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Present Value with the Two-Stage Growth Rate

Present Value with the Two-Stage Growth Rate

This model assumes the future cash flows will grow at different rates for the different periods.

Present value with the two-stage growth rate is often applied to find present value or current price of ordinary share (common stock).

Time Line

Constant growth rate g1 during a first stage of growth from period 0 to period t, and cash flows as follows:

C1= C0 x (1+g1)

C2= C1 x (1+ g1)= C0 x (1+ g1)x(1+ g1)= C0 x (1+ g1)2

C3= C2 x (1+ g1)= C0 x (1+ g1)2 x (1+ g1)= C0 x (1+ g1)3

………………………………………………………………………….

Ct= Ct-1 x (1+ g1)= C0 x (1+ g1)t-1 x (1+ g1)= C0 x (1+ g1)t

Constant growth rate g2 during a perpetual second stage of growth from period t onwards, and cash flows as follows:

Ct+1= Ct x (1+g2)= C0 x (1+ g1)t x (1+g2)

Ct+2= Ct+1 x (1+g2)= C0 x (1+ g1)t x (1+g2) x (1+g2)= C0 x (1+ g1)t x (1+ g2)2

Ct+3= Ct+2 x (1+g2)= C0 x (1+ g1)t x (1+ g2)x (1+g2)= C0 x (1+ g1)t x (1+ g2)3

………………………………………………………………………..

Ct+n= Ct+n-1 x (1+g2)= C0 x (1+ g1)t x (1+ g2)n-1  x (1+g2)= C0 x (1+ g1)t x (1+ g2)n

…………………………………………………………………………..

C0 : base amount at the beginning of period 1 (Period 0)

Question 

Suppose HBN Company has a current dividend of Co = $5, which is expected to  shrink at the rate g1= -10 percent for T = 5 years and thereafter grow at the rate g2= 4 percent. With a discount rate of r = 10 percent, what is the value of the stock?

Solution

Using the two-stage model, present value, Po, is calculated as:

Co=$5, g1= -10%, T = 5 years, g2= 4%, and r = 10%

So PV = $14.25 + $31.78= $46.03

The total present value of $46.03 is the sum of a $14.25 present value of the first five dividends plus a $31.78 present value of all subsequent dividends.

 

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