A person is considering buying the stock of two home health companies that are similar in all respects except the proportion of earnings paid out in dividends. Both companies are expected to earn $6 per share in the coming year, but company D (for dividends) is expected to pay out the entire amount as dividends, while Company G (for growth) is expected to pay out only one-third of its earnings, or $2 per share. The companies are equally risky, and their required rate of return is 15%. D’s constant growth rate is zero and G’s is 8.33 percent. What are the intrinsic values of stocks D & G?

Question

A person is considering buying the stock of two home health companies that are similar in all respects except the proportion of earnings paid out in dividends. Both companies are expected to earn $6 per share in the coming year, but company D (for dividends) is expected to pay out the entire amount as dividends, while Company G (for growth) is expected to pay out only one-third of its earnings, or $2 per share. The companies are equally risky, and their required rate of return is 15%. D’s constant growth rate is zero and G’s is 8.33 percent. What are the intrinsic values of stocks D & G?

Answer 1

To calculate the intrinsic values of stocks D and G, we can use the dividend discount model (DDM). The DDM calculates the present value of all expected future dividends.

For stock D (with a constant growth rate of zero), the DDM formula is:

Intrinsic Value D = Dividend / Required Rate of Return

Since the entire earnings of company D are paid out as dividends, the dividend per share is $6. Therefore,

Intrinsic Value D = $6 / 0.15 = $40 per share

For stock G (with a growth rate of 8.33%), the DDM formula takes into account the future growth of dividends. The formula is:

Intrinsic Value G = Dividend / (Required Rate of Return - Growth Rate)

The dividend per share for company G is $2, and the growth rate is 8.33% or 0.0833. Therefore,

Intrinsic Value G = $2 / (0.15 - 0.0833) = $26.66 per share

So, the intrinsic values of stocks D and G are $40 and $26.66 per share, respectively.

Answer 2

To calculate the intrinsic values of stocks D and G, we can use the discounted cash flow (DCF) model. The DCF formula can be written as:

Intrinsic Value = Dividends / (Required Rate of Return - Growth Rate)

1. Calculate the intrinsic value for stock D:
In this case, Company D pays out its entire earnings as dividends. The dividend per share is $6, and since the constant growth rate is zero, the intrinsic value is:

Intrinsic Value (Stock D) = $6 / (0.15 - 0) = $6 / 0.15 = $40

Therefore, the intrinsic value of stock D is $40.

2. Calculate the intrinsic value for stock G:
For Company G, it pays only one-third of its earnings as dividends, which is $2 per share. The constant growth rate for Company G is 8.33%, which is equivalent to 0.0833. Using these values in the DCF formula:

Intrinsic Value (Stock G) = $2 / (0.15 - 0.0833) = $2 / 0.0667 = $30

Hence, the intrinsic value of stock G is $30.

To summarize:
- The intrinsic value of stock D is $40.
- The intrinsic value of stock G is $30.