Chapter 7, Problem 1PS

Rate of return The level of the Syldavia market index is 21,000 at the start of the year and 25,500 at the end. The dividend yield on the index is 4.2%.

1. a. What is the return on the index over the year?
2. b. If the interest rate is 6%, what is the risk premium over the year?
3. c. If the inflation rate is 8%, what is the real return on the index over the year?

Summary Introduction

To compute: The return on the index over the year.

Explanation of Solution

The return on index over the year can be calculated using the following formula:

$\begin{array}{c}\begin{array}{l}\text{Return on index }\\ \text{over the year}\end{array}\}\text{=}\frac{\left(\begin{array}{l}\text{Dividend yield+Market index at the end of the year}-\\ \text{Market index at the beginning of the year}\end{array}\right)}{\text{Market index at the beginning of the year}}\\ =\frac{4.2+25500-21000}{21000}\\ =25.62\%\end{array}$

Summary Introduction

To compute: Risk premium over the year when the interest rate is 6%.

Explanation of Solution

Risk premium over the year can be calculated using the following formula:

$\begin{array}{c}\text{Risk premium over the year=Return on index over the year-Interest rate}\\ \text{=25}\text{.62 -6\%}\\ \text{=19}\text{.62\%}\end{array}$

Summary Introduction

To compute: The real return on the index over the year when the inflation rate is 8%.

Explanation of Solution

The real return on index over the year can be calculated using the following formula:

$\begin{array}{c}\text{Real return}=\frac{1+\text{Return on index over the year}}{1+\text{Inflation}}-1\\ =\frac{1+25.62\%}{1+8\%}-1\\ =16.31\%\end{array}$