Question: The newspaper reported last week that Huang Enterprises earned $34.2$ million this year. The report also stated that the firm's return on equity is $17$ percent. The firm retains $70$ percent of its earnings.
a. What is the firm's earnings growth rate?
Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., $32.16$.
b. What will next year's earnings be?
Note: Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., $1,234,567$.
a. Earnings growth rate %
b. Next year's earnings
Graph shape: a table/input box appears at the bottom-left with two rows labeled “a. Earnings growth rate” and “b. Next year's earnings”; the first row has a percentage entry field and the second row has a blank dollar entry field. position_hint: bottom-left
1. **State the problem:**
We are given the earnings of Huang Enterprises this year as $34.2$ million, the return on equity (ROE) as $17\%$, and the retention ratio (the fraction of earnings retained) as $70\%$.
We need to find:
a. The firm's earnings growth rate.
b. Next year's earnings in dollars.
2. **Formula for earnings growth rate:**
The earnings growth rate $g$ is given by the formula:
$$g = b \times ROE$$
where $b$ is the retention ratio (fraction of earnings retained), and $ROE$ is the return on equity.
3. **Calculate the earnings growth rate:**
Given:
$$b = 0.70$$
$$ROE = 0.17$$
Calculate:
$$g = 0.70 \times 0.17 = 0.119$$
Convert to percentage:
$$g = 0.119 \times 100 = 11.90\%$$
4. **Calculate next year's earnings:**
Next year's earnings $E_1$ can be found by growing this year's earnings $E_0$ by the growth rate $g$:
$$E_0 = 34.2 \text{ million} = 34,200,000$$
$$E_1 = E_0 \times (1 + g) = 34,200,000 \times (1 + 0.119)$$
$$E_1 = 34,200,000 \times 1.119 = 38,239,800$$
5. **Final answers:**
a. Earnings growth rate = $11.90\%$
b. Next year's earnings = $38,239,800$ dollars