Question

(Related to the Apply the Concept on page 931) Suppose you buy a house for $$\$ 150,000 .$$ One year later, the market price of the house has risen to $$\$ 165,000$$. What is the return on your investment in the house if you made a down payment of 20 percent and took out a mortgage loan for the other 80 percent? What if you made a down payment of 5 percent and borrowed the other 95 percent? Be sure to show your calculations in your answer.

Short answer

The ROI for a 20% down payment is \$15,000/\$30,000 * 100% = 50%. For a 5% down payment, the ROI becomes \$15,000/\$7,500 * 100% = 200%. These results show that the ROI is higher when the down payment (i.e., the original own capital investment) is lower, assuming that the price of the house increases.

Step-by-step solution

Understand the concept of ROI

To calculate return on investment (ROI), the proper formula is: \[ ROI = \frac{(Current value of Investment - Cost of Investment)}{(Cost of Investment)} * 100 \% \] Now, we need to use this formula with the provided information.

Calculate ROI for a down payment of 20%

The original investment with a 20% down payment is $150,000 * 20% = $30,000. So, now we can plug these numbers into the ROI equation:\[ ROI = \frac{(\$165,000 - \$150,000)}{\$30,000} * 100 \% \] The above equation will provide the ROI when a down payment of 20% was made.

Calculate ROI for a down payment of 5%

The original investment with a 5% down payment is $150,000 * 5% = $7,500. Applying these numbers to the ROI formula:\[ ROI = \frac{(\$165,000 - \$150,000)}{\$7,500} * 100 \% \] This gives the ROI when a 5% down payment was made.

Key concepts

ROI Formula

Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment or to compare the efficiencies of several different investments. The ROI formula is a simple yet powerful tool to understand the profitability of an investment.

The general ROI formula is: \[ ROI = \frac{(Current value of Investment - Cost of Investment)}{(Cost of Investment)} \times 100 \% \]
In the context of real estate, this calculation becomes especially important, as it can indicate how well an investment in property is performing. To calculate ROI, you subtract the original cost of the investment (the purchase price) from the current value of the investment (often the current market price), then divide by the original cost and multiply by 100 to get a percentage.

For example, if you buy a house for \$150,000 and it appreciates to \$165,000, your ROI calculation would be: \[ ROI = \frac{(\$165,000 - \$150,000)}{(\$150,000)} \times 100\text{%} \]
That would yield an ROI of 10%. However, when considering a financed purchase with a down payment, the ROI calculation changes because the initial investment cost is your down payment, not the full purchase price.

Investment in Real Estate

Investing in real estate has long been considered a solid strategy for building wealth. When purchasing a property, you're not just acquiring a physical asset but also the potential for appreciation, rental income, and tax benefits. The real estate market can fluctuate based on a myriad of factors, including economics, interest rates, and even local developments, so understanding your potential ROI is critical.

Real estate investments differ from other types of investments like stocks or bonds, due to factors like property management, maintenance costs, and the impact of local real estate markets. These factors can influence both the cost of the investment and the eventual selling price, and consequently, affect the ROI. It's essential to conduct thorough research, accounting for renovations, ongoing upkeep, property taxes, and potential rental income when calculating your expected ROI on a real estate investment.

Down Payment Impact

The down payment on a real estate investment plays a significant role in your financial leverage and the total ROI of the property. A larger down payment means you invest more cash upfront, which can lead to a lower ROI percentage, as your initial investment is higher. Conversely, a smaller down payment increases your financial leverage by allowing you to control a large asset with less money down.

Calculating ROI with different down payments highlights the impact of leverage. For instance, with a 20% down payment on a \$150,000 property, the initial investment is \$30,000. If the property's value increases to \$165,000, the ROI would be:\[ ROI = \frac{(\$165,000 - \$150,000)}{(\$30,000)} \times 100\text{%} = 50\text{%} \]
However, with a 5% down payment, the initial investment is only \$7,500, which results in a much higher ROI since the gain is multiplied over a smaller initial investment:\[ ROI = \frac{(\$165,000 - \$150,000)}{(\$7,500)} \times 100\text{%} = 200\text{%} \]
It's important to note that while a smaller down payment can significantly increase ROI percentage, it also typically comes with higher borrowing costs and can carry more risk, such as increased mortgage payments and potential for negative equity if property values fall.