High School

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Problem 9-9: Growth Rate

The newspaper reported last week that Chen Enterprises earned $34.16 million this year. The report also stated that the firm's return on equity is 15 percent. The firm retains 70 percent of its earnings.

a. What is the firm's earnings growth rate? (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? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)

| Metric | Value |
|------------------------|--------|
| Earnings growth rate | | % |
| Next year's earnings | | |

Answer :

To solve this problem, we need to determine both the firm's earnings growth rate and next year's earnings based on the information provided.

a. Calculating the Earnings Growth Rate:

The firm's earnings growth rate can be determined using the formula for the Sustainable Growth Rate (SGR):

[tex]\text{SGR} = \text{Return on Equity (ROE)} \times \text{Retention Ratio (b)}[/tex]

Where:

  • Return on Equity (ROE) is given as 15%, or 0.15 in decimal form.
  • Retention Ratio (b) is the proportion of earnings retained, which is 70%, or 0.70 in decimal form.

Substituting the given values into the formula:

[tex]\text{SGR} = 0.15 \times 0.70 = 0.105[/tex]

Converting this to a percentage, the firm's earnings growth rate is:

[tex]\text{Earnings Growth Rate} = 10.50\%[/tex]

b. Estimating Next Year's Earnings:

To find next year's earnings, we need to apply the growth rate to this year's earnings. First, let's find out how much earnings are expected to grow:

  • Current Earnings: $34.16 million
  • Growth Rate: 10.50%

Next Year's Earnings can be calculated with the formula:

[tex]\text{Next Year's Earnings} = \text{Current Earnings} \times (1 + \text{Growth Rate})[/tex]

Substitute the known values:

[tex]\text{Next Year's Earnings} = \$34.16 \times (1 + 0.105)[/tex]

[tex]\text{Next Year's Earnings} = \$34.16 \times 1.105 = \$37.7688[/tex]

Rounding to the nearest whole number:

[tex]\text{Next Year's Earnings} \approx \$37,769,000[/tex]

Thus, the firm's projected earnings for next year are approximately $37,769,000.

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