Question

Common stock value—Variable growth  Home Place​ Hotels, Inc., is entering into a​ 3-year remodeling and expansion project. The construction will have a limiting effect on earnings during that​ time, but when it is​ complete, it should allow the company to enjoy much improved growth in earnings and dividends. Last​ year, the company paid a dividend of ​$4.50. It expects zero growth in the next year. In years 2 and​ 3, 5​% growth is​ expected, and in year​ 4, 21​% growth. In year 5 and​ thereafter, growth should be a constant 12​% per year. What is the maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common​ stock?

The maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common stock is ​$

Answer 1

Question 1:

g1 = growth rate = 5%

g2 = growth rate = 21%

g3 = growth rate = 12%

r = required return = 18%

D1 = Dividend in Year 1 = $4.50

D2 = D1 * (1+g1) = $4.50 * (1+5%) = $4.725

D3 = D2 * (1+g1) = $4.725 * (1+5%) = $4.96125

D4 = D3 * (1+g2) = $4.96125 * (1+21%) = $6.0031125

D5 = D4 * (1+g3) = $6.0031125 * (1+12%) = $6.723486

Horizon Value = D5 / (r - g3)

= $6.723486 / (18% - 12%)

= $112.0581

Current price of stock = [D1 / (1+r)^1] + [D2 / (1+r)^2] + [D3 / (1+r)^3] + [D4 / (1+r)^4] + [Horizon Value / (1+r)^4]

= [$4.5 / (1+18%)^1] + [$4.725 / (1+18%)^2] + [$4.96125 / (1+18%)^3] + [$6.0031125 / (1+18%)^4] + [$112.0581 / (1+18%)^4]

= [$4.5 / 1.18] + [$4.725 / 1.3924] + [$4.96125 / 1.643032] + [$6.0031125 / 1.93877776] + [$112.0581 / 1.93877776]

= $3.813559322 + $3.3934214306 + $3.0195699171 + $3.0963386438 + $57.798321351

= $71.121210662

Therefore, The maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common stock is ​$71.12