To calculate the value of company ABC using the discounted future earnings method, we need to follow these steps:

Step 1: Calculate the average annual growth rate.

The short-term growth rate is 7%, and the long-term growth rate is 3%. We need to calculate the average growth rate, which is the weighted average of these two rates based on the time period for each growth rate.

Average Growth Rate = (Short-Term Growth Rate * Short-Term Period) + (Long-Term Growth Rate * Long-Term Period)

Average Growth Rate = (0.07 * Short-Term Period) + (0.03 * Long-Term Period)

Step 2: Determine the discount rate.

The established discount rate for company ABC is 15%.

Step 3: Calculate the present value of future earnings.

To calculate the present value of future earnings, we need to project the earnings for each year and discount them back to the present value using the discount rate. Since you provided the historical earnings, we’ll assume these earnings are for the first year.

Year 1: $1,234,333

Now, let’s assume the average growth rate applies to the earnings in the subsequent years.

Year 2: $1,234,333 * (1 + Average Growth Rate)

Year 3: $1,234,333 * (1 + Average Growth Rate)^2

Year 4: $1,234,333 * (1 + Average Growth Rate)^3

Year 5: $1,234,333 * (1 + Average Growth Rate)^4

Step 4: Discount the projected earnings back to the present value.

To discount the earnings, we’ll use the discount rate of 15%.

Present Value of Year 1 Earnings = Year 1 Earnings / (1 + Discount Rate)

Present Value of Year 2 Earnings = Year 2 Earnings / (1 + Discount Rate)^2

Present Value of Year 3 Earnings = Year 3 Earnings / (1 + Discount Rate)^3

Present Value of Year 4 Earnings = Year 4 Earnings / (1 + Discount Rate)^4

Present Value of Year 5 Earnings = Year 5 Earnings / (1 + Discount Rate)^5

Step 5: Calculate the present value of the terminal value.

The terminal value represents the value of the business beyond the projected period, assuming a steady-state condition. We can calculate it using the last projected year’s earnings divided by the difference between the discount rate and the long-term growth rate.

Terminal Value = Year 5 Earnings * (1 + Long-Term Growth Rate) / (Discount Rate – Long-Term Growth Rate)

Step 6: Sum up the present values of earnings and the present value of the terminal value to determine the total value of the company.

Total Value of Company ABC = Present Value of Year 1 Earnings + Present Value of Year 2 Earnings + Present Value of Year 3 Earnings + Present Value of Year 4 Earnings + Present Value of Year 5 Earnings + Present Value of Terminal Value

Now, you can substitute the given values and perform the calculations to find the value of company ABC.