9) XYZ Inc. expect to pay $10 dividends next year, no dividends two years from now, and $30 dividends three years from now. After that, it will pay dividends each year and dividends will grow at a rate of 10% per year (e.g., in year 4, the dividends will be $33). What should be today's stock price if the expected stock return is 15%.
Dividend Valuation
Dividend refers to a reward or cash that a company gives to its shareholders out of the profits. Dividends can be issued in various forms such as cash payment, stocks, or in any other form as per the company norms. It is usually a part of the profit that the company shares with its shareholders.
Dividend Discount Model
Dividend payments are generally paid to investors or shareholders of a company when the company earns profit for the year, thus representing growth. The dividend discount model is an important method used to forecast the price of a company’s stock. It is based on the computation methodology that the present value of all its future dividends is equivalent to the value of the company.
Capital Gains Yield
It may be referred to as the earnings generated on an investment over a particular period of time. It is generally expressed as a percentage and includes some dividends or interest earned by holding a particular security. Cases, where it is higher normally, indicate the higher income and lower risk. It is mostly computed on an annual basis and is different from the total return on investment. In case it becomes too high, indicates that either the stock prices are going down or the company is paying higher dividends.
Stock Valuation
In simple words, stock valuation is a tool to calculate the current price, or value, of a company. It is used to not only calculate the value of the company but help an investor decide if they want to buy, sell or hold a company's stocks.
![**Problem 9: Valuing Future Dividends of XYZ Inc.**
XYZ Inc. expects the following dividend payments:
- $10 dividends next year (Year 1)
- No dividends in Year 2
- $30 dividends three years from now (Year 3)
After Year 3, XYZ Inc. will pay dividends annually, growing at a rate of 10% per year. For example, in Year 4, the dividend will be $33.
**Question:**
What should be today’s stock price if the expected stock return is 15%?
---
**Solution Approach:**
To determine today's stock price, we need to discount the expected future dividends to their present value using the expected stock return rate of 15%. Here are the steps:
1. Calculate the present value (PV) of the dividends for Year 1 and Year 3.
2. Calculate the present value of the growing dividend starting from Year 4.
**Step-by-Step Calculation:**
1. **PV of dividends in Year 1:**
- Dividend in Year 1: $10
- PV = \( \frac{10}{(1 + 0.15)^1} \)
2. **PV of dividends in Year 3:**
- Dividend in Year 3: $30
- PV = \( \frac{30}{(1 + 0.15)^3} \)
3. **Value of growing perpetuity from Year 4:**
- Dividend in Year 4: $33
- Growth rate: 10%
- The formula for a growing perpetuity: \( P = \frac{D}{r - g} \) where \( D \) is the dividend in Year 4, \( r \) is the discount rate, and \( g \) is the growth rate.
- Value at the end of Year 3 = \( \frac{33}{0.15 - 0.10} \)
- PV of this amount to today = \( \frac{\frac{33}{0.15 - 0.10}}{(1 + 0.15)^3} \)
Finally, sum all these present values to get today's stock price:
\[ PV_{\text{Year 1}} + PV_{\text{Year 3}} + PV_{\text{Perpetuity at Year 3}} \]
By evaluating these calculations, we can determine](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d98c794-b13e-4730-afe8-143f60931f40%2F44e964c0-f616-4cd8-8d26-8c166b307c27%2Fc3wewdrf_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
