Part 1Summit Systems has an equity cost of capital of 11.00 %11.00%, will pay a dividend of $1.501.50 in one year, and its dividends had been expected to grow by 6.00 %6.00% per year. You read in the paper that Summit Systems has revised its growth prospects and now expects its dividends to grow at a rate of 3.00 %3.00% per year forever. a. What is the drop in value of a share of Summit Systems stock based on this information?b. If you tried to sell your Summit Systems stock after reading this news, what price would you be likely to get? Why? Part 1a. What is the drop in value of a share of Summit Systems stock based on this information?The drop in value of a share of Summit Systems stock is $[input]11.2511.25 . (Round to the nearest cent.)Part 2b. If you tried to sell your Summit Systems stock after reading this news, what price would you be likely to get? The price of a share would likely be $[input]enter your response here . (Round to the nearest cent.)

Question

Part 1Summit Systems has an equity cost of capital of 11.00 %11.00%​, will pay a dividend of ​$1.501.50 in one​ year, and its dividends had been expected to grow by 6.00 %6.00% per year. You read in the paper that Summit Systems has revised its growth prospects and now expects its dividends to grow at a rate of 3.00 %3.00% per year forever. a. What is the drop in value of a share of Summit Systems stock based on this​ information?b. If you tried to sell your Summit Systems stock after reading this​ news, what price would you be likely to​ get? Why? Part 1a. What is the drop in value of a share of Summit Systems stock based on this​ information?The drop in value of a share of Summit Systems stock is ​$[input]11.2511.25 .  ​(Round to the nearest​ cent.)Part 2b. If you tried to sell your Summit Systems stock after reading this​ news, what price would you be likely to​ get? The price of a share would likely be ​$[input]enter your response here .  ​(Round to the nearest​ cent.)

BlackTom AI · Accepted Answer

Using the Gordon (constant-growth) dividend-discount model: P = D1 / (r − g). This model values a stock as the present value of a perpetually growing dividend stream when dividends grow at constant rate g and required return is r.

1. Relevant concepts
- D1 is the dividend one year from now ($1.50).
- r is the equity cost of capital (11.00% = 0.11).
- g is the long-run dividend growth rate. Originally g_old = 6.00% (0.06), revised to g_new = 3.00% (0.03).
- Stock value under constant growth: P = D1 / (r − g).

2. Step-by-step reasoning and calculations
a) Compute the original value (before the news) using g_old:
- P_old = D1 / (r − g_old) = 1.50 / (0.11 − 0.06)
- r − g_old = 0.11 − 0.06 = 0.05
- P_old = 1.50 / 0.05 = 30.00

b) Compute the new value (after the news) using g_new:
- P_new = D1 / (r − g_new) = 1.50 / (0.11 − 0.03)
- r − g_new = 0.11 − 0.03 = 0.08
- P_new = 1.50 / 0.08 = 18.75

c) Drop in value:
- Drop = P_old − P_new = 30.00 − 18.75 = 11.25

3. Intermediate steps shown above; all arithmetic is displayed and rounded to the nearest cent.

4. Why this is correct
The Gordon model directly links stock price to the dividend, required return, and growth rate. Lowering g raises the denominator (r − g), thereby lowering the price. The numerical difference $11.25 is exactly the change produced by substituting 6% → 3% in the formula.

5. Why other approaches are incorrect
- Using D0 (current dividend) instead of D1 would mis-time the cash flow and give a different answer. 
- Using the wrong r − g values or arithmetic errors produce incorrect prices. The correct method is D1/(r − g) with the given inputs.

6. Conclusion
The drop in value is $11.25, and the likely price you could sell at after the news is $18.75, which matches the provided answers.

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