Time Value Of Money—Preparing For Homeownership

The Time Value of Money—Preparing for Home Ownership

Upon graduating from Argosy University with a degree in Finance, John Simple found a great job as a banking officer with Capital Two Bank in Dallas. Although he and his partner Joan had several college loans that required payments, their goal was to set aside funds for the next five years so that they could get out of the small apartment in Irving, Texas.

After reviewing the listings in the areas surrounding DFW and speaking to their bosses about possible transfers, John and Joan decided upon Plano as their desired future location for a home. Based on house prices they received from a local realtor, they determined that the home they needed currently costs around $178,000, including 2% closing costs. To avoid paying Private Mortgage Insurance, John and Joan need to make a down payment of 20%. Since they are saving for the potential purchase, it will be five years before they buy the home. This gives them time to save for the down payment, moving, and furniture costs, which they estimate will be 10% more than the required down payment.

They also expect home prices in Plano to continue to increase each year at a 2.5% per annum rate as presented by their realtor. John, being the finance graduate, wanted to adequately prepare for their future purchase and told Joan that he would take all this information and present an overview of how much would be required once their estimated purchase date became a reality. In addition, John would show how much money they needed to save each month in their house investment account at E-Trade, which averages a 5% annual return.

Assignment Tasks

Calculate the estimated purchase price of the home in five years, considering the projected annual home price appreciation of 2.5%. Determine the amount needed for the down payment, the closing, moving, and furniture costs. Use the current savings of $10,000, noting that half was a gift from Joan’s parents, and calculate how much they need to save monthly to reach their goal. Additionally, analyze how changing the investment plan at E-Trade to earn an additional 1.5% per annum affects their monthly savings requirement. Finally, estimate the investment savings by increasing their investment percentage.

Paper For Above instruction

The process of planning for homeownership is a practical application of financial management principles, particularly the time value of money (TVM). TVM underscores the importance of the value of money over time, recognizing that a dollar today is worth more than a dollar in the future due to its capacity to earn interest. In this case, John and Joan’s planning involves calculations regarding future home prices, savings, and investment returns which necessitate an understanding of future value (FV), present value (PV), and compound interest (Brigham & Ehrhardt, 2021).

The initial step is to estimate the future home price. Given the current price of $178,000, with an annual appreciation rate of 2.5%, the future value of the home after five years can be calculated using the compound interest formula:

FV = PV × (1 + r)^n

Where PV = $178,000, r = 0.025, and n = 5 years. Applying these, the future home price becomes approximately:

FV = $178,000 × (1 + 0.025)^5 ≈ $178,000 × 1.1314 ≈ $201,356

This highlights that in five years, the home price is projected to increase to approximately $201,356, which forms the basis for further calculations regarding down payment and other costs.

The down payment, set at 20% of the future price, would be approximately:

Down Payment = 0.20 × $201,356 ≈ $40,271

Adding 10% for closing costs, furniture, and moving expenses, the total initial cash needed would be:

Additional Costs = 0.10 × $40,271 ≈ $4,027

Thus, the total amount for the down payment and related costs sums to about:

Total Initial Outlay = $40,271 + $4,027 ≈ $44,298

Considering they already have $10,000 saved, with half gifted by Joan’s parents, the net amount needed to be accumulated through monthly savings over five years is:

Remaining Savings Needed = $44,298 - $10,000 = $34,298

To determine the monthly savings required, the future value of a series formula is used, considering their investment account at an annual return of 5%:

PMT = FV × [r / ((1 + r)^n - 1)]

Where FV = $34,298, r = 0.05/12 ≈ 0.004167, n = 60 months. Plugging these into the formula yields:

PMT ≈ $34,298 × 0.004167 / [(1 + 0.004167)^60 - 1] ≈ $583

Therefore, John and Joan need to save approximately $583 each month to reach their goal in five years with a 5% annual return.

If they could increase the annual return by 1.5%, bringing the total to 6.5%, the new monthly savings requirement would decrease. Recalculating with r = 0.065/12 ≈ 0.005417:

PMT ≈ $34,298 × 0.005417 / [(1 + 0.005417)^60 - 1] ≈ $541

This demonstrates that a higher investment return significantly reduces their monthly savings, illustrating the impact of investment risk-return trade-off.

Furthermore, increasing their investment percentage could enhance the total savings, but it also involves higher risk. A balanced approach, aligned with their risk tolerance, is essential. Financial theory supports diversifying investments and considering risk-adjusted returns to optimize savings strategies (Brealey, Myers, & Allen, 2019).

In conclusion, applying TVM principles and understanding the effect of investment returns are crucial for effective financial planning toward homeownership. By calculating future values, necessary savings, and analyzing the impact of higher returns, John and Joan can develop a structured plan that aligns with their financial goals and risk preferences.

References

• Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
• Brigham, E. F., & Ehrhardt, M. C. (2021). Financial Management: Theory & Practice (16th ed.). Cengage Learning.
• Investopedia. (2023). Understanding Time Value of Money (TVM). Retrieved from https://www.investopedia.com/terms/t/timevalueofmoney.asp
• Moneychimp. (2023). Stock Investing & Valuation Models. Retrieved from https://www.moneychimp.com/
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• Yahoo Finance. (2023). Home prices data and appreciation rates. Retrieved from https://finance.yahoo.com/
• E-Trade. (2023). Investment tools and calculators. Retrieved from https://us.etrade.com/
• U.S. Census Bureau. (2022). Home Price Index Data. Retrieved from https://www.census.gov/
• National Association of Realtors. (2023). Housing Market Statistics. Retrieved from https://www.nar.realtor/