Math Problem Statement
Assume Stanton Corporation will pay an annual dividend of $3.37 one year from now. Analysts expect this dividend to grow at 17% p.a. thereafter until the third year. After then, growth will level off at 3.6% p.a.. The firm’s equity cost of capital is 10.4% p.a.. What is the intrinsic value of Stanton Corporation? All of these rates are compounded annually. (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)
Solution
To find the intrinsic value of Stanton Corporation, we use the Dividend Discount Model (DDM), which values a stock by the present value of its future dividends. Since there are two growth phases here (high growth for 2 years and then stable growth thereafter), this is a two-stage DDM problem.
Step 1: Define the key inputs
- First dividend:
- High-growth rate for the first two years:
- Constant growth rate after the third year:
- Equity cost of capital (discount rate):
Step 2: Calculate the dividends for the first three years
Step 3: Calculate the terminal value at year 3
After year 3, the dividend grows at the constant rate .
The terminal value at the end of year 3 (using the Gordon Growth Model) is given by: where .
Thus,
Step 4: Discount the dividends and terminal value to the present
Now, discount each of the future cash flows (dividends and terminal value) back to the present using the formula:
- Present value of :
- Present value of :
- Present value of :
- Present value of the terminal value:
Step 5: Calculate the intrinsic value
Finally, sum up the present values of all the dividends and the terminal value:
Thus, the intrinsic value of Stanton Corporation is approximately $61.96.
Would you like further details or have any questions about the solution?
Here are five related questions to expand your understanding:
- How does the Dividend Discount Model change if the growth rate is constant from the start?
- How would the intrinsic value change if the cost of capital increases to 12%?
- Can this model be used for companies that don't pay dividends? Why or why not?
- What are some limitations of using the two-stage DDM for valuing a company?
- How do changes in the long-term growth rate affect the terminal value?
Tip: The Dividend Discount Model assumes dividends will grow indefinitely. Be cautious when applying it to firms in highly volatile industries or those
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Math Problem Analysis
Mathematical Concepts
Finance
Dividend Discount Model
Present Value
Formulas
Dividend Discount Model (DDM): P = D / (r - g)
Present Value: PV = D_t / (1 + r)^t
Gordon Growth Model: TV = D / (r - g)
Theorems
Gordon Growth Model
Suitable Grade Level
College Level (Finance or Economics)
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