A person is considering buying the stock of two home health companies that are similar in all respects except for the proportion of earnings paid out as 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 percent. D's constant growth rate is zero, and G's is 8.33 percent. What are the intrinsic values of Stocks D and G?
To calculate the intrinsic values of Stocks D and G, we will be using the Gordon Growth Model, also known as the Dividend Discount Model (DDM). The formula for this model is:
Intrinsic Value = Dividends / (Required Rate of Return - Growth Rate)
For Stock D:
Since Company D pays out the entire earnings as dividends and has a constant growth rate of zero, the intrinsic value can be calculated as follows:
Intrinsic Value(D) = Earnings per Share = $6 per share
For Stock G:
Since Company G pays out only one-third of its earnings as dividends and has a growth rate of 8.33 percent (or 0.0833 in decimal form), we need to calculate the dividends and then apply the formula.
Dividends(G) = Earnings per Share * Dividend Payout Ratio
Dividends(G) = $6 per share * (1/3) = $2 per share
Now, we can calculate the intrinsic value:
Intrinsic Value(G) = Dividends(G) / (Required Rate of Return - Growth Rate)
Intrinsic Value(G) = $2 per share / (0.15 - 0.0833)
Intrinsic Value(G) = $2 per share / 0.0667
Intrinsic Value(G) ≈ $29.99 per share
Therefore, the intrinsic values of Stocks D and G are as follows:
- Intrinsic Value(D) = $6 per share
- Intrinsic Value(G) ≈ $29.99 per share