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 a constant 20% of earnings in the firm, what must be the discount rate

The answer is 13%

Explanation:

Solution

Recall that:

A stock sells for = $50

The next dividend is = $5 per share

The rate of return = 15%

Company reinvests a constant of = 20%

What is the rate of discount = ?

Now

The first step is to calculate the rate of growth which is shown below:

g = equity return * retention rate

g = 15% * 0.2 = 3%

Thus,

The Gordon growth model is stated below:

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

So,

50 = 5 / (discount - g)

The discount - g = 5/50

Discount - g = 10%

The discount = 10 + 3 = 13%

Therefore the discount rate = 13%