Question

Common stock valuelong dash Variable growth  Personal Finance Problem   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 ​$4.20. It expects zero growth in the next year. In years 2 and​ 3, 5​% growth is​ expected, and in year​ 4, 15​% growth. In year 5 and​ thereafter, growth should be a constant 8​% per year. What is the maximum price per share that an investor who requires a return of 14​% should pay for Home Place Hotels common​ stock?

Answer 1

Maximum foice per share not = PV of all future dividendly = Dit Dg + D t . Dy (1+22. (1+0) 3 to runes hull Ds prof duidends Trowing of constant dot EP do oteprate after yeat y tu Parptates = + 4.2 1145 4.28105 (1.14) 2 + 4.2X(105) + 4.9x105) X ) A (1.14)3 2 s + I . 4.27(105)x145x7.08 v 0.14 - 0.08

Answer 2

SOLUTION :

(Values in $) :

Last dividend, D0  = 4.20

No dividend growth next year.

Dividend next year, D1 = 4.20

Dividend growth in year 2 and 3 = 5.0% = 0.05

Dividend in year 2, D2 = 4.20*(1 + 0.05) = 4.41

Dividend in year 3, D3 = 4.41*(1 + 0.05) = 4.6305

Dividend growth in year 4 = 15% = 0.15

Dividend in year 4, D4 = 4.6305*(1 + 0.15) = 5.3251

Dividend growth in year 5 and in future = 8% = 0.08 (constant)

Dividend in year 5, D5 = 5.3251*(1 + 0.08) = 5.7511

So,

As per constant growth dividend model :

Required rate of return, r = 14% = 0.14

=> 1 + r = 1.17

Growth rate, g = 8% = 0.05 from year 5 onwards.

P4 (price at year 4 end) = D5/(r - g) = 5.7511 /(0.14 - 0.08) = 95.85 

P0 (price today) 

= D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + (D4 + P4)/(1+r)^4

= 4.20/1.14+ 4.41/1.14^2 + 4.6305/1.14^3 + (5.7511+95.85)/1.14^4

= 70.36

Hence,

Maximum price that can be paid for 14% rate of return = $70.36 per share  (ANSWER).