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Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends. However, investors expect Microtech to begin paying dividends, with the first dividend of \(\$ 1.00\) coming 3 years from today. The dividend should grow rapidly \(-\) at a rate of 50 percent per year - during Years 4 and 5 After Year \(5,\) the company should grow at a constant rate of 8 percent per year. If the required return on the stock is 15 percent, what is the value of the stock today?

Short Answer

Expert verified
The stock is valued at $19.87 today.

Step by step solution

01

Identify Key Information

We need to calculate the present value of the future dividends to find the value of the stock. Key information includes a $1.00 dividend in Year 3, growth of 50% in Years 4 and 5, and a constant growth rate (g) of 8% after Year 5. The required return (r) on the stock is 15%.
02

Calculate Expected Dividends

Calculate the dividends for Years 4 and 5 using 50% growth. - Year 3 Dividend (D_3) = \(1.00. - Year 4 Dividend (D_4) = D_3 \times 1.5 = \)1.50. - Year 5 Dividend (D_5) = D_4 \times 1.5 = $2.25.
03

Find the Terminal Value at Year 5

Compute the terminal value (TV_5) using the Gordon Growth Model, which considers constant growth from Year 6 onwards. TV_5 = \frac{D_6}{r-g}, whereD_6 = D_5 \times 1.08 = \(2.25 \times 1.08 = \)2.43.Then, TV_5 = \frac{2.43}{0.15 - 0.08} = $34.71.
04

Calculate Present Value of Dividends and Terminal Value

Find the present value (PV) of each future cash flow using the formula PV = \frac{FV}{(1 + r)^t}, where FV is the future value and t is the time period into the future. - PV of D_3 = \(1.00 / (1.15)^3 = \)0.66.- PV of D_4 = \(1.50 / (1.15)^4 = \)0.86.- PV of D_5 = \(2.25 / (1.15)^5 = \)1.12.- PV of TV_5 = \(34.71 / (1.15)^5 = \)17.23.
05

Compute Total Present Value

Add the present value of all individual cash flows to find the stock's total value today. Total Present Value = 0.66 + 0.86 + 1.12 + 17.23 = $19.87.

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Key Concepts

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

Dividend Growth Model
The Dividend Growth Model is a method used to value a stock by considering expected future dividends that grow at a constant rate. It's often called the Gordon Growth Model. This model is crucial for companies that are expected to pay dividends in the future. It helps investors estimate the intrinsic value of a company based on its future dividend prospects.
The model assumes that a company will continue to pay dividends, and the amount paid will grow at a stable rate indefinitely. In our exercise, Microtech Corporation starts paying dividends from the third year. The model uses different phases of dividend growth; initially rapid at 50% for Years 4 and 5, before settling into a more constant growth rate of 8% thereafter.
To apply the Dividend Growth Model, identify the expected dividends, estimate the growth rates, and then compute the stock's value today. Understanding the various growth phases is vital, as they are the key components of this model.
Present Value
Present Value (PV) is the current value of future cash flows, discounted back at the required rate of return. In stock valuation, it's essential to understand how future dividends are worth in today's terms. This process allows investors to determine what they'd be willing to pay right now for a stock that will provide specific dividends at future dates.
Calculating present value involves using the formula \(PV = \frac{FV}{(1 + r)^t}\), where \(FV\) is the future value, \(r\) is the required rate of return, and \(t\) is the time in years from now. The present value calculation accounts for the time value of money, recognizing that a dollar today is worth more than a dollar tomorrow due to the potential earning capacity.
In the context of our exercise, the present values of dividends expected in Years 3, 4, and 5 were calculated separately, as well as the terminal value of Year 5. These individual values, when summed, provide the overall present value worth of Microtech's stock today.
Required Rate of Return
The Required Rate of Return (RRR) is the minimum return an investor expects to receive for an investment in a stock. Often denoted as \(r\), this rate is critical in discounting future cash flows back to their present value. It reflects the risk premium for holding the stock and the opportunity cost of investing capital elsewhere.
In stock valuation, the required rate of return informs the investor's decision on whether the stock offers a favorable return relative to its perceived risk. For instance, in our example, the RRR for Microtech stock is 15%. This means investors expect to earn at least 15% annual returns for holding the stock.
To ensure accurate valuation, it's important to compare the calculated present value of future cash flows (including expected dividends and terminal value) with the required rate of return. If the stock price calculated is higher than the current market price, it might indicate a worthwhile investment.
Terminal Value
Terminal Value (TV) is an essential component in stock valuation, representing the present value of all future cash flows beyond a forecast horizon, assuming a constant growth rate. It captures the majority of a stock's value, especially when the company is in its early growth phase like Microtech.
In our problem, Terminal Value at Year 5 (\(TV_5\)) was calculated using the formula \(TV_5 = \frac{D_6}{r-g}\), where \(D_6\) is the expected dividend in Year 6, \(r\) is the required rate of return, and \(g\) is the growth rate. The calculation gives the value of dividends from Year 6 onwards, discounted to Year 5 terms.
Understanding Terminal Value is crucial, as it allows investors to see the long-term growth potential of a company beyond the initial fast growth stage. Calculating terminal value companies gives investors insight into what the company will be worth years down the line, assuming it can sustain a steady growth rate.

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Most popular questions from this chapter

Your broker offers to sell you some shares of Bahnsen \& Co. common stock that paid a dividend of \(\$ 2\) yesterday. You expect the dividend to grow at the rate of 5 percent per year for the next 3 years, and, if you buy the stock, you plan to hold it for 3 years and then sell it. a. Find the expected dividend for each of the next 3 years; that is, calculate \(D_{1}, D_{2},\) and \(\mathrm{D}_{3} .\) Note that \(\mathrm{D}_{0}=\$ 2.00\) b. Given that the appropriate discount rate is 12 percent and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the \(\mathrm{PV}\) of \(\mathrm{D}_{1}, \mathrm{D}_{2},\) and \(\mathrm{D}_{3},\) and then sum these \(\mathrm{PVs}\) c. You expect the price of the stock 3 years from now to be \(\$ 34.73 ;\) that is, you expect \(\hat{P}_{3}\) to equal \(\$ 34.73 .\) Discounted at a 12 percent rate, what is the present value of this expected future stock price? In other words, calculate the PV of \(\$ 34.73\) d. If you plan to buy the stock, hold it for 3 years, and then sell it for \(\$ 34.73,\) what is the most you should pay for it today?

Assume that the average firm in your company's industry is expected to grow at a constant rate of 6 percent and its dividend yield is 7 percent. Your company is about as risky as the average firm in the industry, but it has just successfully completed some \(\mathrm{R} \& \mathrm{D}\) work that leads you to expect that its earnings and dividends will grow at a rate of 50 percent \(\left[\mathrm{D}_{1}=\mathrm{D}_{0}(1+\mathrm{g})=\mathrm{D}_{0}(1.50)\right]\) this year and 25 percent the following year, after which growth should match the 6 percent industry average rate. The last dividend paid \(\left(\mathrm{D}_{0}\right)\) was \(\$ 1.00 .\) What is the value per share of your firm's stock?

Investors require a 15 percent rate of return on Levine Company's stock \(\left(\mathrm{k}_{\mathrm{s}}=15 \%\right)\) a. What will be Levine's stock value if the previous dividend was \(D_{0}=\$ 2\) and if investors expect dividends to grow at a constant compound annual rate of \((1)-5\) percent, (2) 0 percent, (3) 5 percent, and (4) 10 percent? b. Using data from part a, what is the Gordon (constant growth) model value for Levine's stock if the required rate of return is 15 percent and the expected growth rate is (1) 15 percent or (2) 20 percent? Are these reasonable results? Explain. c. Is it reasonable to expect that a constant growth stock would have \(g>k_{s}\) ?

Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year in recent years. This same growth rate is expected to last for another 2 years. a. If \(\mathrm{D}_{0}=\$ 1.60, \mathrm{k}=10 \%,\) and \(\mathrm{g}_{\mathrm{n}}=6 \%,\) what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time? 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. c. What will be TTC's dividend yield and capital gains yield 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 yield and capital gains yield over time?

A company currently pays a dividend of \(\$ 2\) per share, \(D_{0}=\$ 2 .\) It is estimated that the company's dividend will grow at a rate of 20 percent per year for the next 2 years, then the dividend will grow at a constant rate of 7 percent thereafter. The company's stock has a beta equal to \(1.2,\) the risk- free rate is 7.5 percent, and the market risk premium is 4 percent. What would you estimate is the stock's current price?

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