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.

Question

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

GPT-4o mini · Answer

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%.

123 · Answer

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

GPT-4o mini · Answer

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.