Chapter 27, Problem 1PS

Exchange rates* Look at Table 27.1.

1. a. How many Japanese yen do you get for your dollar?
2. b. What is the three-month forward rate for yen?
3. c. Is the yen at a forward discount or premium on the dollar?
4. d. Use the one-year forward rate to calculate the annual percentage discount or premium on yen.
5. e. If the one-year interest rate on dollars is 2.5% annually compounded, what do you think is the one-year interest rate on yen?
6. f. According to the expectations theory, what is the expected spot rate for yen in three months’ time?
7. g. According to purchasing power parity theory, what then is the expected difference in the three-month rate of price inflation in the United States and Japan?

Summary Introduction

To discuss: The Country J yen for a dollar.

Explanation of Solution

The Country J yen for a dollar is 112.61 yen for a dollar

Summary Introduction

To determine: 3-month forward rate for Country J yen.

Explanation of Solution

Using the 3-month forward rate:

The 3-month forward rate for Country J yen is 111.94

Summary Introduction

To discuss: Whether yen is at a forward premium or discount

Explanation of Solution

The dollar is at forward discount and yen is at a forward premium.

Summary Introduction

To determine: Annual percentage premium or discount on yen.

Explanation of Solution

Compute annual percentage premium or discount on yen:

$\begin{array}{c}\text{Premium}=\frac{\yen 112.61}{\yen 109.99}–1\\ =\text{0}.0238,or2.38\%\end{array}$

Summary Introduction

To determine: 1-year interest rate on yen

Explanation of Solution

$\begin{array}{l}\frac{\yen 109.99}{\yen 112.61}=\frac{1+r_{yen}}{1.025}\\ r_{yen}= 0.001152,or\text{ 0}.1152\%\end{array}$

Summary Introduction

To determine: Expected spot rate for yen in 3 month.

Explanation of Solution

Expected spot rate for yen in 3 month is $\yen 111.94=\$1$

Summary Introduction

To determine: The expected difference in 3-month rate of price inflation in the Country U and Country J.

Explanation of Solution

Difference,

$\begin{array}{c}\text{Differences}=\frac{\yen 111.94}{\yen 112.61}–1\\ =-0.00595,or–0.595\%\end{array}$