Give step-by-step solution with explanation and final answer:
Home Place Hotels, Inc.,
i
s
entering into
a

3
-
year remodeling and expansion project. The construction will have a
l
i
m
i
t
i

Question

Give step-by-step solution with explanation and final answer: 
Home Place Hotels, Inc., 
i
s
 ﻿entering into 
a

3
-
year remodeling and expansion project. The construction will have a 
l
i
m
i
t
i
n
g
 ﻿effect 
o
n
 ﻿earnings during that time, but when 
i
t
 
i
s
 ﻿ complete, 
i
t
 ﻿should allow the company 
t
o
 ﻿enjoy much improved growth 
i
n
 ﻿earnings and dividends. Last year, the company paid a dividend 
o
f
 ﻿ $ 
2
.
4
0
.
 
I
t
 ﻿expects zero growth 
i
n
 ﻿the next year. 
I
n
 ﻿years 
2
 ﻿and 
3
,
 
4
 
%
 ﻿growth 
i
s
 ﻿ expected, and 
i
n
 ﻿year 
4
,
 
1
9
 
%
 ﻿growth. 
I
n
 ﻿year 
5
 ﻿and thereafter, growth should 
b
e
 ﻿a constant 
5
 
%
 ﻿per year. What 
i
s
 ﻿the maximum price per share that 
a
n
 ﻿investor who requires a return 
o
f
 
1
6
 
%
 ﻿should pay for Home Place Hotels common stock?
The maximum price per share that 
a
n
 ﻿investor who requires a return 
o
f
1
6
 
%
 ﻿should pay for Home Place Hotels common stock 
i
s
 ﻿ $
enter your response here

VIPSolutions · Accepted Answer

Let's break down the problem step by step:

**Given:**
- Last year’s dividend, $ D_0 = \$2.40 $
- Year 1: Zero growth ($ D_1 = D_0 $)
- Years 2 and 3: 4% growth per year
- Year 4: 19% growth
- Year 5 and thereafter: 5% constant growth
- Required rate of return ($ r $): 16%

We are to find the **maximum price an investor should pay for the stock today**.

---

## **Step 1: Calculate Dividends for Each Year**

### **Year 1:**
$$
D_1 = D_0 \times (1 + 0) = \$2.40 \times 1 = \$2.40
$$

### **Year 2:**
$$
D_2 = D_1 \times (1 + 0.04) = \$2.40 \times 1.04 = \$2.496
$$

### **Year 3:**
$$
D_3 = D_2 \times (1 + 0.04) = \$2.496 \times 1.04 = \$2.59584
$$

### **Year 4:**
$$
D_4 = D_3 \times (1 + 0.19) = \$2.59584 \times 1.19 = \$3.0890456
$$

### **Year 5:**
$$
D_5 = D_4 \times (1 + 0.05) = \$3.0890456 \times 1.05 = \$3.2434989
$$

---

## **Step 2: Find the Price at Year 4 (Start of Constant Growth)**

From Year 5 onward, dividends grow at 5% **forever**. We can use the **Gordon Growth Model** to find the price at the end of Year 4 ($ P_4 $):

$$
P_4 = \frac{D_5}{r - g} = \frac{\$3.2434989}{0.16 - 0.05} = \frac{\$3.2434989}{0.11} = \$29.4863536
$$

---

## **Step 3: Discount All Cash Flows to Present Value (Year 0)**

The price today is the **present value** of all expected future cash flows:

$$
P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{D_4}{(1+r)^4} + \frac{P_4}{(1+r)^4}
$$

Plug in the numbers:

- $ r = 0.16 $
- $ D_1 = \$2.40 $
- $ D_2 = \$2.496 $
- $ D_3 = \$2.59584 $
- $ D_4 = \$3.0890456 $
- $ P_4 = \$29.4863536 $

Now, calculate each term:

1. $ \frac{2.40}{1.16^1} = \frac{2.40}{1.16} = 2.06897 $
2. $ \frac{2.496}{1.16^2} = \frac{2.496}{1.3456} = 1.85533 $
3. $ \frac{2.59584}{1.16^3} = \frac{2.59584}{1.560896} = 1.66336 $
4. $ \frac{3.0890456}{1.16^4} = \frac{3.0890456}{1.81063936} = 1.70658 $
5. $ \frac{29.4863536}{1.81063936} = 16.28203 $

Now sum all the present values:

$$
P_0 = 2.06897 + 1.85533 + 1.66336 + 1.70658 + 16.28203 = \boxed{23.58}
$$

---

## **Final Answer**

$$
\boxed{\$23.58}
$$

**The maximum price per share that an investor who requires a 16% return should pay for Home Place Hotels common stock is \$23.58.**

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