Finance-Theory · Unit 10 · Video 1 · Interactive Practice

What Makes a Price a Price, and Why an Exporter Wants to Lock One In

IKey Formulas

Formula	Name	What it says
$\text{dollar revenue} = \dfrac{P}{S}$	Converting foreign sales	$P$ = fixed local price, $S$ = units of foreign currency one dollar buys
$\dfrac{\text{revenue at } S_1}{\text{revenue at } S_0} = \dfrac{S_0}{S_1}$	Currency exposure	From $S_0 = 1$ to $S_1 = 4$ reais per dollar the same machine brings in $\tfrac{1}{4}$ of the dollars
$\text{profit} = \dfrac{P - C_{\text{local}}}{S} - C_{\text{home}}$	Natural hedge	Costs paid in the sales currency offset it: only the net local flow $P - C_{\text{local}}$ is converted

Key Insight: A price is a number at which a buyer and a seller agree to transact. A number nobody trades at is not a price, so suspending mark to market changes the books, not the value.

IIWhat Makes a Number a Price

A price exists only where a buyer's bid meets a seller's ask; a booked number alone is not one.

Best bid 40 Lowest ask 55 Booked value 80

IIIOne Machine, Two Exchange Rates

With the local price fixed, dollar revenue is $P/S$ : every rise in reais per dollar costs the exporter dollars.

Rate when priced, S₀ 1.0 Rate when paid, S₁ 4.0

IVThe Natural Hedge

Paying costs in the currency of the sales leaves only the net local flow exposed to the exchange rate.

Costs paid locally, h 0% Rate when paid, S 2.0

💡 A local plant takes a year or two to build, so a firm facing currency swings today needs a hedge that is available now: forwards and futures.

VQuiz Questions

Problem 1 · Converting Foreign Sales

Given: A US firm sells a machine in Brazil at a fixed price of 360,000 reais. When the customer pays, one dollar buys 2.4 reais. Find the firm's revenue in dollars.

✅ Correct! Each dollar costs the customer 2.4 reais, so 360,000 reais buy 150,000 dollars.

❌ Multiplied instead of divided. The rate is reais per dollar; turning reais into dollars means dividing by it. More reais per dollar must mean fewer dollars, not more.

❌ That skips the conversion. 360,000 is the amount in reais; the firm measures revenue in dollars, and one dollar is worth 2.4 reais.

❌ Check the decimal. The division is right in spirit, but 360,000 divided by 2.4 is ten times larger than this.

❌ Not quite. Dollar revenue is the local price divided by reais per dollar.

Show solution

With $P = 360{,}000$ reais and $S = 2.4$ reais per dollar:

\text{dollar revenue} = \frac{P}{S} = \frac{360{,}000}{2.4} = 150{,}000

The firm receives $150,000.

Problem 2 · The Percentage Trap

Given: A machine's price in Brazil is fixed in reais. Between the order and the payment the exchange rate rises from 2.0 to 2.5 reais per dollar, a 25% rise. By what percentage does the firm's dollar revenue from the machine fall?

✅ Correct! Revenue scales by

S_0/S_1 = 2.0/2.5 = 0.8

: a 20% fall, smaller than the 25% rise in the rate.

❌ The two percentages are not equal. Revenue is

P/S

, not proportional to

S

; a 25% rise in the rate multiplies revenue by

\tfrac{1}{1.25} = 0.8

❌ That is what remains, not the fall. Revenue ends at 80% of plan, so it falls by 20%.

❌ The local price is fixed, the dollar amount is not. The same reais convert into fewer dollars once each dollar costs more reais.

❌ Not quite. Compare

P/2.5

with

P/2.0

Show solution

\frac{\text{revenue at } S_1}{\text{revenue at } S_0} = \frac{P/2.5}{P/2.0} = \frac{2.0}{2.5} = 0.8

Revenue keeps 0.8 of its planned value, so it falls by 20%, whatever $P$ is. Because revenue is proportional to $\tfrac{1}{S}$ , a rise in the rate always cuts revenue by a smaller percentage than the rise itself (going back from 2.5 to 2.0 would raise revenue by 25%).

Problem 3 · Two Firms, One Currency Move

Given: Two exporters each sell 600,000 reais of machines in Brazil, planned at 2.0 reais per dollar. Firm A pays all its costs in the US: $200,000. Firm B built a plant in Brazil and pays its costs in reais: 400,000 reais (the same $200,000 at the planned rate). The rate moves to 3.0 reais per dollar. Find Firm B's profit in dollars.

✅ Correct! Only B's net 200,000 reais is converted, so its profit falls by a third while Firm A's is wiped out.

❌ That is Firm A. A converts all 600,000 reais of revenue (200,000 dollars) and still owes 200,000 dollars of costs. B's costs are in reais and move with its revenue.

❌ The offset is large but not complete. That is the profit at the planned rate. The net 200,000 reais B still converts is exposed to the move.

❌ That is revenue, not profit. 600,000 reais at 3.0 is 200,000 dollars, but B still pays 400,000 reais of costs out of it.

❌ Not quite. Net B's reais revenue and reais costs first, then convert.

Show solution

At the planned rate 2.0 both firms earn the same:

\text{A: } \frac{600{,}000}{2.0} - 200{,}000 = 100{,}000 \qquad \text{B: } \frac{600{,}000 - 400{,}000}{2.0} = 100{,}000

At 3.0:

\text{A: } \frac{600{,}000}{3.0} - 200{,}000 = 0 \qquad \text{B: } \frac{200{,}000}{3.0} \approx 66{,}667

Firm B earns about $66,667. Matching sales and expenses in one currency means a currency move hits both sides; they largely offset, and only the net flow remains exposed.

Problem 4 · Suspending Mark to Market

Given: A bank holds securities with a face value of $10 million. Before a crisis they traded at 90 per 100 of face value; buyers and sellers now transact at 55 per 100. A proposed rule would let the bank keep them on its books at 90. Which statement is right?

✅ Correct! The market sets the value: trades happen at 55, so the holding is worth 5.5 million dollars whatever the books say.

❌ Changing the books creates no value. Nobody will pay more for the securities because the ledger says 90; like telling people to sit down in a smoky theater, it does not put out the fire.

❌ That was a price, and it no longer is. A price is a number at which a buyer and a seller agree to transact now; nobody transacts at 90 today.

❌ Trades are still happening. Buyers and sellers agree at 55, so 55 is a price. Fear lowers the price; it does not make it zero.

❌ Not quite. Ask where a buyer and a seller actually agree to transact.

Show solution

Market value at the price where trades happen:

\text{market value} = 10 \times \frac{55}{100} = 5.5 \text{ million}

Booked value under the proposed rule:

\text{booked value} = 10 \times \frac{90}{100} = 9.0 \text{ million}

The difference, 9.0 − 5.5 = 3.5 million dollars, exists only on the books. The bank could sell for $5.5 million and no more; suspending mark to market changes the number on the books and leaves the securities' value where it was.

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