Kim and Dan Bergholt Are Both Government Workers

Kim and Dan Bergholt are both government workers. They are considering purchasing a home in the WashingtonD.C. area for about $280,000. They estimate monthly expenses for utilities at $220, maintenance at $100, property taxes at $380, and home insurance payments at $50. Their only debt consists of car loans requiring a monthly payment of $350.

Kim's gross income is $55,000/year and Dan's is $38,000/year. They have saved about $60,000 in a money market fund on which they earned $5,840 last year. They plan to use most of this for a 20% down payment and closing costs. A lender is offering 30-year variable rate loans with an initial interest rate of 8% given a 20% down payment and closing costs equal to $1,000 plus 3 points.

Before making a purchase offer and applying for this loan, they would like to have some idea whether they might qualify.

1.Estimate the affordable mortgage and the affordable purchase price for the Bergholts.

2. Suppose they do qualify; what other factors might they consider before purchasing and taking out a home mortgage?

3. What future changes might present problems for the Bergholts?

The real estate agent tells the Bergholts that if they don't care to purchase, they might consider renting. The rental option would cost $1,400/month plus utilities estimated at $220 and renter's insurance of $25/month. The Bergholts believe that neither of them is likely to be transferred to another location within the next five years. After that, Dan perceives that he might move out of government service into the private sector. Assuming they remain in the same place for the next five years, the Bergholts would like to know if it is better to buy or rent the home. They expect that the price of housing and rents will rise at an annual rate of 3% over the next five years. They expect to earn an annual rate of 5% on the money market fund. All other prices, including utilities, maintenance, and taxes are expected to increase at a 3% annual rate. After federal, state, and local taxes, they get to keep only 55% of a marginal dollar of earnings.

4. Estimate whether it is financially more attractive for the Bergholts to rent or to purchase the home over a five-year holding period. (Assuming the contract interest rate of 8%, monthly interest payments over the five-year period would total $87,574.)

5. Suppose it turns out that they have to relocate after one year. Which is the preferred alternative after one year? (Interest payments over the first year would equal $17,852.)

Solution

1)

To be able to answer this question, we would need to calculate the annual expenses (of the mortgage plus their current obligations) and compare those to the combined annual income of the Bergholts:

Annual repayment cost of mortgage:

Since the Bergholts would be making a 20% down payment, then the amount to be financed = $280,000 - $56,000 = $224,000

Final value of mortgage =

= $2,254,035

Sum of repayments (S) =

Since Sum of repayment = Final value of mortgage
Therefore, 113.283A = 2,254,035
A = $19,897

Expenses:

Income
Gross Income from salary = $55,000 + $38,000 = $93,000
Net Income (55% marginal rate) = 93,000 * 55% = $51,150
Income from savings = 60,000 + 5,840 – Down Payment (56,000) = $9,840
5% annual earning on money market fund = 9,840 * 5% = $492
Net annual income after purchase of property = 51,150 + 492 = $51,642

Therefore, Affordability = Net annual income – (expenses + annual repayments) = 51,642 – (13,200 + 19,897)

= $18,545

The Bergholts can afford to purchase the house because their annual income will exceed costs by $18,545 when they make a purchase. The mortgage here is assumed to be the full cost of the house with a down payment of 20%. However, research has shown that couples should purchase a house two and a half times their combined gross salary and repayment should not be more than 35 to 40% of the net salaries. For the Bergholts this means that they can afford a house worth $232,000 and can pay a repayment to the amount of $1,491 which means that the ideal mortgage would be worth $168,905.

2)

Factors to Consider before Taking out Mortgage:

The Bergholts should consider their choices for the various types of loans that may be available to them. For example 15 year loans instead of the current 30 year loan being offered and fixed rate loan instead of the adjustable rate option. Which would be more advantages to them? Adjustable rate mortgages (ARM) carry the advantage that low rates and payments are made in the early period which enables the borrower to invest more and take advantage of falling rates without refinancing. ARM should be attractive to the Bergholts because they particularly suite borrowers who do not want to live in one place for a very long time. However, fixed rate loans are simple to understand and one can make reliable budgeting. ARMs have the disadvantage that rates could climb steeply with the passage of time.

15 year loans will cost the Bergholts more in repayment and they would probably not qualify for the $224,000 mortgage. 30 year loans spread the cost of payment and make it easier to pay repayments. 30 year loans are suitable for the Bergholts because they do not plan to live in the house they intend to purchase for a long time. (Bankrate.com)

There are some very important factors that any borrower should consider. These factors relate to the terms of the loan, such as the interest rate, discount and origination points, closing costs, locking of the interest rate, prepayment penalties, minimum requirement of down payment, qualifying guidelines and the documents that are to be disclosed.

3)

Potential problems that the Bergholts may have to face during the processing of their mortgage could materialize in the form of credit problems. While after the loan is provided the Bergholts may feel the shock of the repayments and would have to adjust their spending accordingly. But, perhaps the worst case scenario would occur when the variable rates start to go up (this can happen due to many reasons) the Bergholts may find that they are unable to pay the rising interest cost in their repayments. The risk of foreclosure due to non payment to annuities can become a reality.

4)

Rent:

Rent at $1,400 per month will cost $16,800 per year.
Utilities will cost $2,640 per year
Insurance will cost $300 per year.
Therefore the rent option will cost the Bergholts $19,740 per year.
Assuming a 3% rise in rent and utilities,
Year 1 costs = $19,740
Year 2 costs = 19,440 * 103% + 25 = $20,048
Year 3 costs = 20,048 * 103% + 25 = $20,675
Year 4 costs = 20,675 * 103% + 25 = $21,320
Year 5 costs = 21,320 * 103% + 25 = $21,985
Total Cost = $103,768
Applying annuity:
S = {19,440 [1.03 ^ 5 – 1] / 0.03} = $103,209
Investment in mutual fund:
S = 65,840 (1.05) ^ 5 = $84,030
Interest earned = $18,190
For the five year period the rent option would cost (103,768 – 18,190) = $85,578
And this figure would be (85,578 *100) / (5 * 51,150) = 33.5% of Bergholts’ net income over the five year holding period

Buy:

Buying would cost $87,574 in interest payment for the five year period
Against this the remaining mutual fund would receive interest:
S = 9,840 (1.05) ^ 5 = $12,558
Interest earned = $2,718
For the five year period buying the house would cost (87,574 – 2,718) / 255,750 = 33.2% of Bergholts’ net income over the five year holding period. Not only would the Bergholts acquire title to the house but they would also save more if they buy and hold for five years.

5)

If the Bergholts relocate in one year then for the first year rent cost would be (19,740 – 3,292 (interest earned)) = $16,448
Compared to this figure interest cost for buying would be $17,852 less interest earned ($492) = $17,360. Add to this figure the closing costs and 3 points = $1,000 + $6,720 = $7,720. The grand total for the cost of buying and relocating in a year would be (17,360 + 7,720) = $25,080. Needless to say this figure is too high and therefore the rent option would be preferable if there is the prospect of relocating in one year.