DFB, Inc., expects earnings at the end of this year of $4.19 per share, and it plans to pay
an annual dividend of $2.43 at that time. DFB will retain $1.76 per share of its earnings to
reinvest in new projects with an expected return of 15% p.a.. Suppose DFB will maintain the
same dividend payout rate, retention rate, and return on new investments in the future and
will not change its number of outstanding shares.
(a) What growth rate of earnings would you forecast for DFB? (ans: 6.3%)

To calculate the growth rate of earnings for DFB, Inc., we can use the **sustainable growth rate** formula, which is based on the retention ratio and the return on retained earnings (i.e., the return on new investments).

The formula is:

\[
\text{Growth rate} = \text{Retention ratio} \times \text{Return on new investments}
\]

Where:
- **Retention ratio** is the portion of earnings that the company retains for reinvestment (rather than paying out as dividends).
- **Return on new investments** is the expected rate of return on the reinvested earnings.

### Step 1: Calculate the retention ratio
The retention ratio is the fraction of the earnings that is not paid out as dividends:

\[
\text{Retention ratio} = \frac{\text{Retained earnings per share}}{\text{Earnings per share}}
\]

Given:
- Retained earnings per share = $1.76
- Earnings per share = $4.19

\[
\text{Retention ratio} = \frac{1.76}{4.19} = 0.42
\]

So, the retention ratio is 42%.

### Step 2: Return on new investments
We are told that the return on new investments is 15%.

### Step 3: Calculate the growth rate
Now, using the formula for the growth rate:

\[
\text{Growth rate} = 0.42 \times 15\% = 6.3\%
\]

Thus, the forecasted growth rate of earnings for DFB, Inc. is **6.3%**, which matches the provided answer.

Would you like any further details or explanations on this? Here are five related questions to expand this topic:

1. How does the dividend payout ratio affect a company's growth rate?
2. What is the relationship between the retention ratio and future growth prospects?
3. How does the return on new investments impact long-term shareholder value?
4. Could changing the number of outstanding shares affect the growth rate?
5. How would changes in the dividend policy alter the sustainable growth rate?

**Tip:** The sustainable growth rate formula assumes that a company maintains a constant return on equity and retention ratio, making it a useful metric for stable companies.

DFB, Inc., expects earnings at the end of this year of $4.19 per share, and it plans to pay an annual dividend of $2.43 at that time. DFB will retain $1.76 per share of its earnings to reinvest in new projects with an expected return of 15% p.a. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares. (a) What growth rate of earnings would you forecast for DFB?

This detailed guide explains how to calculate the growth rate of earnings for DFB, Inc. using the sustainable growth rate formula, which includes the retention ratio and return on new investments. The company retains $1.76 per share, with an earnings per share of $4.19 and a return on investments of 15%. The forecasted growth rate is 6.3%.

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