Chapter 18, Problem 9QP

Exchange Rate Risk. Suppose your company imports computer motherboards from Singapore. The exchange rate is given in Table 18.2. You have just placed an order for 30,000 motherboards at a cost to you of 185.50 Singapore dollars each. You will pay for the shipment when it arrives in 90 days. You can sell the motherboards for $150 each. Calculate your profit if the exchange rate goes up or down by 10 percent over the next 90 days. What is the break-even exchange rate? What percentage rise or fall does this represent in terms of the Singapore dollar versus the U.S. dollar?

Summary Introduction

To find: The profit if the rate of exchange goes up or down, the break-even exchange rate and the percentage change.

Introduction:

The price of a country’s currency that in terms of another nation’s currency is the exchange rate. The rate of exchange can be either floating or fixed. The two components of the exchange rates are the foreign currency and the domestic currency.

Answer to Problem 9QP

The break-even exchange rate is S$1.12367 for a US$, and the percentage change is -5.19%.

Explanation of Solution

Given information:

The exchange rate quotations (Figure 18.2) that are stated in the Journal WS as on 28^th November 2014 (Friday) is as follows:

Country U’s dollar foreign exchange rate in the late City NY trading:

Country/currency	Equivalent US$	US$ VS. % CHG	PER US$
	Friday	YTD	Friday
Singapore dollar	0.7667	3.3	1.3043

Note: The term YTD stands for year to date, the term “chg” refers to change.

Person X’s company imports the motherboards for computers from Country S. Person X have just made an order for 30,000 motherboards at a cost of S$185.50 per motherboard. Person X will make a payment for the shipment when it reaches within ninety days. Person X can sell the motherboards for $150 each. The rate of exchange goes up or down by 10% over the upcoming 90 days.

Formula to compute the profit if the rate of exchange is the same:

$\text{Profit}=\text{Quantity sold}\left[\text{Per unit cost}-\frac{\left(\text{Cost per unit in the currency of Country S}\right)}{\text{Country S dollar per US\$}}\right]$

Computation of the profit:

$\begin{array}{c}\text{Profit}=\text{Quantity sold}\left[\text{Per unit cost}-\frac{\left(\text{Cost per unit in the currency of Country S}\right)}{\text{Country S dollar per US\$}}\right]\\ =30,000\left[\$150-\left(\frac{\text{S\$185}\text{.50}}{\text{S\$1}\text{.3043per US\$}}\right)\right]\\ =\$233,343.56\end{array}$

Hence, the profit is $233,343.56.

Computation of the profit if there is a rise in the rate of exchange:

If there is an increase in the rate of exchange, then the cost has to be adjusted by the increased rate of exchange.

$\begin{array}{c}\text{Profit}=\text{Quantity sold}\left[\begin{array}{l}\text{Per unit cost}-\frac{\left(\text{Cost per unit in the currency of Country S}\right)}{\text{Increase in the rate of exchange}}\\ \times \text{Country S dollar per US\$}\end{array}\right]\\ =30,000\left[\$150-\left(\frac{\text{S\$185}\text{.50}}{\left(1.1\times \frac{\text{S}\$1.3043\text{per US\$}}{1}\right)}\right)\right]\\ =30,000\left[\$150-\left(\frac{\text{S\$185}\text{.50}}{1.1}\right)\times \left(\frac{1}{\text{S}\$1.3043\text{per US\$}}\right)\right]\\ =\$621,221.41\end{array}$

Hence, the profit is $621,221.41.

Computation of the profit if there is a decrease in the rate of exchange:

If there is a decrease in the rate of exchange, then the cost has to be adjusted by the decreased rate of exchange.

$\begin{array}{c}\text{Profit}=\text{Quantity sold}\left[\begin{array}{l}\text{Per unit cost}-\frac{\left(\text{Cost per unit in the currency of Country S}\right)}{\text{Decrease in the rate of exchange}}\\ \times \text{Country S dollar per US\$}\end{array}\right]\\ =30,000\left[\$150-\left(\frac{\text{S\$185}\text{.50}}{0.9\times \frac{\text{S\$1}\text{.3043per US\$}}{1}}\right)\right]\\ =30,000\left[\$150-\left(\frac{\text{S\$185}\text{.50}}{0.9}\right)\times \left(\frac{1}{\text{S\$1}\text{.3043per US\$}}\right)\right]\\ =-\$240,729.38\end{array}$

Hence, the profit is -$240,729.38.

Computation of the break-even exchange rate:

To compute the change in the break-even exchange rate, it is essential to determine the rate of exchange that makes the cost in Country S’s dollars and that must be equivalent to the selling price of Country U’s dollars. Thus, the computation are as follows:

$\begin{array}{c}\$150=\frac{\text{S\$185}\text{.50}}{S_T}\\ S_T=\frac{\text{S\$185}\text{.50}}{\$150}\\ S_T=\text{S\$1}\text{.2367 for a US\$}\end{array}$

Note: $S_T$ is the exchange rate.

Hence, the break-even exchange rate is S$1.12367 for $1.

Formula to compute the percentage change:

$\text{Percentage change}=\frac{\left(S_T-\text{Country S's dollar for a US\$}\right)}{\text{Country S's dollar for a US\$}}$

Computation of the percentage change:

$\begin{array}{c}\text{Percentage change}=\frac{\left(S_T-\text{Country S's dollar for a US\$}\right)}{\text{Country S's dollar for a US\$}}\\ =\left(\frac{\text{S\$1}\text{.2367}-1.3043}{\text{S\$}1.3043}\right)\\ =-0.0519\end{array}$

Hence, the percentage change is - 0.0519 or - 5.19%.