Question

Common stock value long 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 ​$2.30. It expects zero growth in the next year. In years 2 and​ 3, 3​% growth is​ expected, and in year​ 4, 16​% 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

Answer 1

Answer: Current stock price ($P_{0}$) = $ 51.71

Explanation:

First we'll calculate the dividends for the next 5 years and the respective Terminal value in $5^{th}$ year .

i.e. ,

$D_{0}$ = $ 2.30

$D_{1}$ = $D_{0}$ $\times$ (1 + $Growth rate_{year 1}$)

$D_{1}$ = $ 2.30 × ( 1 + 0%) = $ 2.30

$D_{2}$ = $D_{1}$ $\times$ (1 + $Growth rate_{year 2}$)

$D_{2}$ = $ 2.30 × ( 1 + 3%) = $ 2.36

$D_{3}$ = $D_{2}$ $\times$ (1 + $Growth rate_{year 3}$)

$D_{3}$ = $ 2.36 × ( 1 + 3%) = $ 2.43

$D_{4}$ =  $D_{3}$ $\times$ (1 + $Growth rate_{year 4}$)

$D_{4}$ = $ 2.43 × ( 1 + 16%) = $ 2.819

$D_{5}$ =  $D_{4}$ $\times$ (1 + $Growth rate_{year 5}$)

$D_{5}$ =  $ 2.819 × ( 1 + 11%) = $ 3.129

∵ The growth rate after $5^{th}$ year = 11%

Required rate of return (r) = 15%

∴ Terminal value ($P_{5}$) = $\frac{D_{5} \times (1 + Growth rate)}{Required rate of return - Growth rate}$

Terminal value ($P_{5}$) = $\frac{ 3.129 \times (1 + 0.11)}{0.15 - 0.11}$

Terminal value ($P_{5}$) = $ 86.85

Now, we'll compute the price per share :

Current stock price ($P_{0}$) =  $\left [ \frac{D_{1}}{(1 + r)^{n}} + \frac{D_{2}}{(1 + r)^{n}} +\frac{D_{3}}{(1 + r)^{n}} + \frac{D_{4}}{(1 + r)^{n}} + \frac{D_{5}}{(1 + r)^{n}} + \frac{P_{5}}{(1 + r)^{n}}\right ]$

where;

n = respective years

r = required rate of return

∴ Current stock price ($P_{0}$) =  $\left [ \frac{2.30}{(1 + 0.15)^{1}} + \frac{2.36}{(1 + 0.15)^{2}} +\frac{2.43}{(1 + 0.15)^{3}} + \frac{2.819}{(1 + 0.15)^{4}} + \frac{3.129}{(1 + 0.15)^{5}} + \frac{86.85}{(1 + 0.15)^{5}}\right ]$

Current stock price ($P_{0}$) = ( 2 + 1.78 + 1.59 + 1.611 + 1.55 + 43.18)

Current stock price ($P_{0}$) = $ 51.71