Question

Show all your work (use of formula, etc.) in solving the problems. You still need to show your work even if you use the financial calculator to get the answers.

5. Rizzi Co. is growing quickly. The company just paid a $1.6 per share dividend and dividends are expected to grow at a 25%, 15% and 10% rate respectively for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 11 percent, what is the current share price?

Answer 1

D₀ = $ 1.6

Computation of future dividends:

D₁ = D₀ + D₀ x 25 % = $ 1.6 + $ 1.6 x 0.25 = $ 1.6 x 1.25 = $ 2

D₂ = D₁ + D₁ x 15 % = $ 2 x 1.15 = $ 2.30

D₃ = D₂ + D₂ x 10 % = $ 2.30 x 1.1 = $ 2.53

D₄ = D₃ + D₃ x 6 % = $ 2.53 x 1.06 = $ 2.6818

Share price, P₃ in year 3 can be computed using Dividend Discount Model as:

P₃ = D₄ / (k – g)

k = required rate of return = 11 %

g = Constant growth rate of dividend = 6 %

P₃ = $ 2.6818 / (0.11 – 0.06)

     = $ 2.6818 / 0.05 = $ 53.636

Current share price, P₀ = $ 2/ (1+r) + $ 2.3/ (1+r) ² + $ 2.53/ (1+r) ³ + $ 53.636/ (1+r) ³

                                 = $ 2/ (1+0.11) + $ 2.3/ (1+0.11) ² + $ 2.53 / (1+0.11) ³ + $ 53.636/ (1+0.11) ³

                                 = $ 2/ (1.11) + $ 2.3/ (1.11) ² + $ 2.53 / (1.11) ³ + $ 53.636/ (1.11) ³

                                 = $ 2/ 1.11 + $ 2.3/ 1.2321 + $ 2.53 / 1.367631 + $ 53.636/ 1.367631

                                 = $ 1.8018018018 + $ 1.86673159646 + $ 1.84991419469 + $ 39.2181809275

                                 = $ 44.73662852041 or $ 44.74

Current share price is $ 44.74