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

Step-by-step 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)`
`*` (1 +
`Growth rate_(year 1)`)

`D_(1)` = $ 2.30 × ( 1 + 0%) = $ 2.30

`D_(2)` =
`D_(1)`
`*` (1 +
`Growth rate_(year 2)`)

`D_(2)` = $ 2.30 × ( 1 + 3%) = $ 2.36

`D_(3)` =
`D_(2)`
`*` (1 +
`Growth rate_(year 3)`)

`D_(3)` = $ 2.36 × ( 1 + 3%) = $ 2.43

`D_(4)` =
`D_(3)`
`*` (1 +
`Growth rate_(year 4)`)

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

`D_(5)` =
`D_(4)`
`*` (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)`) =
`(D_(5) * (1 + Growth rate))/(Required rate of return - Growth rate)`

Terminal value (
`P_(5)`) =
`( 3.129 * (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 [ (D_(1))/((1 + r)^(n)) + (D_(2))/((1 + r)^(n)) +(D_(3))/((1 + r)^(n)) + (D_(4))/((1 + r)^(n)) + (D_(5))/((1 + r)^(n)) + (P_(5))/((1 + r)^(n))\right ]`

where;

n = respective years

r = required rate of return

∴ Current stock price (
`P_(0)`) =
`\left [ (2.30)/((1 + 0.15)^(1)) + (2.36)/((1 + 0.15)^(2)) +(2.43)/((1 + 0.15)^(3)) + (2.819)/((1 + 0.15)^(4)) + (3.129)/((1 + 0.15)^(5)) + (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