To decide whether to take the lump sum of [tex]$15 million taxed at 45% or the installment plan of $[/tex]15 million taxed at 20% over 30 years, let's evaluate how much you would receive after taxes in each option.
### Lump Sum Option
First, calculate the after-tax amount for the lump sum:
- Lump sum amount: [tex]$15,000,000
- Tax rate on lump sum: 45%
To find the after-tax amount:
\[ \text{After-tax amount} = \text{Lump sum} \times (1 - \text{Tax rate}) \]
Substitute the values:
\[ \text{After-tax amount} = 15,000,000 \times (1 - 0.45) \]
\[ \text{After-tax amount} = 15,000,000 \times 0.55 \]
\[ \text{After-tax amount} = 8,250,000 \]
So, if you take the lump sum, you will receive approximately $[/tex]8,250,000 after taxes.
### Installment Plan Option
Next, calculate the total after-tax amount if you choose the installment plan:
- Total installment amount: [tex]$15,000,000
- Number of years: 30
- Tax rate on installments: 20%
First, find the yearly installment amount:
\[ \text{Yearly installment} = \frac{\text{Total installment amount}}{\text{Number of years}} \]
Substitute the values:
\[ \text{Yearly installment} = \frac{15,000,000}{30} \]
\[ \text{Yearly installment} = 500,000 \]
Now, calculate the after-tax amount for each yearly installment:
\[ \text{After-tax yearly installment} = \text{Yearly installment} \times (1 - \text{Tax rate}) \]
Substitute the values:
\[ \text{After-tax yearly installment} = 500,000 \times (1 - 0.20) \]
\[ \text{After-tax yearly installment} = 500,000 \times 0.80 \]
\[ \text{After-tax yearly installment} = 400,000 \]
Finally, find the total after-tax amount over the 30 years:
\[ \text{Total after-tax amount} = \text{After-tax yearly installment} \times \text{Number of years} \]
Substitute the values:
\[ \text{Total after-tax amount} = 400,000 \times 30 \]
\[ \text{Total after-tax amount} = 12,000,000 \]
So, if you take the installment plan, you will receive $[/tex]12,000,000 after taxes over the 30 years.
### Conclusion
- Lump sum after-tax amount: [tex]$8,250,000
- Installment plan after-tax amount: $[/tex]12,000,000
Comparing the two options, the installment plan provides you with a higher total amount after taxes, [tex]$12,000,000, compared to the lump sum's $[/tex]8,250,000. Therefore, financially, the installment plan is the better choice.
