Find the current stock price.

Question

Microtech Corporation is expanding rapidly and currently needs to retain all of its earnings. Hence it does not pay dividends. However, investors expect Microtech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly, at a rate of 50% per year, during years 4,5, and 6. After that growth rate should be a constant 8% per year.

The company's stock has a market beta of 1.46. Assuming a risk-free rate of 3.5% and an expected return on the stock market of 13%, what is its stock price today?

Answer 1

Final Answer: The current stock price is approximately $18.59 per share.

This problem uses the Dividend Discount Model (DDM), specifically a multistage dividend growth model.

Since Microtech will not begin paying dividends until Year 3, and its dividend growth rate changes over time, we need to calculate the future dividends and discount them back to today.

Step 1: Calculate the Required Rate of Return Using CAPM

First, we need to determine the return investors require for holding Microtech's stock.

The Capital Asset Pricing Model (CAPM) formula is:

Required Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)

Given:

Risk-free rate = 3.5%

Beta = 1.46

Expected market return = 13%

Substitute:

Required Return = 3.5% + 1.46(13% - 3.5%)

Required Return = 3.5% + 1.46(9.5%)

Required Return = 3.5% + 13.87%

Required Return = 17.37%

This is the discount rate we will use to calculate the stock's present value.

Step 2: Calculate the Dividends for Years 3–6

Microtech will pay its first dividend of $1.00 at the end of Year 3.

The dividend then grows by 50% annually during Years 4, 5, and 6.

Year 1 Dividend = $0

Year 2 Dividend = $0

Year 3 Dividend = $1.00

Year 4 Dividend = $1.00 × 1.50 = $1.50

Year 5 Dividend = $1.50 × 1.50 = $2.25

Year 6 Dividend = $2.25 × 1.50 = $3.375

Step 3: Calculate the Dividend for Year 7

After Year 6, the dividend growth rate becomes a constant 8%.

Therefore:

Year 7 Dividend = Year 6 Dividend × (1 + Growth Rate)

D7 = $3.375 × 1.08

D7 = $3.645

This is important because we will use the Year 7 dividend to calculate the stock's value at the end of Year 6.

Step 4: Calculate the Stock's Value at the End of Year 6

Now that the dividend grows at a constant 8% annually, we can use the Gordon Growth Model.

Formula:

P6 = D7 / (r - g)

Where:

P6 = Stock value at the end of Year 6

D7 = Year 7 dividend

r = Required return (17.37%)

g = Constant growth rate (8%)

Substitute:

P6 = $3.645 / (0.1737 - 0.08)

P6 = $3.645 / 0.0937

P6 = $38.90

This means the stock is expected to be worth approximately $38.90 at the end of Year 6, immediately after the Year 6 dividend is paid.

However, we need the stock's value today, not six years from now.

Step 5: Discount All Future Cash Flows Back to Today

We must discount the dividends from Years 3–6 and the stock's terminal value at the end of Year 6.

Present Value Formula:

PV = Future Cash Flow / (1 + r)^t

Where:

r = 0.1737

t = Number of years

Year 3 Dividend:

PV = $1.00 / (1.1737)^3

PV = $0.6185

Year 4 Dividend:

PV = $1.50 / (1.1737)^4

PV = $0.7904

Year 5 Dividend:

PV = $2.25 / (1.1737)^5

PV = $1.0102

Year 6 Dividend:

PV = $3.375 / (1.1737)^6

PV = $1.2910

Terminal Value at Year 6:

PV = $38.9007 / (1.1737)^6

PV = $14.8804

Step 6: Add All Present Values

The current stock price equals the sum of all discounted future dividends and the discounted terminal value.

P0 = 0.6185 + 0.7904 + 1.0102 + 1.2910 + 14.8804

P0 = $18.5905

Final Answer: $18.59 per share

Excel Formula

You can calculate the stock price directly using:

=1/(1.1737^3)+1.5/(1.1737^4)+2.25/(1.1737^5)+3.375/(1.1737^6)+(3.645/(0.1737-0.08))/(1.1737^6)

Result: $18.59

Key Takeaway

When a company has multiple dividend growth stages, follow these steps:

1. Calculate the required return using CAPM.
2. Calculate the dividends during the high-growth period.
3. Use the Gordon Growth Model to find the terminal value when growth becomes constant.
4. Discount all dividends and the terminal value back to today.
5. Add the present values to determine the current stock price.

The most common mistake is forgetting to discount the terminal value back to today.

Also, remember that the terminal value at the end of Year 6 uses the Year 7 dividend, not the Year 6 dividend.

Therefore, Microtech Corporation's estimated current stock price is $18.59 per share.