Chapter 31, Problem 3MC

Ignoring taxes, what are East Coast Yachts’ projected gains or losses from this proposed arrangement at the current exchange rate of $1.34/€? What will happen to profits if the exchange rate changes to $1.25/€? At what exchange rate will the company break even?

Summary Introduction

To calculate: The profit and loss and break even of company.

Exchange rate

Exchange rate defines the value of one country’s currency against the other country’s currency. Exchange rate has two main components, namely domestic currency and foreign currency.

Explanation of Solution

Calculation of production cost:

Given,

Total sales €8,000,000

Exchange rate $1.34/€

Formula to calculate total production:

$\text{Total sales}=\text{sales}\times \text{ exchange rate}$

Substitute €8,000,000 for total sales and $1.34/€ for Exchange rate.

$\begin{array}{c}\text{Total}\text{Sales}=€8,000,000\times \$1.34\\ =\$10,720,000\end{array}$

Hence, total sales is $10,720,000

Calculate production cost:

Given,

Total sales $10,720,000

Total spending by the company on production cost is 80%

Formula to calculate production cost:

$\text{Production cost}=\text{Total sales}\times \text{ total spendings on production}$

Substitute $10,720,000 for Total sales and 80% for total spending by the company on production cost,

$\begin{array}{c}\text{Production cost =\$10,720,000}\times \text{80\%}\\ \text{=\$8,576,000}\end{array}$

Hence, the production cost is $8,576,000.

Production cost remains constant irrespective of the exchange rate.

Calculate profit with the exchange rate of $1.34/€:

Given,

Total sales €8,000,000

Commission rate is 5%

Formula for commission on sales is,

$\text{Commission on sales =Total sales}\times \text{commission rate}$

Substitute €8,000,000 for Total sales and 5% for Commission rate,

$\begin{array}{c}\text{Commission in sales}=€8,000,000\times 5\%\\ =€400,000\end{array}$

Therefore, commission on sales is €400,000.

Calculate sales after commission:

Given,

Total sales is €8,000,000

Commission on sales is €400,000

Formula to calculate sales after commission:

$\text{Sales after commission = Total sales}-\text{Commission paid}$

Substitute €8,000,000 for Total sales and €400,000 for Commission on sales

$\begin{array}{c}\text{Sales after commission}=€8,000,000-€400,000\\ =€7,600,000\end{array}$

Hence, sales after commission are €7,600,000.

Calculation of sales after commission in dollars:

Given,

Sales after commission is €7,600,000.

Exchange rate is $1.34/€.

Formula to calculate sales after commission in dollars:

$\text{Sales after commission in dollars}=\left[\begin{array}{l}\text{Sales after commission}\\ \times \text{Exchange rate}\end{array}\right]$

Substitute €7,600,000 for Sales after commission and $1.34/€ for Exchange rate,

$\begin{array}{c}\text{Sales after commission }=€\text{7,600,000}\times \$\text{1}\text{.34}\\ =\$10,184,000\end{array}$

Hence, sales after commission is $10,184,000.

Calculation of profit in dollars

Given,

Sales after commission in dollars is $10,184,000,

Production cost is $8,576,000,

Formula to calculate profits in dollars:

$\text{Profit in dollars}=\left[\begin{array}{l}\text{Sales after commission in dollars}\\ -\text{Production cost}\end{array}\right]$

Substitute $10,184,000 for Sales after commission in dollars and $8,576,000 for Production cost,

$\begin{array}{c}\text{Profit in dollars}=\$10,184,000-\$8,576,000\\ =\$1,608,000\end{array}$

Hence, profit in dollars is $1,608,000.

Calculate of profit with exchange rate of $1.25/€:

Given,

Total sales €8,000,000.

Commission rate is 5%.

Formula for commission on sales:

$\text{Commission on sales =Total sales}\times \text{commission rate}$

Substitute €8,000,000 for Total sales and 5% for Commission rate.

$\begin{array}{c}\text{Commission in sales}=€8,000,000\times 5\%\\ =€400,000\end{array}$

Therefore, commission on sales is €400,000.

Calculation of sales after commission:

Given,

Total sales is €8,000,000

Commission on sales is €400,000

Formula to calculate sales after commission:

$\text{Sales after commission = Total sales}-\text{Commission paid}$

Substitute €8,000,000 for Total sales and €400,000 for Commission on sales.

$\begin{array}{c}\text{Sales after commission}=€8,000,000-€400,000\\ =€7,600,000\end{array}$

Hence, sales after commission are €7,600,000.

Calculation of sales after commission in dollars:

Given,

Sales after commission is €7,600,000

Exchange rate is $1.25/€

Formula to calculate sales after commission in dollars,

$\text{Sales after commission in dollars}=\left[\begin{array}{l}\text{Sales after commission}\\ \times \text{Exchange rate}\end{array}\right]$

Substitute €7,600,000 for Sales after commission and $1.34/€ for Exchange rate,

$\begin{array}{c}\text{Sales after commission }=€\text{7,600,000}\times \$\text{1}\text{.25}\\ =\$9,500,000\end{array}$

Therefore, sales after commission in dollars are $9,500,000.

Calculate profit in dollars:

Given,

Sales after commission in dollars is $9,500,000.

Production cost is $8,576,000.

Formula to calculate profits in dollars,

$\text{Profit in dollars}=\left[\begin{array}{l}\text{Sales after commission in dollars}\\ -\text{Production cost}\end{array}\right]$

Substitute $9,500,000 for Sales after commission in dollars and $8,576,000 for Production cost,

$\begin{array}{c}\text{Profit in dollars}=\$9,500,000-\$8,576,000\\ =\$924,000\end{array}$

Hence, profit in dollars is $924,000.

Therefore, when the exchange rate changes to $1.25/€the profit of the company will automatically decrease.

Calculate the break- even exchange rate:

Given,

Production cost in dollars is $8,576,000.

Sales after commission in euro is €7,600,000.

Formula to calculate break-even exchange rate:

$\text{Break-even exchange rate}=\frac{\text{Production cost in dollars}}{\text{Sales after commission in euro}}$

Substitute $8,576,000 for production cost in dollars and €7,600,000 for Sales after commission in euro,

$\begin{array}{c}\text{Break-even exchange rate}=\frac{\$8,576,000}{€7,600,000}\\ =\$1.128/€\end{array}$

Hence, the break even exchange rate is $1.128/€.

Conclusion

 If the exchange rate shifts from $1.34/€ to $1.25/€, the company will observe a decline in their profits. The company will break even at the exchange rate of $1.128/€.