To calculate the Net Present Value (NPV) of the property, we need to consider both the cash flows generated by the property over the 5-year holding period and the final sale price of the property. Here's how we'll approach the calculation:

1. Cash Flows: The property generates a monthly cash flow of $1,000 for 5 years.
2. Final Sale Price: The property is sold for $200,000 at the end of 5 years.
3. Discount Rate: The given discount rate is 20% annually.

Step-by-Step Calculation:

1. Convert the Discount Rate to Monthly

Since cash flows are monthly, we need to convert the annual discount rate to a monthly rate:

$\text{Monthly Discount Rate} = (1 + \text{Annual Rate})^{1/12} - 1$

2. Calculate the Present Value of Monthly Cash Flows

The cash flow is $1,000 per month for 5 years (60 months). The present value (PV) of an annuity formula will be used to discount these monthly cash flows:

$PV_{\text{cash flows}} = C \times \frac{1 - (1 + r)^{-n}}{r}$

where:

• $C = 1000$ (monthly cash flow)
• $r = \text{monthly discount rate}$
• $n = 60$ (total number of months)

3. Calculate the Present Value of the Sale Price

The $200,000 sale price is received at the end of 5 years. We discount this future value back to the present using the formula:

$PV_{\text{sale}} = \frac{FV}{(1 + r)^n}$

where:

• $FV = 200,000$
• $r = \text{monthly discount rate}$
• $n = 60$

4. Compute the Net Present Value (NPV)

The NPV is the sum of the present values of the cash flows and the sale price:

$NPV = PV_{\text{cash flows}} + PV_{\text{sale}}$

Let's calculate this step-by-step:The Net Present Value (NPV) of the property, given a 20% annual discount rate, is approximately $119,444.30.

This means that the maximum amount you should have paid for the property at the beginning of the 5-year holding period, to achieve a 20% return on investment, is $119,444.30.

Would you like more details or have any questions about the calculation? Here are some related questions to consider:

1. How would the NPV change if the discount rate was different (e.g., 15% or 25%)?
2. What impact would a change in the monthly cash flow have on the NPV?
3. How does the holding period (e.g., 3 years or 10 years) affect the NPV?
4. What is the significance of NPV in evaluating real estate investments compared to other metrics like IRR (Internal Rate of Return)?
5. How do you calculate the NPV for uneven or variable cash flows?

Tip: NPV is a powerful tool for evaluating investment opportunities, but it's essential to use a discount rate that reflects the opportunity cost of capital or the investor's required rate of return.