Engineering economics case study
Paul and Leslie Smithson are buying a new house. They have saved for several years to
accumulate a down payment and have now found a house that is just perfect for their
needs. It is a beautiful three bedroom Tudor house in a quiet neighborhood in the
suburbs. With the help of their real estate agent and after several rounds of offering and
counter-offering, they have agreed on a price of $103,000 with the sellers. The only thing
that remains to make their new home a reality is to select a mortgage. Paul and Leslie are
unsure about the details of making this type of decision and have come to you for
guidance because of your expertise in this area.
Paul and Leslie are both 30 years old and professionally employed. They earn generous
salaries and fall into the 28% effective tax bracket on their personal income taxes. They
dream long term of retiring at the age of 65 so they can travel the country to take in all its
scenic beauty. It is this dream that drives them to determine a mortgage arrangement that
allows them to generate the maximum retirement account balance that they can create to
supplement their company sponsored retirement plans. They currently have
accumulated $10,000 to use for the down payment and closing costs on their house. Any
excess amount not used in this way could be used as an initial deposit in their retirement
savings account. Alternatively, any excess could be used to make a down payment in
excess of the minimum requirement. After studying their budget and spending patterns
they have determined that they can afford $1,000/month to cover both mortgage
payments and personal retirement savings. They are strongly committed to their
retirement travel plans, so any of the $1,000 not spent on the mortgage will be invested in
the retirement savings account. In addition, any tax savings generated through the
mortgage will be deposited in the retirement account. Although they anticipate salary
increases over the years until they retire, the impact of inflation and changes in lifestyle
will offset these to the extent that the $1,000 per month can be considered constant over
the next 35 years.
They have selected a retirement savings vehicle which involves investment in a tax
sheltered mutual fund which pays an average of 9% per year compounded monthly. Paul
and Leslie, with the help of an investment banker, have studied the history of this fund
and are comfortable that the 9%/yr/mo average return over their 35 year retirement
savings horizon is reasonable. Undoubtedly their will be ups and downs but the long
term average of 9% appears to be reasonable and stable for planning purposes. Since this
is a tax sheltered account, all investments will grow tax free until their retirement.
Paul and Leslie have identified four potential mortgage options. They will make their
selection from among these four based on your recommendation.
15 year fixed rate @ 6.63%/year/2-weeks, bi-weekly payments, minimum 5% down
payment, 1 point closing costs
The mortgage has two options (must solve for both options):
1. Going with minimum down payment and getting more loan, but depositing the remaining of the $10,000 the Smithson’s accumulated in the beginning to the retirement account in time zero.
2. Using the whole $10,000 towards down payment and 1% closing cost and get lower amount of loan, but not having anything to deposit in the beginning (time zero) in the retirement account.
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