Question

A firm expects to pay dividends at the end of each of the next four years of $2.00, $1.50, $2.50, and $3.50. If growth is then expected to level off at 13 percent, and if you require a 18 percent rate of return, how much should you be willing to pay for this stock?

Answer 1

The value of the stock must be calculated with the DCF method here. We sum up the dividends for first 4 years and the terminal value, discounting all these figures to t=0.

Step 1: Dividends

The PV of all flows for first 4 years of the dividend is:

The total of these values of dividend at t=0 is $6.0990

Step 2: Terminal value according to steady dividends year 5 onwards

Next we calculate the value of the stock with dividends steady at 13% at the end of year 5 as per gordon's growth model (Terminal value at year 4)

At year 5 end, with a 13% growth the dividend becomes $3.5*1.13= $3.96

As per the gordon growth model, price at Year 4 end= Dividend of yr 5/r-g

=3.96/(.18-.13) = $3.96/.05=$79.1

In above, 18% is the required rate and 13% is the dividend growth rate every year. Please note the specific detail that the value given by this is year 5 dividend used to give the figure for year 4 end, This value of $79.1 is to be brought to T=0. Thus we must multiply 79.1 with PV factor 0.5158 (derived in excel above) giving us $40.80

Step 3: Dividends + Terminal value = stock value (all figures at T=0)

This becomes

= $5.82+ $40.80 = $46.90

As per the explanation above, the formula for value of stock can also be derived with NPV as: =NPV(18%,2,1.5,2.5,3.5+79.1) giving value of 46.90

This is the value of the stock which yoou will be willing to pay today.

(NOTE: There was a typo error in formula for PV factor in excel sheet snapshot. The fourth year PV value is incorrect because of typo error (1/1.18^4) whereas earlier it was input as 1/1.18^5 (the 5 was a typo error in the formula)