Assume that you purchased a piece of land for $50,000 and hold it for 10 years for future development. Assume that your annual holding costs of property taxes and insurance are $4,000.  Assume that you desire a 10% overall return on all funds invested and spent on this property, how much would your reversion value be?

To determine the reversion value, which is the value at which the property should be sold after 10 years to achieve a 10% return on all funds invested and spent, we need to consider the initial investment, the annual holding costs, and the desired return rate. 

### Step 1: Initial Investment and Annual Costs
- **Initial Purchase Price (P):** $50,000
- **Annual Holding Costs (C):** $4,000 per year for 10 years
- **Desired Return (r):** 10% per year

### Step 2: Future Value of Initial Investment
The future value of the initial investment after 10 years can be calculated using the formula for compound interest:

\[
\text{Future Value of Initial Investment} = P \times (1 + r)^{10}
\]

Substituting the values:

\[
\text{Future Value of Initial Investment} = 50,000 \times (1 + 0.10)^{10}
\]

\[
\text{Future Value of Initial Investment} = 50,000 \times 2.5937 = 129,685
\]

### Step 3: Future Value of Annual Holding Costs
The annual holding costs accumulate each year, and we need to calculate the future value of these costs over 10 years. This is an annuity problem, where each annual payment (C) grows at the rate (r):

The formula for the future value of an annuity is:

\[
\text{Future Value of Annuity} = C \times \frac{(1 + r)^{n} - 1}{r}
\]

Substituting the values:

\[
\text{Future Value of Annuity} = 4,000 \times \frac{(1 + 0.10)^{10} - 1}{0.10}
\]

\[
\text{Future Value of Annuity} = 4,000 \times \frac{2.5937 - 1}{0.10} = 4,000 \times 15.937 = 63,748
\]

### Step 4: Total Future Value
The total future value (Reversion Value) required to achieve the desired return is the sum of the future value of the initial investment and the future value of the holding costs:

\[
\text{Total Reversion Value} = 129,685 + 63,748 = 193,433
\]

### Conclusion
The reversion value, or the amount at which the property should be sold after 10 years to achieve a 10% overall return, is **$193,433**.

Would you like any further details or have any questions about this calculation?

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Here are some related questions:

1. How would the reversion value change if the desired return rate was 8% instead of 10%?
2. What is the impact of holding costs on the total reversion value?
3. How does changing the holding period to 15 years affect the reversion value?
4. How would you calculate the reversion value if the holding costs increased by 5% annually?
5. What if the property appreciates at a different rate than your desired return rate?

**Tip:** When calculating future values, always ensure that the compounding frequency matches the period of the investment for accurate results.

Learn how to calculate the reversion value for a property investment using compound interest and future value of annuity formulas. This problem involves determining the sale price of a property after 10 years to achieve a 10% return on investment. Suitable for financial analysts and property investors.

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