Question

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 %

Answer 1

The discount rate is 13%

Step-by-step 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%