.36
$756,318.60
$758,576.00
Certainty?
Uncertain
Certain
Certain
Certain
Maximum
c)
If Jerry Davies wishes to “play it safe,” he should probably choose the forward hedge as it locks in the lowest
cost of meeting the account payable. Although there is always the possibility that the call option hedge could
be substantially lower than the forward contract, it is uncertain (and therefore not “safe”).
d)
If Jerry Davies is willing to take a reasonable risk (however one might define “reasonable”), and he has a
directional view that the Japanese yen will weaken against the U.S. dollar, he should consider purchasing the call
option on Japanese yen to cover the position but give himself substantial possibility of the ending spot rate being
in his favor and acquiring the Japanese yen on the open market at a greatly reduced rate than that currently
available.
6-3.
Taj Bakeries, Ltd. (A) (page 180 in text)
a)
The equation (page 114 in the text) for the percentage amount of devaluation when the quotation is in terms of
local currency (Indian rupees) per base currency (U.S. dollars) is:
Percentage change '
beginning rate & ending rate
36.96 & 42.00
x 100 '
x 100 ' & 12.0% .
ending rate
42.00
The minus sign indicates a devaluation. (A plus sign would indicate a revaluation.)
b)
Pre-devaluation value of the sale
Post devaluation value of receivable:
Loss experienced by MJ Foods:
The loss can also be calculated as:
$2,400,000 x Rp.36.96/$ = Rp.88,704,000.
Rps. 88,704,000 ÷ Rp.42.00/$ = $2,112,000.
$2,400,000 - $2,112,000 = $288,000.
$2,400,000 x 12.0% = $288,000.
The loss would be realized on the day payment was received, in this instance on December 24th. The exact amount
of loss would depend on the spot exchange rate on that day.
c)
The loss is a transaction loss because it was caused by the drop in value of an outstanding receivable that was
booked before the rupee devalued but settled after the devaluation.
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6-4.
Taj Bakeries, Ltd (B) (page 181 in text)
a)
MJ Foods’ actual exposure dates from August 18th, the date on which MJ Foods made a firm quote in Indian
rupees.
b)
This is a quotation exposure, and was in the amount of Rps.88,704,000, as that was the amount of the receivable.
(“Exposure” is not the same as an eventual loss; it is the base for measuring loss.)
c)
MJ Foods could have avoided this quotation exposure by (1) denominating the quote in dollars instead of rupees
– and risking not receiving the order, or (2) making its rupee quote contingent on the value of the rupee on the
day of order not being less than some specified exchange rate. For example, the quote might have been valid only
so long as the rupee did not fall below, say, Rps.40.00/$. Quotation exposure is a type of transaction exposure that
has not yet been formalized on the company’s books, and that could presumably be avoided by backing away
from the quote given. However to “welsh” on a quote would probably damage the reputation of MJ Foods and
might lead to a lawsuit by Taj Bakeries to recover damages.
d)
On August 22nd, the exposure changed from quotation exposure to “backlog exposure.” Backlog exposure is
another type of transaction exposure that has not yet been formalized. However the consequences of backing
away from the transaction after this date by MJ Foods would certainly hurt MJ Foods’ reputation and would be
more likely to lead to a lawsuit over damages that were suffered.
e)
On September 24th, the exposure changed from backlog exposure to pure transaction exposure.
f)
During October and November the exposure as such did not change. However the measured paper loss (e.g.,
unrealized loss) due to the devaluation steadily increased. This paper loss, however, could have diminished,
disappeared or even turned into a profit if the rupee reversed direction and strengthened.
g)
On December 24th the exposure ceased because MJ Food’s receivable was collected. At this time the exact amount
of loss was firmly established and realized.
6-5.
Chalmers Incorporated (page 181 in text)
This problem demonstrates the “points forward” decision-making rules often used in currency risk management
by multinational firms.
a)
Receivables: A 4-month (120 day) account receivable means that Chalmers will be receiving foreign currency
inflows in the future. It will therefore need to sell new Mexican pesos forward. If the spot rate is Ps.10.2400/$ and
the 120-day forward rates is Ps.11.0400/$, the peso is selling forward at a discount relative to the dollar. Chalmers
will therefore receive fewer dollars from forward contracts than it would receive if paid at today’s spot rate.
Chalmers is “paying the points forward.”
1)
2)
3)
The amount of required forward cover for paying points forward for 120 days is 50% of the exposure, or
Ps.1,000,000. Chalmers could choose to cover more, but this is the minimum required.
If Chalmers expects the spot rate to be Ps.8.1920/$ in 120 days, Chalmers would likely cover only what is
required by company policy and leave the remaining uncovered because the expected spot rate is much more
favorable to Chalmers.
If expectations prove correct, the total receivable will result in realized U.S. dollars of the following:
End-of-Chapter Question Solutions
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Ps.1,000,000 ÷ Ps.11.0400/$ =
Ps.1,000,000 ÷ Ps.8.1920/$ =
Total realized:
b)
$ 90,580 from 50% covered position.
122,070 from uncovered position.
$212,650
Payables: An eight-week account payable of Ps.3,000,000 would require Chalmers to buy new Mexican pesos
forward. If bought at today’s spot rate of Ps.10.2400/$, as opposed to the forward rate of Ps.11.0400/$, Chalmers
would receive more pesos per dollar. Once again Chalmers is “paying the points forward” in the forward market.
a)
The amount of required forward cover for paying points forward 60 days is 75% of Ps.3,000,000, or
Ps.2,250,000.
b) The uncovered position is 25% of Ps.3,000,000, or Ps.750,000.
c) If expectations prove correct, the total payable will be the following:
Ps.2,250,000 ÷ Ps.8.8000/$ = $255,682 from 75% covered position.
Ps.750,000 ÷ Ps.10.0000/$ =
75,000 from uncovered position.
Total paid:
$330,682
6-6.
Juan Garcia of Cemex (page 182 in text)
a)
To check the quotes for their validity, it is necessary to verify that all derivative instruments are actually priced
appropriately given the input assumptions which Juan Garcia has collected. We start with the forward contract.
1 %
.05625 x
90
360
1%
.02500 x
90
360
F 90 ' $ 0.60000/ S$ x
' $ 0.604658/ S$ .
This is the same as the 90-day forward rate quote found by Juan Garcia. The call and put options on Singapore
dollars are the next derivative values to verify. Using the same interest rates, spot rate, and maturity, the only
other value for input for option pricing is the volatility measure on the US$/S$ exchange rate. Using Juan Garcia’s
value for volatility of 7.000%, the call and put option premiums are calculated (using the option.xls spreadsheet):
3-month call option on Singapore dollars at strike price of 65.000:
3-month put option on Singapore dollars at strike price of 65.000:
Calculated
$0.0002/S$
$0.0449/S$
Quoted
$0.0449/S$
$0.0002/S$
The call and put options are therefore “mis-priced” (actually reversed) if the quotes collected by Juan Garcia are
actually true and available from a financial institution. The arbitrage profit potential is actually enormous.
For example, Cemex could buy Singapore dollars forward three months at $0.60465/S$, and simultaneously buy
a three month put option on Singapore dollars at $0.6500/S$. In three months Cemex would execute the forward
contract to buy Singapore dollars, and then exercise the put option to sell them at the $0.65/S$ strike price to earn
an arbitrage profit of:
Sell at put strike price
Purchase at forward rate
Arbitrage profit
$0.65000/S$
- 0.60465/S$
$0.04535/S$
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b)
The simplest way for Cemex to benefit from this pricing or quotation error is to hedge the long Singapore dollar
position buy buying a put option at the reduced price of $0.0002/S$ when it should cost $0.0449/S$ (less than 1%
of the correct price!). If Cemex has any expectation that the Singapore dollar will appreciate versus the U.S. dollar,
buying the put option will allow them unlimited upside potential with downside protection (a strike price of
$0.65/S$, which itself is better than the current spot rate) at essentially no cost.
6-7.
Mini-Case Problem: Seattle Scientific, Inc. (page 183 in text)
Josh Miller should compare two basic alternatives, both of which eliminate currency risk.
1.
Allow the discount and receive payment in Japanese yen in cash.
Account receivable
Discount for cash settlement (4.500%)
Amount paid in cash
Current spot rate
Amount received in U.S. dollars
¥12,500,000.00
- 562,500.00
¥11,937,500.00
¥ 120.23/$
$99,288.86
Under the discount offer, Seattle Scientific would receive $99,288.86 in cash (today). The 4.5% discount
constitutes a dollar-cost of $4,678.53.
2.
Not offer any discounts for early payment and cover all Japanese yen receivables with forwards.
Account receivable
30-day forward rate
Amount paid in cash in US$
¥12,500,000.00
¥119.73/$
$104,401.57
Discount factor for 30 days @ WACC of 12.50%
PV of dollars received in 30 days
$103,325.27
0.9897
Under the no discount/30-day forward approach, Seattle Scientific would receive $104,401.57 in 30 days with
no currency risk. This is then discounted back 30-days to compare it with the discounted cash offer by
Yakusa. The present value of $103,325.27 is superior to the $99,288.86 cash offer.
Josh Miller and Seattle Scientific should not accept the discount offer of Yakusa.
a)
The cost of hedging is often measured as the forward premium, the percentage difference between settlement at
the forward rate and the booked amount at the spot rate. The forward premium on the yen here is:
¥ 120.23 / $ & ¥ 119.73 / $
360
x
x 100 ' 5.01 %.
¥ 119.73 / $
30
It might be said that hedging costs the firm 5.01% of its sales revenues.
End-of-Chapter Question Solutions
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b)
As illustrated above Seattle Scientific will receive $99,288.86 now, with the discount, and $104,401.57 in 30 days,
without the discount, via the forward contract.
c)
Which is preferable in present value terms? The $99,288.86 is in present value terms, and the $104,401.57 falls to
only $103,325.27 when discounted back 30 days. Seattle Scientific is still better off, even in present value terms,
by not accepting the offered discount approach.
d)
What discount rate should Josh Miller probably try to negotiate with Yokasa? Tough question. The fact is that
the Japanese yen forward rates are often so close to those of the spot rate, that there is little direct hedging cost
related to accepting future payment in yen. Since Seattle Scientific’s own WACC is 12.5% per annum, even on
domestic sales to other businesses in the United States, Seattle Scientific should probably offer a discount on
cash sales of 12.50% x (30/360) = 1.04%.
Given that the Japanese yen is actually selling forward at a premium, Seattle Scientific is actually “getting a better
forward rate than a spot rate.” The forward rate is actually reducing the effective cost to Seattle Scientific of
waiting for its payment (partially subsidizing the carrying cost). The bottom line is that if Seattle Scientific is to
offer any discounts to Japanese customers such as Yokasa, it should probably be nothing any larger than 1% for
30 days (12.50% per annum).