Question

Mike is analyzing the value of Tata Chemicals Ltd. (Bombay Stock Exchange: TATACHEM). Tata Chemicals is India’s leading manufacturer of inorganic chemicals, and also manufactures fertilizers and food additives. Mike has concluded that the DDM is appropriate to value Tata Chemicals.

During the last five years (fiscal year ending 31 March 2014 to fiscal year ending 31 March 2018), the company has paid dividends per share (in dollars) 5.50, 6.50, 7.00, 8.00, and 9.00, respectively. These dividends suggest an average annual growth rate in DPS of just above 13 percent. Mike has decided to use a three-stage DDM with a linearly declining growth rate in Stage 2. He considers Tata Chemicals to be an average growth company, and estimates Stage 1 (the growth stage) to be 6 years and Stage 2 (the transition stage) to be ten years. He estimates the growth rate to be 14 percent in Stage 1 and 10 percent in Stage 3. Mike has estimated the required return on equity for Tata Chemicals to be 16 percent. Estimate the current value of the stock.

Answer 1

Above is the formula for finding the price of the stock using the H - model or 3 stage dividend discount model.

N - number of years in the initial growth stage

r - required rate of return

D₁ - next year's dividend

G₁ - growth rate of dividends in the initial stage

G₂ - growth rate of dividends in the final stage

H - half of the duration of the transitionary period

D₀ = 9

G₁ = 14%

G₂ = 10%

r = 16%

H = 5

N = 6

Stock value = [D₀ x (1 + G₁)¹ / (1 + r)¹] + [D₀ x (1 + G₁)² / (1 + r)²] + [D₀ x (1 + G₁)³ / (1 + r)³] + [D₀ x (1 + G₁)⁴ / (1 + r)⁴​​​​​​​] + [D₀ x (1 + G₁)⁵ / (1 + r)⁵​​​​​​] + [D₀ x (1 + G₁)⁶ / (1 + r)⁶​​​​​​​] + [ D₀ x (1 + G₁)⁶ x (1 + G₂) + D₀ x (1 + G₁)⁶ x H x (G₁ - G₂)] / (r - G₂) / (1 + r)^N

= [9 x (1 + 0.14)¹ / (1 + 0.16)¹] + [9x (1 + 0.14)² / (1 + 0.16)²​​​​​​​] + [9x (1 + 0.14)³ / (1 + 0.16)³​​​​​​​] + [9x (1 + 0.14)⁴ / (1 + 0.16)⁴​​​​​​​] + [9x (1 + 0.14)⁵ / (1 + 0.16)⁵​​​​​​] + [9x (1 + 0.14)⁶ / (1 + 0.16)⁶​​​​​​​] + [ 9x (1 + 0.14)⁶ x (1 + 0.1) + 9 x (1 + 0.14)⁶ x 5 x (0.14 - 0.1)] / (0.16 - 0.1) / (1 + 0.16)⁶​​​​​​​

= 122.939