Question:
Erica is analyzing the shares of Songatikamas company. The company currently pays a dividend of $2.50. She believes the company has a new product that will result in supernormal growth of 20% for two years. Once the market for this product is saturated, she expects the Songatikamas’s growth will fall to 3%, which is equal to the level of world economic growth. Erica determines that the required return on Songatikamas should be 12%. What is the value of Songatikamas’s shares?
Value of Songatikamas's Shares
Introduction
To determine the value of Songatikamas's shares, we can use the Dividend Discount Model (DDM), specifically the multistage growth model, which accounts for different growth rates over time. Below is a detailed calculation of the share value.
Step 1: Calculate the dividends during the supernormal growth phase
Given:
 Current dividend (D_{0}) = $2.50
 Supernormal growth rate (g_{1}) = 20% or 0.20
 Number of years of supernormal growth = 2 years
For Year 1:
D_{1} = D_{0} × (1 + g_{1}) = 2.50 × 1.20 = 3.00
For Year 2:
D_{2} = D_{1} × (1 + g_{1}) = 3.00 × 1.20 = 3.60
Step 2: Calculate the dividend after the supernormal growth phase (Year 3 onward)
Given:
 Longterm growth rate (g_{2}) = 3% or 0.03
For Year 3:
D_{3} = D_{2} × (1 + g_{2}) = 3.60 × 1.03 = 3.708
Step 3: Calculate the present value of dividends during the supernormal growth phase
Given:
 Required return (r) = 12% or 0.12
For Year 1:
PV(D_{1}) = D_{1} / (1 + r)^{1} = 3.00 / (1.12)^{1} = 2.6786
For Year 2:
PV(D_{2}) = D_{2} / (1 + r)^{2} = 3.60 / (1.12)^{2} = 2.8690
Step 4: Calculate the terminal value at the end of Year 2 (PV of all future dividends from Year 3 onward)
Terminal value at Year 2 (P_{2}):
P_{2} = D_{3} / (r  g_{2}) = 3.708 / (0.12  0.03) = 41.2
Step 5: Calculate the present value of the terminal value
PV(P_{2}) = P_{2} / (1 + r)^{2} = 41.2 / (1.12)^{2} = 32.8362
Step 6: Calculate the total present value of the shares
The value of Songatikamas's shares is the sum of the present values of the dividends during the supernormal growth phase and the present value of the terminal value.
Value = PV(D_{1}) + PV(D_{2}) + PV(P_{2}) = 2.6786 + 2.8690 + 32.8362 = 38.3838
Final Answer
The value of Songatikamas's shares is approximately $38.38.
Further Reading
For more information on the Dividend Discount Model (DDM), you can refer to the following resources:
Method 2:
Valuing Songatikama's Shares
Understanding the Problem
We're tasked with valuing Songatikama's shares using the Dividend Discount Model (DDM). The company is experiencing a twoyear period of supernormal growth, followed by a steady growth phase.
Key Information
 Current Dividend (D0): $2.50
 Supernormal Growth Rate (g1): 20%
 Normal Growth Rate (g2): 3%
 Required Return (r): 12%
Solution Steps

Calculate Dividends for the Supernormal Growth Period:
 D1 = D0 * (1 + g1) = $2.50 * (1 + 0.20) = $3.00
 D2 = D1 * (1 + g1) = $3.00 * (1 + 0.20) = $3.60

Calculate the Dividend at the Start of the Steady Growth Period:
 D3 = D2 * (1 + g2) = $3.60 * (1 + 0.03) = $3.708

Calculate the Stock Price at the End of Year 2 (P2):
 Using the Gordon Growth Model for the steady growth phase:
 P2 = D3 / (r  g2) = $3.708 / (0.12  0.03) = $41.20
 Using the Gordon Growth Model for the steady growth phase:

Calculate the Present Value of Dividends and Stock Price:
 PV of D1 = D1 / (1 + r) = $3.00 / (1 + 0.12) = $2.68
 PV of D2 = D2 / (1 + r)^2 = $3.60 / (1 + 0.12)^2 = $2.86
 PV of P2 = P2 / (1 + r)^2 = $41.20 / (1 + 0.12)^2 = $32.84

Calculate the Total Value of the Stock:
 Stock Price (P0) = PV of D1 + PV of D2 + PV of P2 = $2.68 + $2.86 + $32.84 = $38.38
Conclusion
The value of Songatikama's shares, according to Erica's analysis, is $38.38.
Method 3:
1. Calculate the dividend for the next two years with 20% supernormal growth:
Year 1: $2.50 x (1 + 0.20) = $3.00
Year 2: $3.00 x (1 + 0.20) = $3.60
2. Calculate the dividend in Year 3, when growth returns to normal (3%):
Year 3: $3.60 x (1 + 0.03) = $3.708
3. Calculate the present value of the dividends for the next two years:
PV = $3.00 / (1 + 0.12)^1 + $3.60 / (1 + 0.12)^2 = $2.67 + $2.93 = $5.60
4. Calculate the present value of the dividends from Year 3 onwards, using the perpetuity formula:
PV = $3.708 / (0.12  0.03) = $3.708 / 0.09 = $41.20
5. Calculate the present value of the dividends from Year 3 onwards, discounted back to the present:
PV = $41.20 / (1 + 0.12)^2 = $41.20 / 1.2544 = $32.78
6. Add the present values of the dividends for the next two years and the present value of the dividends from Year 3 onwards:
Value of Songatikama's shares = $5.60 + $32.78 = $38.38