Alison Pratt

Quantitative Reasoning

Paper 1

 

                                                            To Buy, or to Rent?

           

The question of whether it is more profitable to own a home or rent an apartment is one which I know I will have to face in the next ten years. The model given has offered some insight into this question. It also showed the expenses involved in owning and in renting. The question posed, was, of course, whether it is more profitable to own a home or rent an apartment and invest. The model gave a number of parameters for determining the financial practicalities. By manipulating these parameters, I could see how different variables would affect the cost of either buying or renting. The model, however, does have some flaws, particularly because it is too general in many ways and makes too many assumptions.

            The house value is one of the parameters of this model. The $300,000 value at the beginning is assumed to increase by the monthly inflation rate. $300,000 is very high for the cost of a house. A more modest starter home can be purchased for $220,000-$280,000. The house value increases by the inflation rate, which is another parameter. The yearly inflation rate, 3.5%, is slightly higher than the current rate; however, currently, inflation is low because of the poor economy. 3.5-4% is about average. To obtain a monthly inflation rate, the rate of 3.5% is divided by 12. This number is then multiplied by the house value ($300,000) and as a result, the house value increases each year. However, the model does not take into account that the inflation rate does rise and fall.

Another parameter is the percent down payment on the home, which is set for 10 percent of the house value, or $30,000. This is a fairly realistic starting rate for a down payment, but could be increased if the buyer had more money and wanted to decrease their mortgage payments, because the more money that is put down on the house, the less has to be paid back on the mortgage. The amount to be paid on the mortgage is calculated using the parameter of the down payment on the home. The amount paid down is subtracted from the original house price, in this case, $300,000. This means that the actual amount being borrowed is $270,000. The mortgage is paid on this amount.

The monthly interest payments on the mortgage are another parameter. The model has it set at 6%, which is about where it is right now. It is inconsistent, however. The mortgage interest rate was divided by 12 in order to obtain the monthly interest rate. This number was used to obtain the monthly mortgage payments, another parameter. This is a constant number, since the mortgage is at a fixed rate. Unless you were to refinance because of lower interest rates, the monthly payment would remain the same. The monthly payments are used to pay off the loan. The amount is divided between the principal, or reduction of balance, on the model, and the interest payment. The month’s interest is computed using the monthly interest rate, as well. The balance is multiplied by the monthly interest rate. This number is then subtracted from the monthly mortgage payment, and the remaining amount is the reduction of balance. The reduction is subtracted from the loan amount, yielding the new balance, which becomes the new loan amount for the next month.

The real estate tax rate is a parameter set at 2.5%, which is a reasonable number, and divided by 12 to obtain the monthly real estate tax rate. The real estate tax is based on the assessed value of the house. The amount paid is computed by multiplying the value of the house by the real estate tax rate. As the value of the home increases, so, too, does the tax rate. This is also affected by inflation, because with inflation, the tax rate would increase as a result of an increase in property value.

The maintenance and insurance are parameters which are figured into the monthly costs of the house under ‘other costs,’ which is set at $100 and increases each month with the inflation rate. This is an unrealistic amount of money for a few reasons. First of all, insurance and maintenance cost much more than $100 a month, and frankly, are not constant. For example, one month the roof might need to be fixed, which would cost more than another month when very little maintenance work was necessary. Furthermore, the question of utilities comes into play. The heating and electrical bills alone cost more than $100 a month, which makes the chart a very low estimate of the monthly housing costs unless the ‘other costs’ are increased. The insurance is based on the location of the house. If it is in a high-crime area, it will be more expensive to insure the house. The insurance for my parents’ home in a rural area is approximately $90 a month. The maintenance can be anywhere from $15 a month (trash collection) to $5,000 for a new roof. In short, it is highly difficult to set a constant rate for maintenance. Insurance in a high-crime area would obviously be more than my parents’ rate. A fair estimate for insurance in a higher crime area might be approximately $200 a month. This is where the house costs could significantly increase.

However, the tax savings on the house may help compensate for the maintenance some months. The tax savings are computed by dividing the parameter of income tax rate, 30%, by 100, and multiplying it by the sum of the real estate tax and the interest paid on the mortgage. The tax rate assumes your income falls into that range; it could vary depending on your financial situation. However, 30% is reasonable.

The tax savings is then subtracted from the sum of the mortgage payment, the other house costs and the real estate tax. The end result is the total monthly house costs. The monthly house cost is how much is actually costs to have the home each month. It is used to compute the column of house-rent, which gives the amount which will be divided monthly between the savings account and the IRA for a rental.

The parameter of monthly rent, as mentioned above, is set at $1,200 a month. It is assumed that utilities are included. This amount might pay for a studio in New York. For a full-sized apartment, $2,000-$3,000 a month is more reasonable for an area like New York. However, in a suburban area, $1,200 a month might pay for a reasonably nice place. This clearly outlines a problem with the model; it does not take into account the differences in the cost of living in different areas. This is true with the monthly rent, just as it is when considering insurance costs for a house. The cost varies from place to place.

The savings interest is the money you make on the money invested in your savings account; the parameter of interest rate is set at 10%, which is very generous. It is also subject to change. When the rate decreases, the earnings decrease and the rate at which your savings grows does, too. That means if the rate plummeted to 2%, it would be far more advantageous to have your money invested in a house because the growth rate for the value of the house is greater than the growth rate for the savings account. To find the monthly savings interest rate, the 10% (.1) is divided by 12 and multiplied by the starting amount ($30,000) plus the deposited amount, which is the same as the amount in the “for savings” column. However, the model assumes you have $30,000 to invest, which would have gone toward a down payment on a house. In fact, you may have as little as $100 to invest, and are trying to accrue funds to ultimately buy a house. The interest rate is also used in the IRA account, where it is multiplied by the IRA balance plus the new deposit, to get the interest accumulated in the IRA, which is tax free.

The tax rate is paid on the interest earned in the savings account. As stated above, the tax rate is a parameter set at 30%, and to calculate the monthly taxes on interest, the 30% is converted to .3 and multiplied by the interest amassed that month. Thus, as the interest grows, as the chart assumes it will, so, too will the taxes. However, if the interest rate decreases, so do the taxes on the interest, because the taxes are based on the interest. Also, if the tax rate goes down to 20% for example, putting money into a savings account becomes highly advantageous because you pay less on the interest, assuming it remains at 10%. Another factor is that taxes are based on what you earn; if you get a promotion and make more money, your taxes will go up.

The IRA deposit is set at the maximum of $2500 a year. This amount is the maximum the government will allow invested without imposing taxes. To find the monthly IRA deposit, the $2500 is divided by 12. This parameter is based on income, and is subject to change by the government. Also, it is assumed, once again, that you have $2500 to invest, when, in fact, you might not.

The IRA’s balance each month is computed by adding the IRA balance to the IRA new deposit and the interest on that deposit. The total savings for the month can then be computed by adding the IRA balance to the new balance in the savings account.

The calculation of house-rent is carried out by subtracting the value of the house from the amount in the total savings column at the end of 30 years, or 360 months. With the set parameters, renting is considered the more profitable choice by $1,011.12. However, this number can change a great deal based on changes in the parameters.

            Some changes in the parameters which affected the house-rent calculation a great deal were the rise in inflation, the original cost of the home, and the mortgage rate. The first calculation I carried out was to see the effects of rising inflation.

                                   

Inflation Rate

House-Rent

3.5

-$1,011.12

3.6

$23,880.16

3.7

$49,224.67

3.8

$75,032.06

3.9

$101,312.17

4.0

$128,075.10

 

            Clearly, during times of inflation, you would want to own a house. This table shows a rise in house value during inflationary periods. This is because the house’s value increases with inflation. The rent is increasing monthly with inflation, as well, leaving the renter paying more per month. Furthermore, when inflation increases, the rate of accruing interest in your savings account decreases due to the decreased value of money.

            The other parameters I changed were the initial price of the house and the mortgage interest rate.

           

Price (Across)

Percent interest (Down)

$220,000

$240,000

$260,000

$280,000

7

$368,572.33

$240,502.09

$112,431.85

$-15,638.40

8

$258,781.14

$120,729.88

$17,321.38

$155,372.64

9

$144,382.18

$-4,068.98

$-152,520.15

$-300,971.32

10

$25,908.30

$-133,313.22

$-292,534.74

$-451,756.26

           

            This clearly put owning a house into perspective for me. A starter house can be bought for $220,000 with 10% down. Even when the mortgage interest rate was 10%, which is very high, it was more profitable to have a home. However, once the house price increased, the profitability decreased as the mortgage interest rate increased because more interest is paid toward the loan taken out, which, of course is larger with a more expensive house. Furthermore, the monthly mortgage payments increased with the interest rate, as well as the house price. The tax rate also decreased as a result of the lower cost of the house. From this model, I did conclude that once I had enough to put down 10% for a $220,000 home and when the mortgage interest rate was low, I would definitely buy a home.

            This model showed me how valuable an asset a house can be. During inflation, the house can be sold for a profit. It also showed me how the equity of a house builds. The model also showed me all of the expenses involved in owning a home. Clearly, the model cannot completely account for all of these expenses accurately, especially since the monthly maintenance for a house varies a great deal. The chart also assumes everything stays the same, when it is very true that the economy is changing all of the time, causing the advantages of renting versus owning to vary, as well.

I did see what I would be paying for renting an apartment and how the rent will go up with inflation; I held the misconception that the rent stayed the same. This showed me otherwise. The $1,200 is probably about what I would be paying for rent, including insurance and utilities; I priced studios in a Boston suburb, and they were $700 a month, then I figured $500 a month utilities and insurance. However, unlike the model, I do not have $30,000 to invest. I have debts, as a matter of fact. While I probably will go to graduate school with funding, which will enable me to rent an apartment, I know I will not be making any money for at least five years. However, the model did help me understand why my parents saved up to purchase a house; Clearly, owning a home is a solid investment, as it builds equity and can save on taxes, something renting cannot do. I hope that within ten years, I will be able to own a home of my own.