Question

Would you explain how you get the following answer $47.5

The risk free rate is 5%, the return on the market is 10%, and Stability Inc. has a beta of 2. The most recent dividend was $2. Dividends are expected to increase at a constant rate of 100 percent for the next three years, decrease by 50% for two years, and then increase at a constant rate of 5% rate thereafter. What is the value of the stock today?

Answer 1

r = rF + beta[rM - rF]

= 5% + 2[10% - 5%] = 5% + 10% = 15%

P0 = [D0(1 + g1) / (1 + r)] + [D0(1 + g1)² / (1 + r)²] + [D0(1 + g1)³ / (1 + r)³] +

[D0(1 + g1)³(1 + g2) / (1 + r)⁴] + [D0(1 + g1)³(1 + g2)² / (1 + r)⁵] +

[D0(1 + g1)³(1 + g2)²(1 + gC) / (r - gC)(1 + r)⁵]

= [($2 x 2) / 1.15] + [($2 x 2²) / 1.15²] + [($2 x 2³) / 1.15³] + [($2 x 2³ x 0.5) / 1.15⁴] +

[($2 x 2³ x 0.5²) / 1.15⁵] + [($2 x 2³ x 0.5² x 1.05) / {(0.15 - 0.05) x 1.15⁵}]

= $3.48 + $6.05 + $10.52 + $4.57 + $1.99 + $20.88 = $47.49, or $47.5