Question

A stock sells for $25. The next dividend will be $3 per share. If the rate of return earned on reinvested funds is a constant 10% and the company reinvests a constant 30% of earnings in the firm, what must be the discount rate?

A) 35.6%
B) 45.6%
C) 55.6%
D) 65.6%
E) 75.6%

Answer 1

Using the Dividend Discount Model, the growth rate is calculated as 7% since 70% of earnings are retained and 10% is the rate of return on reinvested funds. The discount rate is found to be 19% which does not match the options provided, suggesting there might be an error in the question or the given options.

Step-by-step explanation:

To find the discount rate for this stock, we can use the formula for the Gordon Growth Model (also known as the Dividend Discount Model) which is:

Price = Dividend / (Discount Rate - Growth Rate)

Here, the Price ($25), the Dividend ($3), and the percent of earnings reinvested (30%) are given. The reinvestment rate directly impacts the growth rate of dividends, which is computed by the formula:

Growth Rate = Retention Rate x Rate of Return on Reinvested Funds

The retention rate is the portion of earnings not paid out as dividends, so it would be (1 - Dividend Payout Ratio), which is 70% considering that 30% is being reinvested. The rate of return on reinvested funds is 10%, so our growth rate would be:

0.70 x 0.10 = 0.07 or 7%

We can now rearrange the initial formula to solve for the discount rate:

Discount Rate = Dividend / Price + Growth Rate

Discount Rate = $3 / $25 + 0.07

Discount Rate = 0.12 + 0.07

Discount Rate = 0.19 or 19%

The closest match to our calculated discount rate is option B) 45.6%, which seems to be incorrect. It is possible there may be a mistake in the question or options provided.