Question

Assume that you are deciding to purchase a house for investment in the ideal location you prefer

You would ignore all the taxes, realtor agency fees, and the transition fee in the calculation. Only
consider the purchasing price as the total cost. Also, ignore the house insurance fee, etc. Only
consider the purchasing price, monthly mortgage and rent.
You find and decide to buy a 3-bedroom single-family house in New Haven, CT.
 The listing price is $250,000.
 Your downpayment is 20% of the price. This will be a fixed 80% payment mortgage loan
with a 20% down payment. It means you will pay a 20% down payment at the purchase and
finance 80% with a 30-year mortgage. The 30-year fixed mortgage rate is 7.5%.
 You will lease the property out right after you buy it. Assume the monthly rent in the first
year of your purchase is $1500/month and will stay the same for the next 30 years. The
rental period is 30 years, the same as your mortgage period. In other words, you will pay off your
mortgage and end the rental in 30 years.
 In 30 years, you will sell the property. Assume the value of the property increases by 5%
each year after you buy it.
1) Calculate the following value and total return. ( tips: 1) All the discount rates are the same as
the mortgage rate; 2) you must show the calculation in the report to get the credit.)
A. calculate the monthly mortgage payment (5 points)
B. calculate the PV of the monthly mortgage payment (5 points)
C. calculate the PV of the monthly rent (5 points)
D. calculate the PV of the resale value of the property in 30 years (5 points)
2) Then calculate the total return of your investment in the house. The discount rate is the
mortgage rate. The total return on your investment property is calculated as:
return = (PV of cash flows subsequent to the initial investment / Initial investment) – 1
(5 points)
3) After you get the total return in 30 years, calculate the annual compound rate of return. (5 points)
4) Next, assume you don’t purchase an investment property. Instead, you invest the same
amount of your total investment in the S&P500 index. Over the past 15 years, the S&P 500
index is 4378.41 in 2023 and 1378.76 in 2008. Calculate the annual compound rate of return of
the S&P 500 index from 2008 to 2023. (5 points)
5) Which one could you invest in, this house or S&P 500 index? Justify your conclusion. You
need to consider the factors more than the return. (5 points)

Answer 1

The financial analysis of purchasing an investment property involves calculating the monthly mortgage, PV of cash flows, total return, and annual compound rate of return, and comparing these with historical returns of the S&P 500 index, taking into account factors such as risk, liquidity, and costs.

Step-by-step explanation:

When considering the purchase of a house for investment, it is essential to calculate various financial metrics to determine the potential return on investment (ROI). For example, for a house in New Haven, CT, we can calculate the monthly mortgage, the present value (PV) of mortgage payments, the PV of monthly rent, and the PV of the property's resale value after 30 years, using a given mortgage rate of 7.5% and an annual property value increase of 5%. To get the total return, we compare the PV of cash flows to the initial investment.

To determine the annual compound rate of return, we use the formula for compound annual growth rate (CAGR). Additionally, one can compare this investment to investing in the S&P 500 index, which had a specific historical annualized return from 2008 to 2023, and decide which investment is preferable by considering factors beyond the return rate such as market risk, liquidity, and maintenance costs associated with property investment.

When comparing investment options, stocks historically offer higher average returns than bonds or savings accounts, albeit with higher risks. High-risk investments do not necessarily mean low returns; however, they are associated with greater volatility. The concept of opportunity cost and present discounted value play a critical role in these financial decisions. One must consider opportunity costs and interest rates when assessing potential investments.