91Ó°ÊÓ

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 \(g_{n}=6 \%\). a. If \(\mathrm{D}_{0}=\$ 1.60\) and \(\mathrm{r}_{\mathrm{s}}=10 \%,\) what is \(\mathrm{TTC}\) 's stock worth today? What are its expected dividend and capital gains yields at this time, that is, during Year \(1 ?\) b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect the price, dividend yield, and capital gains yield? Answer in words only. c. What will TTC's dividend and capital gains yields 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. d. Of what interest to investors is the changing relationship between dividend and capital gains yields over time?

Step by step solution

01

Calculate Dividends for Year 1 and Year 2

Given that \\( D_0 = \\(1.60 \) and the growth rate is 20%, the dividend for Year 1 is: \\[ D_1 = D_0 \times (1 + g) = \\)1.60 \times 1.20 = \\(1.92 \] \Similarly, the Year 2 dividend is: \\[ D_2 = D_1 \times (1 + g) = \\)1.92 \times 1.20 = \$2.304 \]

02

Calculate Stock Price at Year 2 with Constant Growth

When the growth rate shifts to \( g_n = 6\% \), calculate the stock price at Year 2 using the Gordon Growth Model: \\[ P_2 = \frac{D_3}{r_s - g_n} \] \where \\( D_3 = D_2 \times (1 + g_n) = \\(2.304 \times 1.06 = \\)2.44224 \) \Thus, \\[ P_2 = \frac{2.44224}{0.10 - 0.06} = \frac{2.44224}{0.04} = \$61.056 \]

03

Calculate Present Value of Dividends and Stock Price

To find the stock price today, calculate the present value of the Year 1 and Year 2 dividends and the Year 2 stock price. \The present value of Year 1 dividend: \\[ PV(D_1) = \frac{1.92}{1.10^1} = \\(1.745 \] \Year 2 dividend: \\[ PV(D_2) = \frac{2.304}{1.10^2} = \\)1.905 \] \Year 2 stock price: \\[ PV(P_2) = \frac{61.056}{1.10^2} = \$50.556 \]

04

Calculate Total Stock Value Today

Add the present values calculated in the previous step to find the total stock value today: \\[ P_0 = 1.745 + 1.905 + 50.556 = \\(54.206 \] \Thus, the stock is worth \\)54.206 today.

05

Determine Dividend and Capital Gains Yields for Year 1

Dividend Yield for Year 1: \\[ \text{Dividend Yield} = \frac{D_1}{P_0} = \frac{1.92}{54.206} = 0.0354 \text{ or } 3.54\% \] \Capital Gains Yield for Year 1 is the growth rate during supernormal growth, which is \( g = 20\% \).

06

Assess Impact of Extended Supernormal Growth

With a 5-year supernormal growth period, the stock price would increase because more dividends grow at a higher rate for longer. The dividend yield might decrease as the initial stock price is higher, while the capital gains yield remains high over the longer high-growth period.

07

Steady-State Dividend and Capital Gains Yields

Once the supernormal growth phase ends and only the constant growth of 6% remains, both the dividend and the capital gains yield equal the constant growth rate: 6%. This holds true regardless of the duration of the supernormal growth period.

08

Relevance of Changing Yields

Investors can find the changing relationship between dividend and capital gains yields informative because it indicates the source of returns over time and helps in calculating the anticipated future returns.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Supernormal Growth

Supernormal growth refers to a period in which a company experiences higher-than-average growth rates. This phase is characterized by rapid earnings and revenue increases, typically above the long-term sustainable growth rate. For TTC, the supernormal growth rate is set at 20% per year, anticipated to last for 2 years initially.

• It's essential to understand that supernormal growth is temporary and will eventually slow down to a more sustainable rate, known in our case as the constant growth rate of 6%.
• This phase impacts stock valuation significantly, as it temporarily boosts predicted future dividends, leading to an elevated stock price during this period.
• If the supernormal growth period is extended, as in scenario b where it lasts 5 years, this increases the future dividends expected over these additional years, often increasing the present stock price.

When valuing a company in a supernormal growth phase, investors must estimate how long this rapid growth will continue and how it transitions back to a steady state.

Capital Gains Yield

Capital gains yield is a key component of total investment return, referring to the price appreciation percentage of a stock. It is calculated during periods of supernormal growth as the expected percentage increase in stock price due to this growth. For TTC, during the supernormal growth phase, this rate is equal to the growth rate of 20%.

• The capital gains yield reflects how much the stock price is expected to increase due to anticipated growth.
• In the TTC example, even if the exact holding period isn't known, knowing the phase helps predict that capital gains will be closely tied to growth expectations.
• After supernormal growth ends, the capital gains yield usually stabilizes to match the long-term growth rate, in this case, 6%.

Investors rely on capital gains yield to predict potential appreciation in their investments during erratic growth phases, understanding that long-term stability follows.

Dividend Yield

Dividend yield is a financial ratio (annual dividends per share divided by the price per share) expressed as a percentage that indicates how much a company pays out in dividends relative to its stock price. For TTC, during the supernormal growth phase, the dividend yield can be seen as unstable due to fluctuations in stock price.

• Calculated by dividing the expected annual dividends by the current stock price, it reflects the income aspect of an investment.
• During supernormal growth, the potential for dividends to grow rapidly is significant, but as the stock price rises due to high growth, dividend yield may decrease initially.
• Once the company enters its steady growth period post-supernormal phase, the dividend yield stabilizes. In the TTC scenario, it aligns with the constant growth rate of 6%.

From an investor's perspective, understanding the variation in dividend yield through different growth phases helps in assessing the risk and income profile of the investment.