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Personal Finance - Kim and Dan Bergholt are both government workers

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.

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 Preview

Please see the attached file.

1. Calculate their gross monthly income.

Kim's gross income is $55,000/year and Dan's is $38,000/year
Total annual income = $55,000 + $38,000 = $93,000
Gross monthly income = $93,000/12 = $7,750

2. Deduct car loan from the total.
Gross monthly income - Car loan/month = $7,750 - $350 = $7,400

3. Multiply the resulting figure by 38% to get "income-to-debt ratio."
The answer will conform with generally accepted lenders standards of what borrowers can afford, after a down payment of 20%.
$7,400 x 38% = $2,812

4. Deduct the monthly taxes and insurance cost from both figures at in Step 3.
The result is the monthly payment on principal and interest affordable to pay on a mortgage.
Monthly taxes + monthly insurance cost = $380 + $50 = $430

$2,812 - $430 = $2,382

Then, we will find the affordable purchase price through annuity equation. The monthly payment is an annuity, which is a series of equal payments made at fixed intervals for a specified number of periods.

where PVA is the present value of annuity
PMT is the Amount of each payment
i = Discount Rate Per Period
n = period

As this is the monthly payment, which divides the payment into 12 times per year, then, we need to divide the yearly interest by 12 and multiply the number of payment made by 12.

r = i/Periods per year
8%/12 = 0.667%

Periods = Years x Periods per year
30 x 12 = 360

Then, we replace them into the equation, whereby PVA is the amount of home loan today.

PVA = PMT x 1 - 1/10.94877
PVA = 2,382 x 136.2
PVA = $324,503.96

The affordable mortgage is $2,382.
The affordable purchase price is $324,503.96.

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

There are many things to consider about a property ...

Solution Summary

The solution calculates, for the Kim and Dan case study, the affordable mortgage and affordable purchase price as well as other factors to consider before taking out a mortgage.