Question

Common stock value Variable growth Personal Finance Problem Home Place Hotels, Inc., is entering into a 3-year remodeling and expansion project. The construction will mave a limiting effect on earnings during that time, but when it is complete, it should alow the company to enjoy much improved growth in earnings and dividends. Last year, the company paid a dividend of $3.80. It expects zero growth in the next year. In years 2 and 3,3% growth is expected, and in year 4, 18% growth. In year 5 and thereafter, growth should be a constant 11% per year. What is the maximum price per share that an investor who requires a return of 15% should pay for Home Place Hotels common stock? The maximum price per share that an investor who requires a return of 15% should pay for Home Place Hotels common stock is $ (Round to the nearest cent.)

Answer 1

Maximum price per share is equal to the present value of all future dividends
Year	Dividend	PV Factor	PV
1	3.8	0.869565217	3.304347826
2	3.914	0.756143667	2.959546314
3	4.03142	0.657516232	2.65072409
4	4.7570756	0.571753246	2.719873414
Terminal Value	132.0088479	0.571753246	75.47648723
		Price	87.11097888
Hence, maximum price to be paid = $87.11

Answer 2

SOLUTION :

(Values in $) :

Last dividend, D0  = 3.80 

No growth in dividend next year.

Dividend next year, D1 = 3.80

Dividend growth in year 2 and 3 = 3.3% = 0.033

Dividend in year 2, D2 = 3.80*(1 + 0.033) = 3.9254

Dividend in year 3, D3 = 3.9254*(1 + 0.033) = 4.0550

Dividend growth in year 4 = 4.18% = 0.0418 

Dividend in year 4, D4 = 4.0550*(1 + 0.0418) = 4.2245

Dividend growth in year 5 and in future = 11% = 0.11 (constant)

Dividend in year 5, D5 = 4.2245*(1 + 0.11) = 4.6892

So,

As per constant growth dividend model :

Required rate of return, r = 15% = 0.15

=> 1 + r = 1.15

Growth rate, g = 11% = 0.11 from year 5 onwards.

So, 

P4 (price at year 4 end) = D5/(r - g) = 4.6892/(0.15 - 0.11) = 117.23 

P0 (price today) 

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

= 3.80/1.15 + 3.9254/1.15^2 + 4.0550/1.15^3 + (4.2245+117.23)/1.15^4

= 78.38 

Hence,

Maximum price that can be paid for 15% rate of return = $78.38  (ANSWER).