Given that your stock portfolio is expected to yield 8% annually (a more realistic and sustainable rate), we need to reassess the comparison between selling stock and taking a loan based on this expected return.
### Option 1: Selling Stock
1. **Current Value of Stock Portfolio**: $600,000
2. **Original Value of Stock Portfolio**: $600,000 / 1.3 = $461,538.46
3. **Capital Gain**: $600,000 - $461,538.46 = $138,461.54
4. **Tax on Capital Gain**: 25% of $138,461.54 = $34,615.39
#### Amount to Sell to Raise $250,000
1. **Net Proceeds from Selling Stock**:
- To raise $250,000 after taxes, you need to sell more than $250,000 worth of stock.
2. **Effective Tax Rate**: 25% on capital gain portion of the sold stock.
Let's find the amount \( X \) of stock to sell to get $250,000 after taxes:
\[ X = \frac{250,000}{(1 - \text{tax rate on capital gain})} \]
\[ X = \frac{250,000}{1 - \frac{\text{capital gain on } X}{X} \times 0.25} \]
\[ X = \frac{250,000}{1 - \frac{138,461.54}{600,000} \times 0.25} \]
\[ X = \frac{250,000}{1 - 0.057692} \]
\[ X = \frac{250,000}{0.942308} \]
\[ X \approx 265,151.52 \]
3. **Capital Gain on Sold Stock**:
\[ \text{Capital Gain on Sold Stock} = \frac{138,461.54}{600,000} \times 265,151.52 \]
\[ \text{Capital Gain on Sold Stock} = 61,517.95 \]
4. **Tax on Sold Stock Capital Gain**:
\[ \text{Tax on Sold Stock Capital Gain} = 0.25 \times 61,517.95 \]
\[ \text{Tax on Sold Stock Capital Gain} = 15,379.49 \]
5. **Net Proceeds after Tax**:
\[ \text{Net Proceeds after Tax} = 265,151.52 - 15,379.49 \]
\[ \text{Net Proceeds after Tax} = 249,772.03 \]
### Option 2: Taking a Loan
1. **Loan Amount**: $250,000
2. **Interest Rate**: 7% per year
3. **Loan Term**: 10 years
#### Monthly Payment Calculation
\[ M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \( P \) = $250,000
- \( r \) = 7% / 12 = 0.005833
- \( n \) = 10 \times 12 = 120
\[ M = \frac{250,000 \cdot 0.005833 \cdot (1 + 0.005833)^{120}}{(1 + 0.005833)^{120} - 1} \]
\[ M \approx 2,901.17 \]
#### Total Payment Over 10 Years
\[ \text{Total Payment} = M \times n \]
\[ \text{Total Payment} = 2,901.17 \times 120 \]
\[ \text{Total Payment} = 348,140.40 \]
#### Total Interest Paid
\[ \text{Total Interest Paid} = \text{Total Payment} - \text{Loan Amount} \]
\[ \text{Total Interest Paid} = 348,140.40 - 250,000 \]
\[ \text{Total Interest Paid} = 98,140.40 \]
### Comparison
#### Cost of Selling Stock
- **Immediate cost**: $15,379.49 in taxes.
- **Opportunity cost**: Potential future gains on the sold stock amount ($265,151.52).
#### Cost of Taking a Loan
- **Total interest paid**: $98,140.40 over 10 years.
### Opportunity Cost Calculation
If you keep the $265,151.52 in your stock portfolio and it grows at 8% annually for 10 years, the future value can be calculated using the formula for compound interest:
\[ \text{Future Value} = P \times (1 + r)^n \]
Where:
- \( P = 265,151.52 \)
- \( r = 0.08 \)
- \( n = 10 \)
\[ \text{Future Value} = 265,151.52 \times (1 + 0.08)^{10} \]
\[ \text{Future Value} \approx 265,151.52 \times 2.158924 \]
\[ \text{Future Value} \approx 572,844.38 \]
### Conclusion
- **Cost of Selling Stock**:
- Immediate tax cost: $15,379.49
- Opportunity cost: $572,844.38 - $265,151.52 = $307,692.86 (future value minus initial amount)
- **Cost of Taking a Loan**:
- Total interest paid: $98,140.40
### Decision
Taking a loan for 10 years at a 7% interest rate is better in terms of overall cost. Although the immediate cost of selling stock is lower ($15,379.49), the opportunity cost of losing future gains ($307,692.86) far exceeds the total interest paid on the loan ($98,140.40).
Therefore, **taking the loan is more tax-efficient and results in less money used overall** when considering both immediate costs and future opportunity costs.
