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A company currently pays a dividend of $2.6 per share (d0 = $2.6). it is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 8% thereafter. the company's stock has a beta of 1.8, the risk-free rate is 7.5%, and the market risk premium is 4.5%. what is your estimate of the stock's current price?

Sagot :

The stock's current price  is  53.413455.

What is CAPM ?

  • The capital asset pricing model (CAPM) is an idealized portrayal of how financial markets price securities and thereby determine expected returns on capital investments.
  • The model provides a methodology for quantifying risk and translating that risk into estimates of expected return on equity.

The capital asset pricing model (CAPM) to know the value of the stock

[tex]Ke = rf + \beta ( r_{m} - r_{f} )[/tex]

risk free = 0.085

premium market =(market rate - risk free) = 0.045

beta(non diversifiable risk) 1.3

Ke = 0.085 + 1.3(0.045)

Ke = 0.14350

Now we need to know the present value of the future dividends:

D0 = 2.8

D1 = D0 × ( 1 +g ) = 2.8  = 2.8 * 1.23 = 3.444

D2 3.444 x 1.23 = 4.2361200

The next dividends, which are at perpetuity will we solve using the dividned grow model

[tex]\frac{divends}{return - growth} = Intrinsic value[/tex]

In this case dividends will be:

4.23612 x 1.07 = 4.5326484

return will be how return given by CAPM and g = 7%

plug this into the Dividend grow model.

[tex]\frac{4.5326484}{0.1435 - 0.07} = Intrinsic value[/tex]

value of the dividends at perpetity: 61.6686857

Finally is important to note this values are calculate in their current year. We must bring them to present day using the present value of a lump sum:

[tex]\frac{principal}{(1 + rate)^{time} } = PV[/tex]

[tex]\frac{3.444}{(1 + 1. 1435)^{1} } =PV[/tex]

3.011805859

[tex]\frac{4.23612}{( 1 + 0.1435)^{2} } = PV[/tex]

3.239633762

[tex]\frac{61.6686857}{(1 + 0.1435)^{2} } = PV[/tex]

47.16201531

We add them and get the value of the stock  is 53.413455.

Learn more about CAPM

brainly.com/question/17154996

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