Chapter 12, Problem 1P

Summary Introduction

To determine: The equity cost of capital of Company P’s stock.

Introduction:

Cost of capital refers to the return that the investors expect on a particular investment. In other words, it refers to the compensation demanded by the investors for using their capital.

Answer to Problem 1P

The equity cost of capital of Company P’s stock is 5.85 percent.

Explanation of Solution

Given information:

Company P’s stock has a beta of 0.57. The risk-free rate is 3 percent and the market portfolios expected return is 8 percent.

The formula to calculate the expected return using CAPM is as follows:

Note: The cost of capital is estimated by computing the expected return. The Capital Asset Pricing Model (CAPM) can be used to compute the expected return as follows:

$E(R_i)=R_f+\left[E(R_M)-R_f\right]\times {\beta }_i$

Here

“E (R_i)” refers to the expected return on a risky asset.

“R_f” refers to the risk-free rate.

“E (R_M)” refers to the expected return on the market portfolio.

“β_i” refers to the beta coefficient of the risky asset relative to the market portfolio.

Calculate the expected return or cost of the capital as follows:

$\begin{array}{c}E(R_i)=R_f+\left[E(R_M)-R_f\right]\times {\beta }_i\\ =\frac{3}{100}+\left[\frac{8}{100}-\frac{3}{100}\right]\times 0.57\\ =0.03+\left[0.08-0.03\right]\times 0.57\\ =0.03+0.05\times 0.57\end{array}$

$\begin{array}{c}=0.03+0.0285\\ =0.0585\text{ or 5}\text{.85\%}\end{array}$

Hence, the cost of capital is 5.85%.