Mark Collins, luthier and businessman, builds and sells custom-made acoustic and electric stringed instruments. Although located in Maryville, Tennessee, he purchases raw materials from around the globe. For example, his top-of-the line acoustic guitar with onboard electronics, the MC-28, is constructed from rosewood and mahogany imported from a distributer in Mexico, spruce harvested in and imported from Canada, and ebony and the electronics imported from a Japanese distributer. Other parts are obtained in the U.S. When broken down on a per-guitar basis, the component and finishing costs are as follows:

Rosewood and mahogany: 2,750 Mexican pesos Spruce: 200 Canadian dollars Ebony and electronics: 12,400 Japanese Yen Other parts plus woodworking labor: $600

Collins sells some of this model in the U.S., but the majority of the units are sold in England where he has developed a loyal following and the guitars have become something of a cult symbol. There, his guitars fetch 1,600, excluding shipping. Mark is concerned about the effect of exchange rates on his materials costs and profit.

You will find Tables 17-1, 17-2, and 17-3 useful for this problem.

TABLE 17-1

Exchange rates of select major currencies, relative to the U.S. dollar

Note: The pound and euro are quoted as direct quotations. Other currencies are quoted as indirect quotations. Blue denotes the actual quotes, which are reported out to digits to the right of the decimal; orange is the inverse of the provided quote and is not rounded.

Note: only blue cells need to be updated with current quotes.

Direct

Indirect

Quotations

Quotations

(1)

(2)

Canadian dollar

0.7822

1.2784

Japanese yen

0.0082

121.4200

Mexican peso

0.0646

15.4878

Swiss franc

0.9944

1.0056

British pound

1.4744

0.6782

Euro

1.0497

0.9527

Key Currency Cross-Exchange Rates

Note: these do not need to be updated because they are derived from the quotes in previous table and are not rounded.

Dollar

Euro

Pound

SFranc

Peso

Yen

CdnDlr

Canada

1.2784

1.3419

1.8849

1.2713

0.0825

0.0105

....

Japan

121.4200

127.4546

179.0216

120.7438

7.8397

....

94.9781

Mexico

15.4878

16.2575

22.8352

15.4016

....

0.1276

12.1150

Switzerland

1.0056

1.0556

1.4827

....

0.0649

0.0083

0.7866

United Kingdom

0.6782

0.7120

....

0.6745

0.0438

0.0056

0.5305

Euro

0.9527

....

1.4046

0.9473

0.0615

0.0078

0.7452

United States

....

1.0497

1.4744

0.9944

0.0646

0.0082

0.7822

a. How much, in dollars, does it cost for Mark Collins to produce his MC-28? What is the dollar sale price of the MC-28 sold in England?

Input Data

Cost of rosewood and mahogany (pesos)

2,750

Cost of spruce (CdnDlr)

200

Cost of ebony and electronics (yen)

12,400

Cost of parts and labor (U.S. dollars)

$600

Sale price of the MC-28 (pounds)

1,600

We will convert the cost of each component to dollars, and find the total cost of the SY-20. We will do the same to find the

dollar sale price.

Rosewood and mahogany

Cost of rosewood and mahogany in $

=

Cost in pesos

x

Direct spot exchange rate ($/peso)

Cost of rosewood and mahogany in $

=

x

Cost of rosewood and mahogany in $

=

Spruce

Cost of spruce in $

=

Cost in CdnDlr

x

Direct spot exchange rate ($/CdnDlr)

Cost of spruce in $

=

x

Cost of spruce in $

=

Ebony and electronics

Cost of ebony and electronics in $

=

Cost in yen

x

Direct spot exchange rate ($/yen)

Cost of ebony and electronics in $

=

x

Cost of ebony and electronics in $

=

Parts and labor

Cost of parts and labor in $

=

Cost in dollars

Cost of parts and labor in $

=

Cost of parts and labor in $

=

TOTAL COST OF THE MC-28 (in dollars) =

Revenue from sale of the MC-28 in England

Sale price (in $)

=

Price in pounds

x

Direct spot exchange rate ($/pound)

Sale price (in $)

=

x

Sale price (in $)

=

MC-28 SALES PRICE (in dollars) =

b. What is the dollar profit that Collins makes on the sale of the MC-28? What is the percentage profit?

The dollar profit from the sale of the SY-20 is simply the sales revenue minus the total cost.

Dollar profit =

Sales price

Total cost

Dollar profit =

Dollar profit =

The percentage profit is determined as the dollar profit divided by the total cost.

% profit =

$ profit

Total cost

% profit =

% profit =

c. If the U.S. dollar were to depreciate by 10% against all foreign currencies, what would the dollar and percentage profits be for the MC-28?

Since dollar is depreciating, a dollar buys fewer units of foreign currency than before its depreciation. Therefore, the indirect quotes (which show the number of units of foreign currency per dollar) should all be reduced by 10%. Then we convert the new indirect quotes to direct quotes (divide 1 by an indirect quote to get a direct quote).

Change in dollar versus all currencies (positive is appreciation, negative is depreciation):

We will reproduce the table from the top of the spreadsheet, but we will add a column for the new exchange rates.

Old Direct

Old Indirect

New Indirect Quotations (3)

New Direct Quotations (4)

Quotations

Quotations

(1)

(2)

Canadian dollar

0.78223

1.27840

Japanese yen

0.00824

121.42000

Mexican peso

0.06457

15.48780

Swiss franc

0.99443

1.00560

British pound

1.47440

0.67824

Euro

1.04970

0.95265

Now, we will recompute the component costs and sales price of the MC-28.

Rosewood and mahogany

Cost of rosewood and mahogany in $

=

Cost in pesos

x

Direct spot exchange rate ($/peso)

Cost of rosewood and mahogany in $

=

x

Cost of rosewood and mahogany in $

=

Spruce

Cost of spruce in $

=

Cost in CdnDlr

x

Direct spot exchange rate ($/CdnDlr)

Cost of spruce in $

=

x

Cost of spruce in $

=

Ebony and electronics

Cost of ebony and electronics in $

=

Cost in yen

x

Direct spot exchange rate ($/yen)

Cost of ebony and electronics in $

=

12,400.00

x

Cost of ebony and electronics in $

=

Parts and labor

Cost of parts and labor in $

=

Cost in dollars

Cost of parts and labor in $

=

Cost of parts and labor in $

=

TOTAL COST OF THE MC-28 (in dollars) =

Revenue from sale of the MC-28 in England

Sale price (in $)

=

Price in pounds

x

Direct spot exchange rate ($/pound)

Sale price (in $)

=

x

Sale price (in $)

=

MC-28 SALES PRICE (in dollars) =

The dollar profit from the sale of the MC-28 is simply the sales revenue minus the total cost.

Dollar profit =

Sales price

-

Total cost

Dollar profit =

-

Dollar profit =

The percentage profit is determined as the dollar profit divided by the total cost.

% profit =

$ profit

/

Total cost

% profit =

/

% profit =

The total costs go up because the dollar has depreciated against the currencies' of the suppliers, making it more expensive in dollars for Collins to purchase the raw materials. However, the depreciation of the dollar versus the pound increases the dollar value of sales. The net effect is a small increase in profits for this example, but that will not always be the case.

d. If the U.S. dollar were to depreciate by 10% only against the pound and remained constant relative to all other foreign currencies, what would the dollar and percentage profits be for the MC-28?

Since dollar is depreciating relative to the pound, a dollar buys fewer pounds than before its depreciation. Therefore, the indirect quote for pounds (which shows the number of pounds per dollar) should be reduced by 10%. Then we convert the new indirect quote to a direct quote (divide 1 by the indirect quote to get the direct quote). The is no need to change any other direct quotes because the dollar is neither depreciation nor appreciating relative to them.

Change in dollar strength against the pound

Direct

Indirect

New Indirect Quotations (3)

New Direct Quotations (4)

Quotations

Quotations

(1)

(2)

Canadian dollar

0.7822278

1.27840

0.78223

Japanese yen

0.0082359

121.42000

0.00824

Mexican peso

0.0645669

15.48780

0.06457

Swiss franc

0.9944312

1.00560

0.99443

British pound

1.4744

0.67824

Euro

1.0497

0.95265

1.04970

Now, we will recompute the component costs and sales price of the MC-28.

Rosewood and mahogany

Cost of rosewood and mahogany in $

=

Cost in pesos

x

Direct spot exchange rate ($/peso)

Cost of rosewood and mahogany in $

=

x

Cost of rosewood and mahogany in $

=

Spruce

Cost of spruce in $

=

Cost in CdnDlr

x

Direct spot exchange rate ($/CdnDlr)

Cost of spruce in $

=

x

Cost of spruce in $

=

Ebony and electronics

Cost of ebony and electronics in $

=

Cost in yen

x

Direct spot exchange rate ($/yen)

Cost of ebony and electronics in $

=

x

Cost of ebony and electronics in $

=

Parts and labor

Cost of parts and labor in $

=

Cost in dollars

Cost of parts and labor in $

=

Cost of parts and labor in $

=

TOTAL COST OF THE MC-28 (in dollars) =

Revenue from sale of the MC-28 in England

Sale price (in $)

=

Price in pounds

x

Direct spot exchange rate ($/pound)

Sale price (in $)

=

x

Sale price (in $)

=

MC-28 SALES PRICE (in dollars) =

The dollar profit from the sale of the MC-28 is simply the sales revenue minus the total cost.

Dollar profit =

Sales price

-

Total cost

Dollar profit =

-

Dollar profit =

The percentage profit is determined as the dollar profit divided by the total cost.

% profit =

$ profit

/

Total cost

% profit =

/

% profit =

Because sales are made in pounds, dollar revenues increase when the dollar depreciates relative to the pound--there are fewer pounds per pound, but there are more dollars per pound.

e. The rate of return on 90-day U.S. treasury securities is 3.9% and the rate of return on 90-day U.K. risk-free securities is 5.0%. Using the spot exchange information from Table 17-1, estimate the 90-day forward exchange rate.

Using knowledge of interest rate parity, the following problem is set up.

Spot exchange rate (direct quotation) =

Home nominal interest rate =

3.9%

Foreign nominal interest rate =

5.0%

Time to maturity on securities (in years) =

0.25

Home periodic interest rate =

Foreign periodic interest rate =

ft / (spot exchange rate)

=

[ (1+rh) / (1+rf) ]

ft

=

(spot exchange rate) [ (1+rh) / (1+rf) ]

ft

=

f. Assuming that purchasing power parity holds, what would the sale price of the MC-28 be if it were sold in France rather than England? (Hint: assume England is the home country.)

Purchasing power parity allows us to establish the following problem.

Price in pounds

=

Exchange rate (pounds per euro) =

P h

=

( P f )

x

( e0 )

pounds per euro

(in pounds)

=

( P f )

x

=

( P f )