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

^{………………………………………………………………………….}

C_t= C_t-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:

C_t+1= C_t x (1+g₂)= C₀ x (1+ g₁)^t x (1+g₂)

C_t+2= C_t+1 x (1+g₂)= C₀ x (1+ g₁)^t x (1+g₂) x (1+g₂)= C₀ x (1+ g₁)^t x (1+ g₂)²

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

^{………………………………………………………………………..}

C_t+n= C_t+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.