Question

Instructions: You are required to use a financial calculator or spreadsheet (Excel) to solve the problems (provided on page 4) related to risk and return characteristics and stock/bond valuation. You are required to show the following three steps for each problem (sample problems and solutions are provided for guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

A company’s stock had a required return of 11.50% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Now, suppose there is a shift in investor risk aversion, and the market risk premium increases by 2.00%. The risk-free rate and the beta remain unchanged. What is this company’s new required return (round your answer to two decimal places)?

Answer 1

i)

Given information,

Company's stock return last year = 11.50%

Risk free rate = 5.50%

Market risk premium = 4.75%

We have given this information. To calculate required return we have many formulae but here, we have given last year's data.

Risk measure as beta remains constant. It is assumed that given stock return of 11.50% is company's expected rate of return.

ii)

We generally use CAPM model to derive required rate of return. Here the information provided is related to the Capital Asset Pricing Model. Hence, we will use Capital Asset Pricing Model for further calculations. We have provided market risk premium which is difference between market risk and risk free rate. CAPM formula is

Here, R_m - R_f is market risk premium under CAPM.

E_(R) indicates expected or required return of stock or bond. R_f is risk free rate of return. indicates Beta of return.

To calculate company's new required rate of return , we have given that market risk premium increases by 2.00%. As per given formula, we need beta of stock which is not given. We can calculate beta by using last year's data as we have given that risk free rate and beta remains unchanged. Hence, we will use Capital Asset Pricing Model to solve this problem.

iii)

CAPM formula is

By using this, we will calculate beta as we have other information of last year.

11.50 = 5.50 + * 4.75

11.50-5.50 = 4.75*

6 = 4.75*

6/4.75 =

1.2632 =

= 1.2632

As we have given that beta and risk free rate remains unchanged for next year, for calculating new required return, risk free rate will be 5.50%, as calculated above 1.2632 and market risk premium increased by 2.00% i.e. new market risk premium is 4.75%+2.00%=6.75%

Therefore new required rate of return is,

E_(R) = 5.50 + 1.2632*6.75

= 5.50 + 8.5266

E_(R) = 14.03%

Therefore, company's new required rate of return is 14.03%