You own a house that you are currently leasing for $30,000 a year. You believe demand is strong enough to support 7.0% annual increases for the next three years, but then an expected big increase in rental housing stock planned for the future means that you will probably settle for 4.0% increases each year after that.

What's important to you is deciding whether to keep leasing the house or sell it. Your time frame is 10 years. At that time, you believe you will move away from the area and you will want to get out of the owner/landlord game. If you sell, you think you might do this in one year and get $350,000. You have no mortgage. And for the purposes of this analysis, assume away taxes and other expenses. Take the cash flows given as net annual cash flows at the end of each year.

If you usually earn 8.0% annually on any invested funds, what is the better financial deal: Sell in one year or hold on and collect rents for the next 10 years?

Specifically, evaluate buying vs collecting rents, and enter here the difference between these two options. Just use an absolute value of the difference (so no need to worry about what value is subtracted from the other value).

To decide whether to sell the house in one year for $350,000 or to hold on and collect rents for 10 years, we will compare the present value (PV) of each option. Since the opportunity cost is 8.0%, we will discount the cash flows at that rate.

### Option 1: Selling in One Year
In this scenario, the cash flow in one year will be the sale price of $350,000. The present value is simply the discounted value of this future sale price.

\[
PV_{\text{sell}} = \frac{350,000}{(1 + 0.08)^1}
\]

### Option 2: Holding and Collecting Rents for 10 Years
In this case, we will need to calculate the present value of the rent cash flows for 10 years.

- For the first 3 years, the rent will increase by 7.0% annually.
- For the next 7 years, the rent will increase by 4.0% annually.

We will calculate the rent for each year and then discount them back to the present value.

Let’s break this down year by year:
1. Rent at Year 1: $30,000
2. Rent at Year 2: $ 30,000 \times 1.07 $
3. Rent at Year 3: $ 30,000 \times 1.07^2 $
4. Rent at Year 4: $ 30,000 \times 1.07^3 \times 1.04 $
5. Rent at Year 5: $ 30,000 \times 1.07^3 \times 1.04^2 $
6. And so on...

We will then discount these rents to the present value using the formula:
\[
PV_{\text{rent}} = \sum_{t=1}^{10} \frac{\text{Rent}_t}{(1 + 0.08)^t}
\]

After calculating the present value of both options, we will find the absolute difference between the two present values.

Let me now compute this.The present value (PV) of selling the house in one year is approximately $324,074.07, while the present value of collecting rents for the next 10 years is approximately $251,896.79.

The absolute difference between these two options is approximately **$72,177.28**. Therefore, selling in one year results in a higher financial return by this amount, assuming an 8% opportunity cost.

Would you like further details or explanations?

Here are some related questions:
1. How do future rent increases impact the decision to sell vs. hold?
2. What would the analysis look like if the growth rate in rent were different?
3. How would changes in the opportunity cost (discount rate) affect the result?
4. What role do taxes and expenses play if they are included in the analysis?
5. What if the selling price after one year is uncertain—how would that affect the analysis?

**Tip:** When evaluating long-term investments, considering alternative uses of capital, like reinvesting proceeds, helps in making better financial decisions.

Compare the financial outcome of selling a property in one year for $350,000 or collecting rent for 10 years with annual increases of 7.0% (first 3 years) and 4.0% (next 7 years). Calculate the present value of cash flows using an 8.0% discount rate, and evaluate which option offers a higher return.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation