Question

Gritz Blitz is a corporation specializing in instant grits. An analyst has measured the beta for Gritz at 1.19. Currently, the risk free rate in the economy is 3.00%, while the market portfolio risk premium is 5.00%. Gritz currently trades at $10.00 per share. The analyst predicts a trading value of $10.48 next year for the company.

What is the required return based on the analyst's information?

Answer 1

Based on the expected trading value in one year, what dividend per share must Gritz pay for the stock to generate its required return?

Answer 2

To calculate the required return for Gritz Blitz, we can use the Capital Asset Pricing Model (CAPM). The formula for CAPM is:

\[
\text{Required Return} = \text{Risk-Free Rate} + \beta \times (\text{Market Risk Premium})
\]

Where:
- Risk-Free Rate = 3.00% or 0.03
- Beta for Gritz = 1.19
- Market Risk Premium = 5.00% or 0.05

Now, we can plug in the values into the formula:

\[
\text{Required Return} = 0.03 + 1.19 \times 0.05
\]

Calculating the product of beta and market risk premium:

\[
1.19 \times 0.05 = 0.0595
\]

Now add this to the risk-free rate:

\[
\text{Required Return} = 0.03 + 0.0595 = 0.0895
\]

To convert this to percentage:

\[
\text{Required Return} = 0.0895 \times 100 = 8.95\%
\]

Thus, the required return based on the analyst's information is **8.95%**.

Answer 3

To calculate the required dividend per share that Gritz must pay to generate its required return, we can use the following formula:

\[
\text{Total Return} = \frac{\text{Dividend} + \text{Price Change}}{\text{Current Price}}
\]

Where:
- Total Return is equal to the required return (in decimal form),
- Price Change is the expected trading value in one year minus the current price,
- Current Price is the current trading price of the stock.

From the earlier calculation, we know:
- Required Return = 8.95% or 0.0895
- Current Price = $10.00
- Expected Trading Value in one year = $10.48

First, calculate the price change:

\[
\text{Price Change} = \text{Expected Trading Value} - \text{Current Price} = 10.48 - 10.00 = 0.48
\]

Now, substitute the values into the total return formula:

\[
0.0895 = \frac{\text{Dividend} + 0.48}{10.00}
\]

Now, multiply both sides by 10.00 to isolate the numerator:

\[
0.895 = \text{Dividend} + 0.48
\]

Now, solving for the dividend:

\[
\text{Dividend} = 0.895 - 0.48 = 0.415
\]

Thus, the dividend per share that Gritz must pay in order to generate its required return is **$0.415**.