Chapter 19, Problem 3PS

Summary Introduction

(a)

To calculate:

The number of shares that an investor can purchase by investing $\$10000$ in a British firm when the rate of exchange is $\$2/\text{pound}$

Introduction:

For investing in a British firm, investor of U.S. has to change its funds into the pound and then should compute the number of shares which he can invest in the firm.

Answer to Problem 3PS

The number of shares that can be purchased by investor in British firm is $125\text{ shares}$ .

Explanation of Solution

Given:

  $\begin{array}{c}\text{Current price per share}=\text{Pound }40\text{ per share}\\ \text{Total investment}=\$10000\\ \text{Rate of exchange}=\$2/\text{pound}\end{array}$

To calculate total number of shares, first total investment given in dollars should be converted to Euro which is calculated on the basis of Rate of Exchange and then, the total investment should be divided with current price per share.

  $\begin{array}{c}\text{Investment value in pound}=\frac{\$10000}{\$2}\\ =\text{Pound }5000\end{array}$

  $\begin{array}{c}\text{Number of shares}=\frac{\text{Pound }5000}{\text{Pound }40}\\ =125\text{ shares}\end{array}$

Thus, number of shares that can be purchased is $125\text{ shares}$ .

Summary Introduction

(b)

To calculate:

The rates of return in dollar-denominated after one year in different scenarios and pound-denominated return.

Introduction:

For investing in a British firm, investor of U.S. has to change its funds into the pound and then should compute the number of shares which he can invest in the firm.

Answer to Problem 3PS

Below table highlights the values for all nine cases:

Per share price (£)	Pound-Denominated Return (%)	Dollar-Denominated Return (%) for year-end exchange Rate
		$\$1.80/\pounds$	$\$2.00/\pounds$	$\$2.20/\pounds$
£ $35$	$-12.5\%$	$-21.25\%$	$-12.5\%$	$-3.75\%$
£ $40$	$0.0\%$	$-10.00\%$	$0.00\%$	$10.00\%$
£ $45$	$12.5\%$	$1.25\%$	$12.5\%$	$23.75\%$

Explanation of Solution

Given:

  $\begin{array}{c}\text{Current price per share}=\text{Pound }40\text{ per share}\\ \text{Total investment}=\$10000\\ \text{Rate of exchange}=\$2/\text{pound}\end{array}$

Let's first calculate the pound-denominated return and for that, the following formula is used:

  $\text{Pound-denominated return}=\frac{\left[\text{Number of shares}\left(\text{Current price}-\text{Base price}\right)\right]}{\text{Initial investment in Pound}}$

By using the above formula, Pound-denominated return is computed as follows:

Per share price (£)	Pound-Denominated Return (%)
$\pounds 35$	$\begin{array}{c}\text{Return}=\frac{125\left(\pounds 35-\pounds 40\right)}{\pounds 5000}\\ =\frac{\pounds 4375-\pounds 5000}{\pounds 5000}\\ =-12.5\%\end{array}$
$\pounds 40$	$\begin{array}{c}\text{Return}=\frac{125\left(\pounds 40-\pounds 40\right)}{\pounds 5000}\\ =\frac{\pounds 5000-\pounds 5000}{\pounds 5000}\\ =0.00\%\end{array}$
$\pounds 45$	$\begin{array}{c}\text{Return}=\frac{125\left(\pounds 45-\pounds 40\right)}{\pounds 5000}\\ =\frac{\pounds 5625-\pounds 5000}{\pounds 5000}\\ =12.5\%\end{array}$

Now, calculate the dollar-denominated return and for that, the following formula is used:

  $\text{Dollar-denominated return}=\frac{\left[\text{Number of shares}\left(\left(\text{Current price}\times \text{new rate}\right)-\left(\text{Base price}\times \text{base rate}\right)\right)\right]}{\text{Initial investment in Dollar}}$

By using the above formula, Dollar-denominated return is computed as follows:

Per share price (£)	Dollar-Denominated Return (%) for year-end exchange Rate
	$\$1.80/\pounds$	$\$2.00/\pounds$	$\$2.20/\pounds$
$\pounds 35$	$\begin{array}{c}\text{Return}=\frac{\$7875-\$10000}{\$10000}\\ =-21.25\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$8750-\$10000}{\$10000}\\ =-12.5\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$9625-\$10000}{\$10000}\\ =-3.75\%\end{array}$
$\pounds 40$	$\begin{array}{c}\text{Return}=\frac{\$9000-\$10000}{\$10000}\\ =-10\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$10000-\$10000}{\$10000}\\ =0.00\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$11000-\$10000}{\$10000}\\ =10\%\end{array}$
$\pounds 45$	$\begin{array}{c}\text{Return}=\frac{\$10125-\$10000}{\$10000}\\ =1.25\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$11250-\$10000}{\$10000}\\ =12.5\%\end{array}$	$\begin{array}{c}\text{Return}=\frac{\$12375-\$10000}{\$10000}\\ =23.75\%\end{array}$

Summary Introduction

(c)

To calculate:

The situation in which the dollar-denominated return will be equal to the pound-denominated return.

Introduction:

For investing in a British firm, investor of U.S. has to change its funds into the pound and then should compute the number of shares which he can invest in the firm.

Answer to Problem 3PS

The situation is when there will be no change in the exchange rates.

Explanation of Solution

Given:

  $\begin{array}{c}\text{Current price per share}=\text{Pound }40\text{ per share}\\ \text{Total investment}=\$10000\\ \text{Rate of exchange}=\$2/\text{pound}\end{array}$

The dollar denomination returns will be equal to the pound denomination return when there is no change over the exchange rate in one year even if the price of the share changes.