Lesson: Nonconstant Growth Stock Valuation

Lesson: Constant Growth, Fundamentals of Financial Management (15th Edition)

Chapter 9

Exercise 9-18

Nonconstant growth stock valuation

Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This same growth rate is expected to last for another 2 years, then decline to gn = 6%

⭐ a.) If D0 = $1.60 and rs = 10%, what is TTC's stock worth today? What are its expected dividend, and capital gains yields at this time, that is during Year ?

Answer:

P0 = D1 / (rs - g1) = 1.92 / (10% - 20%) = 1.92 / (0.10 - 0.20) = -$19.20

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"Additional information"

To calculate the stock's worth today and its expected dividend and capital gains yields, we'll use the dividend discount model (DDM). The DDM formula is as follows:

Formular:

P0 = D1 / (rs - g1)

Where:

P0 = Stock price today

D1 = Expected dividend next year

rs = Required rate of return

g1 = Growth rate in the first period

Given the information provided:

D0 = $1.60 (current dividend)

rs = 10% (required rate of return)

g1 = 20% (growth rate in the first two years)

gn = 6% (growth rate after two years)

To find the expected dividend next year (D1), we can calculate it by multiplying the current dividend (D0) by (1 + g1):

Dt = expected dividend a the end of the year t

D1 = D0 × (1 + growth rate) = 1.60 × (1 + 20%) = 1.60 × (1 + 0.20) = $1.92

Now we can calculate the stock's worth today (P0):

P0 = D1 / (rs - g1) = 1.92 / (10% - 20%) = 1.92 / (0.10 - 0.20) = -$19.20

Remark: The result of -$19.20 doesn't make sense for a stock price. It appears there might be an error or missing information in the given data.

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⭐ b.) Now assume that TTC’s period of supernormal growth is to last for 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield? Answer in words only. (g1 = g2 = g3 = g4 = g5 = 20%)

Answer:

If the period of supernormal growth for TTC is extended to 5 years (g1 = g2 = g3 = g4 = g5 = 20%), it would have the following effects on its price, dividend yield, and capital gains yield:

1. Price: The stock price today would be higher compared to the previous scenario. Since the high growth rate is expected to last for a longer period, the future dividends would be discounted over a longer time horizon, resulting in a higher present value. Consequently, the stock's price would increase.

2. Dividend Yield: With the extended period of high growth, the dividend yield would be lower. Dividend yield is calculated by dividing the dividend per share by the stock price. As the stock price increases due to the longer duration of supernormal growth, the dividend yield decreases, assuming the dividend remains constant.

3. Capital Gains Yield: The capital gains yield, which represents the growth in the stock price, would be higher. The extended period of supernormal growth implies that the stock price is expected to experience significant appreciation over the 5-year period. This would result in a higher capital gains yield, reflecting the potential for increased returns through price appreciation.

In summary, extending the period of supernormal growth to 5 years would lead to a higher stock price, lower dividend yield, and higher capital gains yield.

⭐ c.) What will TTC’s dividend yield and capital gains yield be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy.)

Answer:

Once the period of supernormal growth ends for TTC, the dividend yield and capital gains yield will be the same regardless of whether the period was 2 years or 5 years.

After the supernormal growth period, the company is expected to transition to a stable growth phase with a constant growth rate, gₙ. In this phase, the dividend growth rate remains constant, and the stock price increases at the same rate.

The dividend yield can be calculated as the dividend per share divided by the stock price. Since the dividend growth rate is constant, the dividend per share will also grow at the same rate as the stock price. Therefore, the dividend yield will be equal to the constant growth rate, gₙ.

Similarly, the capital gains yield represents the rate at which the stock price increases. In the stable growth phase, the stock price increases at a constant rate, which is also the constant growth rate, gₙ. Hence, the capital gains yield will also be equal to the constant growth rate, gₙ.

To summarize, once the period of supernormal growth ends, both the dividend yield and capital gains yield will be equal to the constant growth rate, gₙ, regardless of whether the supernormal growth period was 2 years or 5 years.

⭐ d.) Explain why investors are interested in the changing relationship between dividend and capital gain yields over time.

Answer:

Investors are interested in the changing relationship between dividend and capital gain yields over time because it provides insights into the potential returns and overall investment performance of a stock.

1. Income Generation: Dividend yield represents the income generated by a stock through dividend payments. Investors seeking a steady stream of income often look for stocks with a higher dividend yield. A higher dividend yield can be attractive for income-focused investors who rely on regular cash flow from their investments.

2. Growth Potential: Capital gains yield reflects the potential for the stock price to appreciate over time. Investors interested in capital appreciation are more concerned with the growth potential of the stock rather than immediate income. A higher capital gains yield indicates the potential for the stock's value to increase, leading to capital appreciation and higher overall returns.

3. Risk and Return Trade-Off: The changing relationship between dividend and capital gain yields can provide insights into the risk and return characteristics of a stock. In general, stocks with higher dividend yields tend to be more stable and less volatile, while those with higher capital gains yields often involve higher growth potential but also higher risk. Investors evaluate this trade-off between income stability and capital appreciation potential based on their risk tolerance and investment objectives.

4. Market Sentiment and Investor Preferences: The changing relationship between dividend and capital gain yields can also reflect shifts in market sentiment and investor preferences. For example, during periods of economic uncertainty or market downturns, investors may prioritize stable income and be more interested in stocks with higher dividend yields. In contrast, during periods of economic expansion or bullish market conditions, investors may focus more on stocks with higher capital gains potential.

Overall, monitoring the changing relationship between dividend and capital gain yields provides investors with valuable information about the income generation, growth potential, risk profile, and market sentiment associated with a particular stock. By understanding this relationship, investors can make more informed decisions about their investment strategies and portfolio allocations.

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Further Reading:

- Eugene F. Brigham and Joel F. Houston. Fundamentals of Financial Management.

- https://books.google.co.th/books?id=l3YcCgAAQBAJ&pg=PA337&lpg=PA337&dq=constant+growth+Your+broker+offers+to+sell+you+some+shares+of+Bahnsen+%26+Co.+common+stock+that+paid+a+dividend+of+$2.00+yesterday.+Bahnsen%27s+dividend+is+expected+to+grow+at+5%25+per+year+for+the+next+3+years.+If+you+buy+the+stock,+you+plan+to+hold+it+for+3+years+and+then+sell+it.+The+appropriate+discount+rate+is+12%25.&source=bl&ots=ZDSdCkNaVK&sig=ACfU3U3OocbaH6QE2AbBdV41vW5K5daN7A&hl=en&sa=X&ved=2ahUKEwjC77bx-PH-AhVZTGwGHX-AClUQ6AF6BAgYEAM#v=onepage&q&f=false