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A stock sells for $50. The next dividend will be $5 per share. If the rate of return earned on reinvested funds is a constant 15% and the company reinvests 20% of earnings in the firm, what must be the discount rate? (Do not round intermediate calculations. Enter your answer as a whole percent.) Discount rate %

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Answer:

The discount rate is 13%

Explanation:

Step 1. Given information.

  • Stock sells $50.
  • Next dividend will be $5.
  • Rate of return is constant 15%.
  • Company reinvests 20% of earnings.

Step 2. Formulas needed to solve the exercise.

  • First we will calculate growth rate:

        g = return on equity * retention rate

  • According to gordon growth model:

        Stock price = dividend in next year/ (discount - g)  

Step 3. Calculation.

 g = 15 * 0.2 = 3%

According to gordon growth model:

Stock price = dividend in next year/ (discount - g)

50 = 5/ (discount - g)

discount - g = 5/50

Discount - g = 10%

discount = 10 + 3 = 13%

Step 4. Solution.

The discount rate is 13%

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