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    Kim and Dan Bergholt: Estimate the affordable mortgage and the affordable purchase price

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    Kim and Dan Bergholt are both government workers. They are considering purchasing a home in the Washington D.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.

    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.)

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    Solution Preview

    In case the Berghots purchase the property, then they will have to pay a down payment of about $56,000 and pay the interest over the period of 5 years that will be equal to $87,574.
    In case of the rented house, the monthly rent is 1400, the utilities will be 220 and the insurance will be 25 dollars a month giving a total of 1645. If this is multiplied by 12 we get the annual cash outflow of 19740. Please note that because ...

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