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: D1=3.37D_1 = 3.37
  • High-growth rate for the first two years: g1=17%=0.17g_1 = 17\% = 0.17
  • Constant growth rate after the third year: g2=3.6%=0.036g_2 = 3.6\% = 0.036
  • Equity cost of capital (discount rate): r=10.4%=0.104r = 10.4\% = 0.104

Step 2: Calculate the dividends for the first three years

  • D2=D1×(1+g1)=3.37×(1+0.17)=3.37×1.17=3.9429D_2 = D_1 \times (1 + g_1) = 3.37 \times (1 + 0.17) = 3.37 \times 1.17 = 3.9429
  • D3=D2×(1+g1)=3.9429×1.17=4.6142D_3 = D_2 \times (1 + g_1) = 3.9429 \times 1.17 = 4.6142

Step 3: Calculate the terminal value at year 3

After year 3, the dividend grows at the constant rate g2=3.6%g_2 = 3.6\%.

The terminal value at the end of year 3 (using the Gordon Growth Model) is given by: Terminal Value at Year 3=D4rg2\text{Terminal Value at Year 3} = \frac{D_4}{r - g_2} where D4=D3×(1+g2)=4.6142×1.036=4.7804D_4 = D_3 \times (1 + g_2) = 4.6142 \times 1.036 = 4.7804.

Thus, Terminal Value at Year 3=4.78040.1040.036=4.78040.068=70.297\text{Terminal Value at Year 3} = \frac{4.7804}{0.104 - 0.036} = \frac{4.7804}{0.068} = 70.297

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=Dt(1+r)t\text{Present Value} = \frac{D_t}{(1 + r)^t}

  • Present value of D1D_1: 3.37(1+0.104)1=3.371.104=3.0534\frac{3.37}{(1 + 0.104)^1} = \frac{3.37}{1.104} = 3.0534
  • Present value of D2D_2: 3.9429(1+0.104)2=3.94291.219=3.2344\frac{3.9429}{(1 + 0.104)^2} = \frac{3.9429}{1.219} = 3.2344
  • Present value of D3D_3: 4.6142(1+0.104)3=4.61421.346=3.4282\frac{4.6142}{(1 + 0.104)^3} = \frac{4.6142}{1.346} = 3.4282
  • Present value of the terminal value: 70.297(1+0.104)3=70.2971.346=52.241\frac{70.297}{(1 + 0.104)^3} = \frac{70.297}{1.346} = 52.241

Step 5: Calculate the intrinsic value

Finally, sum up the present values of all the dividends and the terminal value: Intrinsic Value=3.0534+3.2344+3.4282+52.241=61.957\text{Intrinsic Value} = 3.0534 + 3.2344 + 3.4282 + 52.241 = 61.957

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:

  1. How does the Dividend Discount Model change if the growth rate is constant from the start?
  2. How would the intrinsic value change if the cost of capital increases to 12%?
  3. Can this model be used for companies that don't pay dividends? Why or why not?
  4. What are some limitations of using the two-stage DDM for valuing a company?
  5. 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)