Question

A company currently pays a dividend of $2.4 per share (D₀ = $2.4). It is estimated that the company's dividend will grow at a rate of 23% per year for the next 2 years, and then at a constant rate of 7% thereafter. The company's stock has a beta of 1.1, the risk-free rate is 9.5%, and the market risk premium is 5%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

$  

2. You buy a share of The Ludwig Corporation stock for $21.90. You expect it to pay dividends of $1.07, $1.1374, and $1.2091 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.31 at the end of 3 years.

1. Calculate the growth rate in dividends. Round your answer to two decimal places.

     %

2. Calculate the expected dividend yield. Round your answer to two decimal places.

     %

3. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock's expected total rate of return (assume market is in equilibrium with the required rate of return equal to the expected return)? Do not round intermediate calculations. Round your answer to two decimal places.

     %

Answer 1

1. cost of equity=risk free rate+(beta*market risk premium)=9.5%+(1.1*5%)=15%

D1=D0*(1+23%)=$2.4*1.23=2.952

D2=D1*(1+23%)=2.952*1.23=3.63

D3=D2*(1+7%)=3.63*1.07=3.885

Horizon value at year2=D3/(cost of equity-growth rate)=3.885/(15%-7%)=$48.56

Value of the Stock=(D1/(1+15%))+((D2+Horizon value at year2)/(1+15%)^2)

=(2.952/1.15)+(52.2/1.15^2)

=2.57+39.47

=$42.03

2. a. growth rate=((Year3 Dividend/Year1 dividend)^(1/2))-1 (2 beacause of 2 years of growth)

=((1.2091/1.07)^(1/2))-1

=6.3%

b. Expected dividend yield=D1/Current Share price=1.07/21.90=4.89%

c. Expected total rate of return=dividend yield+growth rate=4.89%+6.3%=11.19%