https://file.aiquickdraw.com/mathbot/file/17282678298737zxxq6wj.jpg

To solve this, we will use the **Capital Asset Pricing Model (CAPM)** formula, which calculates the expected rate of return on an investment.

The CAPM formula is:

\[
r_e = r_f + \beta \times (r_m - r_f)
\]

Where:
- $ r_e $ = expected return on the equity investment
- $ r_f $ = risk-free rate (1.4% or 0.014 in decimal)
- $ \beta $ = beta of the investment (1.8 for PayPal)
- $ r_m $ = expected return of the market (9% or 0.09 in decimal)

Now, plugging the given values into the CAPM formula:

\[
r_e = 0.014 + 1.8 \times (0.09 - 0.014)
\]

Let's compute this step-by-step:

1. $ r_m - r_f = 0.09 - 0.014 = 0.076 $
2. Multiply by Beta: $ 1.8 \times 0.076 = 0.1368 $
3. Add the risk-free rate: $ 0.014 + 0.1368 = 0.1508 $

Thus, the expected return $ r_e $ is **0.1508**, or **15.08%**.

Would you like more details or have any further questions?

Here are five related questions:
1. What factors influence a company's beta in the CAPM model?
2. How does a higher risk-free rate affect the expected return?
3. What are the limitations of using CAPM for investment decisions?
4. How does CAPM differ from other models, such as the Arbitrage Pricing Theory (APT)?
5. How can market conditions affect the accuracy of the CAPM predictions?

**Tip:** Always express the expected return as a percentage in financial models to ensure clarity when comparing different investment opportunities.

BlackRock is planning to make an equity investment in PayPal Inc. They need the expected rate return on this investment to compare it to an alternative investment. Use the CAPM to find it. The expected return of the market is 9% and the return on a risk-free asset equals 1.4%. PayPal's Beta equals 1.8 and projects operating income of $7,099,252.

Discover how to calculate the expected rate of return on an equity investment in PayPal using the CAPM formula. Given a market return of 9%, a risk-free rate of 1.4%, and PayPal's beta of 1.8, this step-by-step solution explains how to apply CAPM in financial decision-making.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation