15. Eric Systems located in Georgia expects a 10% after-tax rate of return on equipment investments. The state income tax rate is 6%. If the company is in the 21% federal tax, estimate the before-tax rate of return required.
15. Eric Systems located in Georgia expects a 10% after-tax rate of return on equipment investments. The state income tax rate is 6%. If the company is in the 21% federal tax, estimate the before-tax rate of return required.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Problem 15: Calculating the Before-Tax Rate of Return**
Eric Systems, located in Georgia, expects a 10% after-tax rate of return on equipment investments. The state income tax rate is 6%. If the company is subject to a 21% federal tax rate, estimate the before-tax rate of return required.
**Solution Explanation:**
To find the before-tax rate of return, we need to account for the combined effect of both state and federal taxes. The formula generally used for this situation is:
\[ \text{Before-Tax Rate of Return} = \frac{\text{After-Tax Rate of Return}}{1 - (\text{Federal Tax Rate} + \text{State Tax Rate} - \text{Federal Tax Rate} \times \text{State Tax Rate})} \]
1. **Federal Tax Rate**: 21% or 0.21
2. **State Tax Rate**: 6% or 0.06
Using the formula:
\[ \text{Combined Tax Rate} = 0.21 + 0.06 - (0.21 \times 0.06) \]
\[ = 0.21 + 0.06 - 0.0126 \]
\[ = 0.2574 \]
Therefore:
\[ \text{Before-Tax Rate of Return} = \frac{0.10}{1 - 0.2574} \]
\[ = \frac{0.10}{0.7426} \]
\[ \approx 0.1347 \text{ or } 13.47\% \]
Thus, Eric Systems requires an estimated before-tax rate of return of approximately 13.47% to achieve a 10% after-tax rate on equipment investments.
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Transcribed Image Text:**Problem 15: Calculating the Before-Tax Rate of Return**
Eric Systems, located in Georgia, expects a 10% after-tax rate of return on equipment investments. The state income tax rate is 6%. If the company is subject to a 21% federal tax rate, estimate the before-tax rate of return required.
**Solution Explanation:**
To find the before-tax rate of return, we need to account for the combined effect of both state and federal taxes. The formula generally used for this situation is:
\[ \text{Before-Tax Rate of Return} = \frac{\text{After-Tax Rate of Return}}{1 - (\text{Federal Tax Rate} + \text{State Tax Rate} - \text{Federal Tax Rate} \times \text{State Tax Rate})} \]
1. **Federal Tax Rate**: 21% or 0.21
2. **State Tax Rate**: 6% or 0.06
Using the formula:
\[ \text{Combined Tax Rate} = 0.21 + 0.06 - (0.21 \times 0.06) \]
\[ = 0.21 + 0.06 - 0.0126 \]
\[ = 0.2574 \]
Therefore:
\[ \text{Before-Tax Rate of Return} = \frac{0.10}{1 - 0.2574} \]
\[ = \frac{0.10}{0.7426} \]
\[ \approx 0.1347 \text{ or } 13.47\% \]
Thus, Eric Systems requires an estimated before-tax rate of return of approximately 13.47% to achieve a 10% after-tax rate on equipment investments.
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