• Estimate the affordable mortgage and the affordable purchase price for the Bergholts.
• Suppose they do qualify; what other factors might they consider before purchasing and taking out a home mortgage?
• 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.
• 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.)
• 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.)
Answer:

Qualification and Affordability
If the Bergholts apply for the 30 year variable rate loan the first factor that would be judged is weather the Bergholts can afford the loan or not. Therefore we need to find out all the annual costs relating to the loan plus other expenses for the year. The figure obtained for costs would be compared to the combined annual income of the Bergholts.
Annual repayment cost of mortgage
Final value of mortgage = (280,000 – 56,000) * (1.08) ^ 30
= 2,254,035
Sum of repayments S = {[A (R ^ n -1)] / R-1} = [A (1.08^30 – 1)] / (1.08 – 1)
= 113.283A

Since Sum of repayment = Final value of mortgage
Therefore, 113.283A = 2,254,035
A = $19,897
Expenses
Maintenance…………………………………….100
Property tax……………………………………..380
Home Insurance…………………………………50
Total expenses relating to property………………530
Utilities………………………………………….220
Car loan………………………………………...350
Total Monthly Expenses………………………...1100
Total Annual Expenses………………………….$13,200

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.

Issue of Qualification
If the Bergholts want a full mortgage on the cost of the house then the rules of qualification state that the gross monthly salary should be 35% greater than sum of the monthly mortgage, monthly tax and other monthly debt payments.
Monthly mortgage = 19, 897 / 12 = $1,658
Monthly debt = $350
Estimated tax = $380 (property tax)
Monthly salary = 93,000 / 12 = 7,750
Therefore, (1,658 + 350 + 380) * 135% = $3,223 which is clearly less than the gross monthly salary.

The Bergholts can afford the home and qualify for the mortgage; however, there are other factors that will be considered. For example:
• Credit Score (creditworthiness is tested and a score between 350 and 900 is given)
• Debt ratios (% of gross income that will go towards debt)
• Loan to value ratio (the amount borrowed as a percentage of the cost of the home)
• Recent payment history regarding all loans and especially mortgages (Bankrate.com)
After much evaluation mortgage lenders assign a grade to borrowers from a range of A to E. When an A is assigned then the lender will most probably offer the best rates and loans. The Bergholts will probably get a good grade, however, no credit history of the Bergholts has been provided in this question and the only evaluation criteria left are the debt ratio and loan to value ratio.
Debt ratio = [Net Monthly Debt ($2,388) * 100] / Gross Monthly Salary ($7,750)
= 31%
Loan to Value Ratio = (224,000 *100) / 280,000
= 80%

These two ratios suggest that the Bergholts are not heavily geared but they are financing 80% of the value of the house by mortgage. Such a decision will make refinancing difficult for the Bergholts and it will also be unlikely that they would be able to qualify for further loans.
The Bergholts can apply for a pre qualification which is not a bid for the loan and consequently they can acquire a pre approval which will make it easier for them to get the loan of their choice.
Also, closing costs plus 3 points = $1,000 + $6,720 = $7,720 is significant amount which adds to the cost of the loan, this figure in particular should be negotiated.

Factors to Consider before Taking out Mortgage and Problems That Might Arise
After giving due consideration to what they can afford in the present as well as the future, 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. (Bankrate.com)

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 Bargholts 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. (Bankrate.com)

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.

The Rent Vs Buy Option
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 aquire title to the house but they would also save more if they buy and hold for five years.
One Year and Subsequent Relocation
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.