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.

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?

Solutions

Expert Solution

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)

jeff jeffy answered 2 years ago

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