20.5: Growth Models and the Cost of Common Equity

Question 1

Why is it important to adjust for growth when valuing a firm’s stock?

Answer 1

Adjusting for growth is crucial because firms typically expect earnings to increase over time due to factors like inflation or real business activity.

Growth prospects significantly impact a firm’s valuation.

Question 2

How can you assess a firm’s growth prospects using stock prices?

Answer 2

By comparing the stock’s market price with the perpetuity value of its current dividend and examining the remaining percentage attributed to future growth opportunities.

Question 3

How is the perpetuity value of a stock calculated using its dividend?

Answer 3

Perpetuity Value = DPS / Dividend Yield
where:
- DPS = Dividend Per Share
- Dividend Yield = Annual dividend payment divided by stock price

Question 4

What is the formula for the constant growth model (Gordon Model)?

Answer 4

P0 = D1 / (ke - g)
where:
- P0 = Price of the stock today
- D1 = Expected dividend next year
- ke = Required return by investors
- g = Constant growth rate

Question 5

How is the cost of equity calculated using the discounted cash flow model?

Answer 5

ke = (D1 / P0) + g
where:
- D1 = Expected dividend next year
- P0 = Current stock price
- g = Growth rate of dividends

Question 6

How do you calculate the cost of common equity using internal funds for a firm with a $25 stock price and $1.05 expected dividend?

Answer 6

ke = ($1.05 / $25) + 0.05 = 0.042 + 0.05 = 9.2%

Question 7

What is the formula to adjust the cost of equity for new share issues?

Answer 7

kne = D1 / NP + g
where:
- NP = Net proceeds from the stock issue
- D1 = Expected dividend next year
- g = Growth rate of dividends

Question 8

How do you calculate the cost of equity when issuing new shares with 5% flotation costs?

Answer 8

With NP = $23.75,

ke = ($1.05 / $23.75) + 0.05 = 9.42%

Question 9

How does growth impact the valuation of common equity?

Answer 9

Growth affects the expected future cash flows, impacting the present value of dividends and the overall valuation of the firm’s equity.

Question 10

What are the limitations of using a simple perpetuity model for valuing stocks?

Answer 10

The perpetuity model assumes constant dividends and growth, which is unrealistic for firms with expected earnings changes. It works best for firms with no growth prospects.

Question 11

What is the Dividend Discount Model (DDM) used for?

Answer 11

The Dividend Discount Model is used to estimate the value of a stock based on the present value of expected future dividends, accounting for a constant growth rate.

Question 12

What does the perpetuity value represent in stock valuation?

Answer 12

The perpetuity value represents the value of a stock based on the assumption that dividends are constant and continue indefinitely without growth.

Question 13

How do growth opportunities influence a stock’s price?

Answer 13

Growth opportunities can significantly increase a stock’s price by enhancing investor expectations of future earnings, thus attributing more value to potential growth than to current dividends.

Question 14

What are the limitations of using perpetuity models for stock valuation?

Answer 14

Perpetuity models assume constant dividends and growth, which may not accurately reflect firms with changing earnings. They are best suited for companies with stable, predictable cash flows.

Question 15

How does expected growth affect the required return on equity?

Answer 15

Expected growth reduces the required return on equity because investors anticipate higher future earnings, allowing them to accept a lower return today in exchange for potential growth.

Question 16

What role does dividend yield play in stock valuation?

Answer 16

Dividend yield represents the annual dividend payment relative to the stock price and is a critical factor in assessing a stock’s income-generating potential relative to its price.

Question 17

How can you determine the percentage of a stock’s price attributed to growth?

Answer 17

To determine the percentage attributed to growth, compare the stock price to its calculated perpetuity value and analyze the difference as growth-related.

Question 18

How is the growth rate of a firm estimated using ROE?

Answer 18

The growth rate is estimated by multiplying the firm’s retention rate (b) by its Return on Equity (ROE), given as:
Growth Rate (g) = b × ROE
where:
- b = Retention rate (1 - payout ratio)
- ROE = Return on Equity

Question 19

What is the sustainable growth rate, and why is it important?

Answer 19

The sustainable growth rate is the maximum growth rate a firm can achieve without increasing financial leverage, based on its ability to reinvest earnings.

It’s crucial for maintaining a stable financial structure.

Question 20

How does the constant growth model incorporate ROE?

Answer 20

In the constant growth model, the price per share is given by:
P0 = D1 / (ke - b × ROE)
where:
- P0 = Current stock price
- D1 = Expected dividend next year
- ke = Required rate of return
- b = Retention rate
- ROE = Return on Equity

Question 21

What is the relationship between a firm’s ROE and its share price?

Answer 21

A higher ROE typically leads to a higher share price because investors anticipate better returns from reinvested earnings, resulting in larger future dividends and earnings.

Question 22

How does the retention rate impact a firm’s growth potential?

Answer 22

The retention rate impacts growth by determining how much of the firm’s earnings are reinvested.

A higher retention rate can lead to more growth if ROE is sufficient to justify reinvestment.

Question 23

What is the hurdle rate, and why is it significant in investment decisions?

Answer 23

The hurdle rate is the minimum required return on an investment to create value. Investments below this rate destroy value and should not be pursued.

Question 24

Distinguish between a growing firm and a growth firm.

Answer 24

A growing firm increases its earnings and dividends steadily, while a growth firm has opportunities to reinvest at a high ROE, potentially creating more value and higher returns for shareholders.

Question 25

How does ROE affect firm valuation and investor expectations?

Answer 25

ROE affects firm valuation by influencing investor expectations of future earnings growth.

High ROE can attract investment, while low ROE may signal inefficiencies or lack of growth opportunities.

Question 26

How does a firm’s dividend payout policy affect shareholder value?

Answer 26

The dividend payout policy affects shareholder value by balancing between returning profits to shareholders and retaining earnings for reinvestment, which can drive growth and increase share price.

Question 27

What does earnings yield indicate about a firm’s cost of equity?

Answer 27

Earnings yield, the inverse of the P/E ratio, indicates the return expected by investors.

It should align with the firm’s cost of equity to ensure that the stock is priced fairly relative to its earnings potential.

Question 28

How does the retention rate influence the share price?

Answer 28

The retention rate influences share price through its effect on growth expectations. If the rate is too high without adequate ROE, it might not increase share price; if it’s optimal, it can boost the price by enhancing growth prospects.

Question 29

How is the expected dividend yield calculated in relation to ROE?

Answer 29

Expected Dividend Yield = (1 - b) × ROE
where:
- b = Retention rate
- ROE = Return on Equity

Question 30

What is a multiple-stage growth model in finance?

Answer 30

The multiple-stage growth model is a version of the Discounted Dividend Model (DDM) that accounts for different levels of growth in a firm’s earnings and dividends over time, reflecting varying growth phases.

Question 31

What does the Present Value of Existing Opportunities (PVEO) represent?

Answer 31

PVEO is the value of a firm’s current operations, assuming no further investments are made, reflecting the perpetuity value of existing earnings.

Question 32

How is the Present Value of Growth Opportunities (PVGO) defined?

Answer 32

PVGO is the net present value (NPV) of a firm’s future investments, representing the potential additional value from anticipated growth opportunities beyond existing operations.

Question 33

How is the stock price calculated using PVEO and PVGO in the multiple-stage growth model?

Answer 33

P0 = (ROE1 × BVPS) / ke + [Inv / (1 + ke)] × [(ROE2 - ke) / ke]
where:

• P0 = Current stock price
• ROE1 = Return on Equity for existing opportunities
• BVPS = Book value per share
• ke = Required rate of return
• Inv = Investment amount for future growth
• ROE2 = Return on Equity for future growth opportunities

Question 34

What are the different firm types based on growth potential?

Answer 34

What are the different firm types based on growth potential?
A: Firms are categorized as:
- Star: High PVEO and high PVGO
- Cash Cow: High PVEO and low PVGO
- Turnaround: Low PVEO and high PVGO
- Dog: Low PVEO and low PVGO

Question 35

What are the characteristics of a “Star” firm?

Answer 35

A “Star” firm has high existing operational value (PVEO) and excellent growth prospects (PVGO), indicating strong current and future potential.

Question 36

What defines a “Cash Cow” firm?

Answer 36

A “Cash Cow” firm generates significant cash flows from existing operations (high PVEO) but has limited future growth opportunities (low PVGO).

Question 37

What is a “Turnaround” firm?

Answer 37

A “Turnaround” firm has low current operational value (low PVEO) but possesses substantial growth opportunities (high PVGO) that can lead to improved performance.

Question 38

What is a “Dog” firm in financial analysis?

Answer 38

A “Dog” firm has both low existing operational value (PVEO) and limited growth prospects (PVGO), making it a candidate for poor investment returns or potential takeover.

Question 39

How do earnings yield and growth opportunities correlate?

Answer 39

Firms with low earnings yield often have high growth opportunities (high PVGO), indicating investors expect future returns from growth rather than current earnings.

Question 40

Why is it important to evaluate investment decisions based on ROE and PVGO?

Answer 40

Evaluating investments based on ROE and PVGO ensures that investments are made at rates exceeding the cost of equity, creating value for shareholders.

Question 41

Why are growth opportunities crucial in firm valuation?

Answer 41

Growth opportunities significantly influence a firm’s valuation by providing potential for future earnings expansion, which can enhance shareholder value.

Question 42

What is the Fed model used for in finance?

Answer 42

The Fed model is used to assess whether the stock market is over- or undervalued by comparing the expected earnings yield of the stock market to the yield on long-term treasury bonds.

Question 43

What is the equation for the Fed model to evaluate market valuation?

Answer 43

V_actual / V_Fed = V_actual / [Exp(EPS) / (kTBond - 1%)]
where:
- V_actual = Actual market value
- V_Fed = Market value estimate from the Fed model
- Exp(EPS) = Expected earnings per share
- kTBond = Yield on long-term U.S. treasury bonds

Question 44

How do you interpret the Fed model in terms of fair valuation?

Answer 44

Fair valuation occurs when the expected earnings yield of the market is equal to the yield on long-term treasury bonds minus 1%.

This implies that the equity risk premium is less than the growth rate in nominal GDP.

Question 45

How is the Fed model applied to assess stock market conditions?

Answer 45

The Fed model is applied by comparing the earnings yield of the S&P 500 to the yield on 10-year treasury bonds, adjusted by a 1% deduction.

If the earnings yield is higher, the market may be undervalued, and vice versa.

Question 46

What is the relationship between earnings yield and bond yield according to the Fed model?

Answer 46

According to the Fed model, the earnings yield should ideally match the bond yield adjusted for risk, reflecting the market’s fair value considering expected earnings and bond yields.

Question 47

How can the Fed model be used to estimate the market’s required rate of return?

Answer 47

The Fed model estimates the market’s required rate of return by aligning the expected earnings yield with the yield on long-term treasury bonds, adjusted for a nominal GDP growth rate and market risk.

Question 48

What is a common criticism of the Fed model?

Answer 48

A common criticism of the Fed model is that it oversimplifies the relationship between stock and bond yields, ignoring factors like risk premiums and market dynamics that can influence valuation beyond interest rates.

Question 49

How do changes in interest rates affect market valuation according to the Fed model?

Answer 49

Changes in interest rates affect market valuation by altering the expected earnings yield required to achieve fair valuation.

Lower rates typically make equities more attractive compared to bonds.

Question 50

What does historical data suggest about the Fed model’s accuracy?

Answer 50

Historically, the Fed model has shown periods of deviation where market valuations did not align with the model’s predictions, highlighting times of “irrational exuberance” or pessimism.

Question 51

Why is earnings yield considered an appropriate discount rate in the Fed model?

Answer 51

Earnings yield is considered an appropriate discount rate because it reflects the return expected by investors, aligning with long-term growth expectations and bond yield benchmarks.