Stock P/E Ratio Calculation Example

Stock P/E Ratio Calculation

Prev Question Next Question

Question

A stock has a beta of 0.9 and the risk-free rate is 5%. Its dividend growth rate is 2.2% and the dividend payout ratio is 55%. If the market risk premium is 8%, the

P/E ratio of the stock equals ________.

Answers

Explanations

Click on the arrows to vote for the correct answer

A. B. C. D.

D

Using CAPM, the expected return on the stock equals 5% + 0.9 * 8% = 12.2%. Using the Dividend Discount Model, P/E = (dividend payout ratio)/(K - g). This gives

P/E = 0.55/(12.2% - 2.2%) = 5.5

To calculate the P/E (price-to-earnings) ratio of the stock, we need to use the dividend discount model (DDM) and the formula for the P/E ratio.

The dividend discount model (DDM) is used to value a stock by discounting its future dividends back to the present value. The formula for the DDM is:

P0=D1r−gP_0 = \frac{D_1}{r - g}

Where:

  • P0P_0 is the current price of the stock.
  • D1D_1 is the dividend expected to be received in the next period.
  • rr is the required rate of return.
  • gg is the dividend growth rate.

In this case, we need to find the price of the stock (P₀) in order to calculate the P/E ratio. However, we don't have the required rate of return (r) directly. We can use the capital asset pricing model (CAPM) to estimate the required rate of return, which is given by:

r=Rf+β×(Rm−Rf)r = R_f + \beta \times (R_m - R_f)

Where:

  • RfR_f is the risk-free rate (5% in this case).
  • β\beta is the beta of the stock (0.9 in this case).
  • RmR_m is the expected market return (market risk premium plus the risk-free rate).

We are given the market risk premium as 8%, so we can calculate RmR_m as follows:

Rm=Rf+Market Risk Premium=5R_m = R_f + \text{Market Risk Premium} = 5% + 8% = 13%

Now we can substitute the values into the CAPM formula to calculate the required rate of return (r):

r=5r = 5% + 0.9 \times (13% - 5%) = 5% + 0.9 \times 8% = 5% + 7.2% = 12.2%

Next, we need to calculate the expected dividend (D₁) using the dividend payout ratio and the dividend growth rate. The formula for the expected dividend is:

D1=D0×(1+g)D₁ = D₀ \times (1 + g)

Where:

  • D0D₀ is the current dividend.

Since we don't have the current dividend (D₀), we can calculate it using the formula:

D0=D11+gD₀ = \frac{D₁}{1 + g}

The dividend growth rate (g) is given as 2.2%, and the dividend payout ratio is 55%. Assuming the earnings and dividends are the same, we can write:

D0=D11+g=E0×Payout Ratio1+g=E0×0.551+0.022D₀ = \frac{D₁}{1 + g} = \frac{E₀ \times \text{Payout Ratio}}{1 + g} = \frac{E₀ \times 0.55}{1 + 0.022}

Now we can substitute the values into the formula to calculate D0D₀.

Finally, we can substitute the calculated values into the DDM formula to find the price of the stock (P₀):

P0=D1r−gP₀ = \frac{D₁}{r - g}

With the calculated values, we can find the P₀.

Once we have the P₀, we can calculate the P/E ratio by dividing the price of the stock by the earnings per share (EPS). The P/E ratio formula is:

P/E=P0EPSP/E = \frac{P₀}{EPS}

Since the earnings per share (EPS) is not given, we can't calculate the P/E ratio without additional information.

Prev Question Next Question