# Vogt Corporation has a beta of 0.7. The U.S. government T-Bill is expected to yield 0.05, and the...

## Question:

Vogt Corporation has a beta of 0.7. The U.S. government T-Bill is expected to yield 0.05, and the S&P 500 is expected to yield 0.11 in the near future.

What is Vogt's required rate of return?

## Capital Asset Pricing Model (CAPM)

One method used to determine the required rate of return is the Capital Asset Pricing Model (CAPM). CAPM takes into account the expected risk of an investment relative to other securities in the market.

The following formula is used to compute the rate of return using CAPM:

{eq}r_{i} = r_{f} + \beta (r_{m}-r_{f}) {/eq}

where

{eq}r_{i} = expected\ rate\ of\ return \\ r_{f} = risk-free\ rate \\ \beta = beta\ of\ the\ investment \\ r_{m} = market\ return {/eq}

The beta of a potential investment represents the relative risk of the investment when added as part of a portfolio of investments. An investment with a beta of more than 1 has a higher risk compared to the portfolio. An investment with a beta of less than 1 has a lower risk compared to the portfolio.

The difference between the market return and risk-free rate represents the market risk premium. This is the additional return expected due to the additional risk assumed by investing in the market.

To compute for Vogt Corporation's required rate of return, we substitute the given figures to the formula above:

{eq}r_{f} = 0.05 \\ \beta = 0.7 \\ r_{m} = 0.11 {/eq}

{eq}r_{i} = 0.05 + 0.7(0.11-0.05) = 0.092 {/eq}

Using the formula, we derive the company's required rate of return of 0.092 or 9.20%.