Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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![**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](https://content.bartleby.com/qna-images/question/8d98c794-b13e-4730-afe8-143f60931f40/44e964c0-f616-4cd8-8d26-8c166b307c27/c3wewdrf_processed.jpeg)
Transcribed Image Text:**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
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