Stock W plans to retain ali earnings for
5
years. Their first dividend in year
6
is expected to be $
2
.
6
.
The growth rate is expected to be
7
.
2
%
.
The required return is
1
7
.
1
%
.

Question

Stock W plans to retain ali earnings for 
5
 ﻿years. Their first dividend in year 
6
 ﻿is expected to be $
2
.
6
.
 ﻿The growth rate is expected to be 
7
.
2
%
.
 ﻿The required return is 
1
7
.
1
%
.
 ﻿What price should 
W
 ﻿sell for in 
5
 ﻿years?
1
0
1
2
1
4
1
6
1
8
2
0
2
2
2
4
2
6
2
8

VIPSolutions · Accepted Answer

Given:

- **First dividend ($D_6$)**: $2.60  
- **Dividend growth rate ($g$)**: 7.2%  
- **Required return ($r$)**: 17.1%  
- **You want the price at the end of year 5 ($P_5$), i.e., just before the first dividend is paid.**

This is a classic **delayed dividend** or **non-dividend paying period** problem.

### Step 1: Price at Year 5 ($P_5$)
At the end of year 5, the price of the stock should be the present value of all future dividends starting from year 6, which is a growing perpetuity:

$$
P_5 = \frac{D_6}{r - g}
$$

### Step 2: Plug in the values

- $D_6 = 2.60$
- $r = 17.1\% = 0.171$
- $g = 7.2\% = 0.072$

$$
P_5 = \frac{2.60}{0.171 - 0.072} = \frac{2.60}{0.099} \approx 26.26
$$

### Step 3: Closest Answer Choice

From your options:

1. 10
2. 12
3. 14
4. 16
5. 18
6. 20
7. 22
8. 24
9. 26
10. 28

The closest is **26**.

---

## **Final Answer**

$$
\boxed{26}
$$
Stock W should sell for **$26** in 5 years.

✨ VIPSolutions

Stock W plans to retain ali earnings for 5 years. Their first dividend in year 6 is expected to be $ 2 . 6 . The growth rate is expected to be 7 . 2 % . The required return is 1 7 . 1 % . What price should W sell for in 5 years? 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8

Question:

Final Answer:

📢 Instructions:

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