Sara Torelli
Quantitative Reasoning Paper1
Introduction
The decision that is to be made in this paper is whether it is financially more worthwhile to purchase a house or to rent. Using the model, the costs of purchasing a house over a thirty year period are compared to the total savings acquired from renting for thirty years. Inflation rates, tax rates, mortgage rates, rental rates, and savings rates have all been accounted for. The numerical difference between the value of a $300,000 house after thirty years versus the savings from renting over thirty years, is only $1, 011.12. I find this monetary difference to be such a small sum in the overall picture, that it should not be a factor in one’s decision. Based on this model, although there is an insignificant savings by renting versus owning, it seems more profitable to own a house versus renting because there are more long term benefits to owning. A rental generally imposes many restrictions upon the renters, such as what changes they can make on the rental, whether they are able to own pets, the number of people who can live in the rental, etc. Owning a house, on the other hand, affords one many options. The owner can make changes if they wish, and most importantly, after thirty years they will actually own the house and the property. Although a renter may have a significant sum of money in savings, after thirty years they would lack a tangible investment. When the parameters that have been chosen- extra maintenance costs and the initial price of the house- are manipulated, owning a house seems much more financially costly than renting. Yet, in order to be realistic, many other factors should be manipulated and accounted for that would increase the price of renting. Thus, after the models’ limitations have been taken into consideration, and such factors as emotional costs and benefits are integrated, it seems that purchasing a house is a better decision than renting.
Economic Parameters
Inflation
Inflation occurs when currency decreases in value. Prices tend to increase, and currency has less purchasing power than it previously had. In the model, an inflation rate of 3.5% was chosen, and it was converted to a monthly rate of 0.002916667%. A realistic range of inflation values would be anywhere from 1% up to 4%.
Inflation rate per month
Inflation rate per month is the percent of yearly inflation divided by 12 months. The spreadsheet is computed by month, so it is necessary to convert inflation rate by month as well. Thus, the chosen value of 3.5% was computed in order to convert it into months.
Tax rate
The tax rate is based on one’s income bracket. Assuming that I can afford the house, I have placed myself in the 30% tax bracket. Realistically, I am assuming that my annual income is between $55,000-60,000. Even with this income I can barely afford payments on the house, so anything below a 30% tax bracket would not be realistic.
House Costs Parameters
House initial price
The initial price of a house is the agreed upon purchasing price. This value is a chosen value of $300,000. Yet, house prices vary greatly depending upon location, size of house, quality of construction, etc. A reasonable price that I could afford would be from about $250,000 to 300,000. Assuming that my yearly income is between $50,000-55,000, purchasing a house priced over $300,000 is unrealistic.
Down payment
The down payment is a percentage of the initial price of a house that is paid at the time of purchase. Thus, a down payment is a computed value based on the initial house price. In general, a minimum down payment is 10% of the cost of the house- ($300,000)(.10)=$30,000. Yet, it seems that it is to one’s advantage to pay as large a down payment as they can, since this would lower one’s mortgage, and they would then be paying less money in interest overall. Realistically, at the time of purchase, I probably would not have any more than 10% of the initial price of the house in savings.
House mortgage interest
A house mortgage interest is a fixed interest rate that is paid on the mortgage. This fixed rate of interest is based on current stock market conditions. As a chosen value of 6% yearly, this number is converted to a monthly interest rate of 0.005. A realistic range of interest rates would be from 4% to 8%. Also, if the interest rate decreases, one always has the option of re-financing. Yet, there is a fee involved with re-financing, so it would only be to one’s benefit to re-finance if the interest rate decreased significantly.
Monthly interest
The monthly interest rate is the house mortgage interest rate converted from a yearly percentage to a monthly percentage of 0.005%. This is a computed value.
Monthly payment
The monthly payment is the sum of money that one pays each month towards their mortgage. This is a computed value that is based upon the mortgage interest rate and the principle. This figure is highly dependent upon the cost of the house and the mortgage interest rate. The formula used for this calculation is:
Payment=(Loan amount) (monthly interest/(1-1/(1+.005)^360)
The interest rate is compounded over a period of 30 year (1-1/1+.005^360), and then monthly mortgage interest rate is divided by the compounded interest rate. This number is then multiplied by the loan amount of $270,000.
The monthly payment is a set, computed value of $1,618.79. This number would only vary if the loan amount changed, the monthly interest changed, or the length of the mortgage changed.
House costs
House costs consist of maintenance, insurance, and utilities (which were not included in the model). Utilities consist of water, heat, garbage, and sewer services. The bank requires homeowner’s Insurance, and I am approximating that it will cost $200 a month. House maintenance consists of replacement of the roof at least once over 30 years, house painting at least 4 times (usually every 7 years), and any broken pipes, drainage problems, etc. that might occur. Overall, I am approximating that monthly house costs are much more than the unrealistic chosen model value of $100 per month. In the monthly house costs computation, inflation is incorporated to account for changes in prices over the 30 year span. The formula is:
100 (1+3.5)
Thus, the allotted house costs of $100 is multiplied by the inflation rate. This number could vary significantly depending on what factors are figured into house costs and what the inflation rate is. As with this parameter, inflation was factored into columns that incorporated tax, or items such as rent that are dependent upon inflation rate.
Real estate tax rate
Real estate tax rate is the rate that is determined for tax depending upon the value of the piece of property. This rate is a yearly percentage, so it must be computed to months by dividing by 12. Since this rate is based upon an assessed house value, it varies depending upon the inflation rate. The chosen tax rate for this model is 2.5%. A realistic range would be from 2.5% to 3.5%.
In the spreadsheet, the monthly real estate tax has been converted by dividing the yearly tax rate of 2.5% by 12 months, and then multiplying this figure by the house value for that month. Real estate tax=(2.5/1200) (house value). The monthly real estate tax rate is also heavily dependent upon inflation rates, since the house value is factored into the formula. The only difference in the computation from month to month is the house value for that month, which will hopefully be increasing.
Rental Costs Parameters
Monthly rent
Monthly rent is the amount of money a tenant pays to the owner of the apartment. This amount includes insurance costs. Since rent control is unlikely, inflation is factored into the model. The chosen monthly rate is $1,200, and this number is multiplied by the inflation rate in order to determine the total monthly rent. Yet, aside from inflation, other rental increases are not accounted for in this model. Rental costs are heavily dependent upon the location of the apartment, as well as the size of the apartment. If the apartment and the house are in similar locations, a realistic range of rental costs would be from $1,000 to $1,300 per month.
Savings Parameters
Savings interest
The savings interest rate is the designated percentage that is multiplied by the amount of money one has in savings- the investors return rate. The chosen savings interest rate is 10%, although this amount is highly dependent upon the condition of the stock market. If the stock market is doing well, the interest rate is generally higher. The same savings rate is used for both taxable and tax-free savings.
IRA deposit (yearly)
The IRA deposit is the amount of money that one can put into retirement accounts tax free. Congress has the ability to change this number and impose restrictions on the amount that can be invested. The chosen number of $2,500 annually must be converted into a monthly figure. $2,500 is divided by 12 in order to compute the monthly sum.
Results of Model Calculations
|
House initial price |
House value- total rental savings |
|
$320,000 |
$-119,568.20 |
|
$310,000 |
$-60,289.65 |
|
$290,000 |
$58,267.42 |
|
$280,000 |
$117,545.96 |
In this table, I have changed one parameter, which is the initial house price. I felt these values were the most realistic variations on the model value. After changing the initial house price, I subtracted the new house value from the new total rental savings. According to these results, it appears that the more costly the house, the more one saves by renting. Conversely, the less expensive the house, the more one saves by owning instead of renting. For example, for a $290,000 house, one would save a total of $58,267.42 over a thirty year period by purchasing instead of renting. For a $310,000 house, one would save $119,568.20 over a thirty year period by renting instead of purchasing. Overall, it appears that houses under $300,000 provide a savings for the owner. According to this model, houses priced over $300,000 are more costly over 30 years, and one would be better off renting. Yet, these conclusions have been made according to a very specific circumstance, and many factors could change the results, such as inflation rate.
|
Other house costs |
House value-total rental savings |
|
$300/month |
-364,022.26 |
|
$350/month |
-454,775.04 |
|
$400/month |
-545,527.82 |
|
$450/month |
-636,280.61 |
|
$500/month |
-727,033.39 |
The above table indicates how increasing the additional house costs effects the overall cost of a house. The additional house costs that I have accounted for in this table are utilities, such as water, heat, garbage, and sewer, as well as mandatory house insurance, a roof replacement, and re-painting the house (about every seven years). These average monthly costs do not incorporate other home improvements, such as remodeling or replacing old carpet. The second column of the table shows the monetary difference between owning a house and renting an apartment. According to the model, rent is $1,200 per month. It is extremely unrealistic to think that one could rent a house that is equivalent to the $300,000 house for $1,200 per month. Thus, I have decided that the rental must either be a duplex or a fairly large apartment. As house maintenance increases, one saves more by renting instead of owning a house.
|
House price (across) Monthly house costs (down) |
$320,000 |
$310,000 |
$290,000 |
$280,000 |
|
$300/month |
$-482,579.33 |
$-423,300.79 |
$-304,743.72 |
$-245,465.18 |
|
$350/month |
$-573,332.11 |
$-514,053.57 |
$-395,496.50 |
$-336,217.96 |
|
$400/month |
$-664,084.90 |
$-604,806.36 |
$-486,249.28 |
$-426,970.74 |
|
$450/month |
$-754,837.68 |
$-783,287.57 |
$-577,002.07 |
$-517,723.53 |
|
$500/month |
$-845,590.46 |
$-786,311.92 |
$-667,754.85 |
$-608,476.31 |
This table represents the effects of two manipulated parameters- initial house price, and monthly additional house costs. Although according to the model the value of the house is unaffected by monthly additional house costs, in reality the up-keep of a house is essential for maintaining the value of a house. If a house is not maintained, it will depreciate. Even though the model does not account for depreciation if a house is not maintained, it is an important fact to keep in mind. The unbolded numbers are the difference between the indicated bold initial house price and the new total rental savings that incorporates the effects of both a change in house costs and a change in initial house price. The box in the upper left corner with the number $-482,579.33, indicates what the total rental savings would be for someone who owns a $320,000 house and is paying $300 per month in house maintenance costs. When a greater sum of money is allocated for monthly house maintenance costs, the overall costs of owning a house significantly increase.
With this consideration in mind, it appears that renting is a much cheaper option than owning. The greater the initial price of the house, and the more money paid in maintenance per month, the greater the savings is for a rental. Yet, one must also consider the fact that although owning is more expensive in this scenario, there are many benefits to owning a house versus renting. Although owning may appear to be more costly, owning a house is an investment, and after the mortgage has been paid off, the house becomes a liquid asset. Owners also have more freedoms than renters do. For example, most renters are not allowed to remodel the structure, and generally are not allowed to own pets. These are just a few considerations, indicating that manipulating one or two parameters does not give one a thorough enough picture to make the decision to own or to rent, because numerous factors interplay.
Assess the Model
Overall, the model indicates that the cost of owning a house versus renting is very similar over a span of thirty years. The exact difference between the house value and the total rental savings is only $1,011.12. The difference is so miniscule, that even though renting is $1,011.12 cheaper, one still seems better off owning a house, because after thirty years they would actually own a piece of property instead of owning nothing. Yet, the model is not very realistic because it does not take into consideration many extra costs that exist in the real world. $1,200 per month is not a reasonable price for renting a house that is equivalent to a $300,000 home- it would be significantly more expensive. Also, inflation is not constant over a thirty year span, and is not the only factor that should be accounted for when determining rental price changes. It would be very rare to rent a place in which the price only increases by 3.5% annually. Rental prices usually increase by significantly more than 3.5%, because the landlord incorporates property tax increases into the rental costs.
Furthermore, the model cost of owning a house is also unrealistic. The model essentially dismisses the costs of maintenance, insurance, and utilities. These costs are both necessary and realistic in the real world, and must be accounted for. One is given no information about the condition of the house at the time of purchase, so perhaps a significant amount of expensive work needs to be done. Also, the effects of inflation are relied upon too heavily in this model. The location of both the house and rental greatly effect maintenance prices, utility prices, and property taxes due to differences in costs of living as well as the job market. Over the course of thirty years a location could change from thriving to a state of depression. In this scenario, the value of the house would be greatly diminished. Yet, the opposite scenario could occur as well, and one’s house could appreciate significantly. Thus, purchasing a house is a gamble, because there are so many factors that affect the costs, and since one cannot foretell the future, there is no way of knowing how prices will change. Still, I feel that owning a house is a more worthwhile venture than renting.