Question

Your task is to value the stock price of Harrington Ltd with the Dividend Discount Model (DDM) in stable growth. You have the following information:

Dividends per share DIV0	€1.89
Risk-free rate rF	3.00%
Beta β	1.182
Expected return on stocks	8.50%
Estimated long-term dividends growth rate	2.75%

Required:
(a) Calculate the value of the stock of Harrington Ltd using the Dividend Discount Model (DDM) in stable growth;

(b) The stock currently trades at €39.40 in the stock market; would you recommend buying it?

Answer 1

Part a:

We can calculate discount rate using Capital asset pricing model (CAPM) formula.
Discount rate =Risk free rate + Beta*(market rate of return- risk free rate of return)
Given that:
Risk-free rate=3%
Beta=1.182
Expected return on stocks (or market rate of return)=8.50%
Discount rate=3+1.182*(8.5-3)
=3+1.182*(5.5)
=3+6.50
=9.50% or .095

Value of stock using the method of dividend discount model in stable growth is given by the formula Div1/(r-g)
r= Discount rate
r =9.5% or .095 as we have calculated above
g=Long-term dividends growth rate
As given in the question, the value of g=2.75%=0.0275
Now, dividends per share (Div0)=€1.89
Div1= Dividend per share expected to be received at the end of first year = Div0*(1+g)
=1.89*(1+2.75/100)=1.89*(1+.0275)
=1.89*(1.0275)=1.94198

Using the values in the formula Div1/(r-g), we get
Value of the stock=1.94198/(.095-.0275)
=1.94198/.0675
=28.77
The value of the stock is €28.77

Part b:
The stock is currently trading at €39.40. It means that the stock is over valued. We would not recommend to buy an overvalued stock.