Question

Assume that dividends in the next three years (starting from year 2017) will grow at a rate of 13% annually. Further, it is assumed that dividends will grow at a rate of 11% for the next four years (year 4 to 7). Thereafter it is assumed that the company will grow at a constant growth rate of 7% per annum. The last dividend paid (for 2016) is $1.52. Assume a required rate of return of 12%.

Clearly show the following:

Present Value of First Stage

Present Value of Second Stage

Present Value with constant growth rate

Stock Intrinsic Value

Answer 1

According to Dividend Discount model, the intrinsic stock price today is equal to present value of all the future dividends discounted using required rate of return.

The first stage is the period of 3 years where dividends grow at the rate of 13% annually.

Dividend in year 1 (2017) will be 1.52*1.13 = $1.7176

Dividend in year 2 (2018) will be 1.52*1.13*1.13 = $1.9409

Dividend in year 3 will be 1.52*1.13*1.13*.1.13 = $2.1932

The required rate of return is 12%

Thus present value of first stage is as under where D1,D2,D3 are dividends in year 1,2,3 respectively and r is the discount rate

= D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3

= 1.7176/1.12 +(1.9409/1.12^2) + (2.1932/1.12^3)

=1.5336+1.5473+ 1.5610

=$4.6419

Thus present value of first stage is $ 4.64

The second stage is from year 4 to year 7 where dividends grow at 11%

Thus D4 = D3*1.11 = 2.1932*1.11 = $2.4345

D5 = D4*1.11 = $2.7022

D6= D5*1.11=$ 2.9995

D7=D6*1.11 = $ 3.3294

Thus present value of second stage is

D4/(1+r)^4 + D5/(1+r)^5 + D6/(1+r)^6 + D7/(1+r)^7

= 2.4345/1.12^4 + 2.7022/1.12^5 + 2.9995/1.12^6 + 3.3294/1.12^7

= $ 6.1062

Thus present value of second part is $ 6.11

Present value of last portion with constant growth rate can be found using constant dividend growth model as under

D8/{(r-g)*(1+r)^7}

According to the model, D8/(r-g) is the present value of all future cash flows till perpetuity in a year before that is in year 7. Discounting is done to bring year 7 value to today.

= D7*1.07/{(0.12-0.07)*(1.12^7)}

= 3.3294*1.07/{0.05*(1.12^7)}

= $32.2295

Thus present value of constant growth portion is $32.23

Stock intrinsic value would be the sum of all the present values calculated above of stage one stage two and constant growth stage.

= $(4.64+6.11+32.23)

=$42.98

Thus intrinsic stock price is $42.98

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