Questions:
What is a two-stage discount model for valuation?

I am trying to value a stock in my portfolio. The stock paid a dividend of $5 recently. Based on the most recent earnings call, I expect the dividend will keep on growing for the next 5 years at a rate of 10% per year and then have a constant growth rate of 2% from that point on. My required rate of return in this portfolio is 12%. 

What will be the value of this stock using the two stage dividend discount model?

Reference answers:
A two-stage discount model is a method used in finance and economics to value a company or project by applying different discount rates to different phases or stages of its cash flows. 

In the initial stage, the company or project is expected to experience high growth. This phase might reflect early development, rapid market penetration, or significant expansion. Cash flows during this stage are often uncertain but are expected to grow rapidly.

After the high-growth phase, the company or project is expected to reach a more stable growth rate. Cash flows in this stage are typically more predictable and grow at a more moderate rate.

# Formula

Stock Value = Stock Value for the first first short period + Stock value onwards for the period of indefinite growth 

Stock Value for the first shorter period = D (1+g1)^1 / (1+r)^ 1+ D (1+g1)^2 / (1+r)^ 2+ D (1+g1)^3 / (1+r)^ 3+ ... + D(1+r)^n/(1+r)^n + [Dn(1+g2) / (r-g2) ] / (1+r) ^ n 

Where:
D = The current dividend 
g1 = The growth rate for the first part. 
r = the required rate of return 
N = number of periods 

Stock Value for the period of indefinite growth = D (1+g1)^n (1+g2) / (r-g2)(1+r)^n

## Step 1

Stock Value = Stock Value for the first 5 years + Stock value onwards 

Stock Value for the first 5 years =  [5 (1+0.1)^1 / (1+0.12)^ 1] + [5 (1+.1)^2 / (1+.12)^ 2] + [5 (1+.1)^3 / (1+.12)^ 3] + [5 (1+.1)^4 / (1+.12)^ 4] + [5 (1+.1)^5 / (1+.12)^ 5] 

= 4.91 + 4.82 + 4.74 + 4.65 + 4.57 

= 23.68  

## Step 2

Stock Value for the period of indefinite growth = D (1+g1)^n (1+g2) / (r-g2)(1+r)^n

= 5(1+ 0.1)^5 (1 + 0.02) / (0.12 - 0.2) (1 + 0.12)^5

= 46.60 

## Step 3: Total Value

Stock Value = Stock Value for the first first short period + Stock value onwards for the period of indefinite growth 

Stock Value = 23.68 + 46.60  = 70.28  


The value of this stock using the two stage dividend discount model is $70.28.