Question

9. (RWJ, exercise 5.19) Whizzkids Inc., is experiencing a period of rapid growth. Earnings and dividends are expected to grow at a rate of 18% during the next two years, 15% in the third year, and at a constant rate of 6% thereafter. Whizzkids' last dividend, which has just been paid, was $1.15. If the required rate of return on the stock is 12%, what is the price of the stock today?

Answer 1

The variable-growth model is a dividend valuation approach that allows for a change in the dividend growth rate.

The company has paid $1.15 as last years' dividend, therefore D_{0 =} 1.15

Step 1: To calculate the expected dividends for First, Second and Third Year

Therefore, D_{1 =} D₀ (1+g)

Where, D₁ is the expected dividend to be paid at the end of year 1
g = growth rate
D_{0 =} Last years' dividend

D_{1 =} 1.15 ( 1 + 0.18 ) = 1.357
D_{2 =} D1 (1+g) = 1.357 ( 1+0.18 ) = 1.60126
D_{3 =} D₂ ( 1+g) = 1.60126 ( 1+ 0.15 ) = 1.8414

Step 2: Present value of the dividends for First, second and Third Year with the discounting rate of 12%.

Year	Dividend	Discounting factors @ 12 %	Present value of Dividends
1	1.3570	0.8929	1.2116
2	1.6013	0.7972	1.2765
3	1.8414	0.7118	1.3107
			3.7988

Present values of dividends can be calculated by multiplying Dividend column by discounting factor column.

Therefore, the sum of present values of dividends is $3.7988

Step 3: Calculation of the value of the share at the end of year 3 when the dividend is growing at a constant rate.

D_{4 =} D3( 1+g) = 1.8414 ( 1 + 0.06 ) = 1.9519

Using constant growth Model,

P_{3 =} D₄ / (K_e - g)

Where, P₃ is the price of the share at the end of Third Year
  D₄ is the expected dividend at the end of year 4
g is the growth rate at which share is expected to grow constantly i.e 6%
K_e is the rate of return expected by the investors i.e. 12%

Therefore, P_{3 =}1.9519/ (0.12- 0.06) = 32.5317

Step 4: Calculation of the Present value of the share at the end of year 3 when the dividend is growing at a constant rate

  P₃ * discounting factor @ 12% for the Third Year

= 32.5317 * 0.7118 = $23.157

Step 5: Calculation of the price of the share today

P_{0 =} (Present Value of the dividends for first, second and third Year) + (Calculation of the Present value of the share at the end of year 3)

= 3.7988 + 23.157

= $26.9558

Hence, the price of the stock today is $26.9558.