**“House Hunters” Due Date:** Wednesday, December 12, 2018

(submit to Blackboard)

**Purpose:**

Buying a house can be difficult work. It requires balancing the needs of you and your family with the condition of both your current and future finances. How much house do I need, in what location, and will I be able to afford it? And this balance is often nowhere to be found on the HGTV series *House Hunters*. On each episode of this reality-based show, we meet prospective home buyers, often a young couple, and learn about their lives and their jobs while a TV realtor walks them through several luxurious properties for them to choose from. But how “real” is this reality show? Could the clients *really* afford a mortgage on the houses they’re browsing, on the salaries they’re making, in the locations they’re hunting?

In this project you’ll assume the role of a mortgage lender hired by the *House Hunters* producers to help the buyers finance the house they purchase. Using the information available about the buyers, the location, and the house in the episode, you’ll determine: **Could these buyers really afford this** **house? **You’ll prepare a written report of your analysis to share with the show’s producers, and/or summarize your findings in a slide presentation for the buyers.

**Skills you’ll gain:** This assignment will help you practice the following skills that are essential to your success in this course, in your career, and beyond:

- Determining the effects of changing loan parameters (especially interest rate and amount financed) on monthly payments.
- Using an algebraic model to make an informed forecast of future events based on historical data.
- Using basic descriptive statistics (mean, median, standard deviation) to communicate distributions and uncertainty in measured quantities.
- Communicating mathematical and quantitative reasoning in ways appropriate for an audience.
- Making and supporting decisions drawn from quantitative evidence.
- Using basic spreadsheet functions to organize and visualize quantitative information.
- Preparing an effective slide presentation.
- Locating and assessing information from public data sources online.

**Knowledge: **This assignment will also familiarize you with the following mathematical content knowledge.

- Descriptive statistics associated with a data set (mean, median, mode, standard deviation)
- Normal distributions (“bell curves”) and their percentile ranks

**Tasks: **

- Select and watch an episode of
*House Hunters*( Dr. S will provide links to episodes via http://bsumath105.slack.com ). Take notes on the following information, as specifically as the episode permits. Some data may be missing.- Buyers’ names and age(s)
- Buyers’ jobs/careers
- Buyers’ length of time in current career
- Buyers’ additional assets (savings, investments, etc.)
- Buyers’ stated budget (“We have $… to spend” or “We’ve been approved up to $…”)
- Location of property (city and state; neighborhood if given)
- Type of property (single-family home / multi-family / condominium / etc.)
- Size of living space, in square feet
- Size of lot, in square feet or acres
- Number of bedrooms and bathrooms in property
- Any extra fees listed in episode, such as homeowners’ association fees

- Determine the
**buyers’ probable annual income.**- Research the annual wages of their jobs from the U.S. Bureau of Labor Statistics’ public database: Record the
*mean annual wage*as well as the*10%, 25%, median, 75% and 90% percentiles*for their jobs**nationwide**. - Repeat the previous step, but first select the closest metropolitan area to where the buyers’ house is located to obtain
**local estimates**as well. - Use the information above to
**decide on an estimated annual income**for your buyers. Make this a single number, and divide it by 12 to**estimate their monthly income**as well. - Write a page (and/or a slide) describing your findings. You may wish to address questions such as
- How does the mean wage compare to the median wage in this sector of the workforce? What does that suggest to you about the distribution of wages — is it skewed left or right, and why might that be important for your decision? Do these data suggest possibilities for promotion and advancement in their current careers?
- How do the wages in the buyers’ local market compare to the nationwide averages? What, if anything, does that suggest about the cost of living in the community where they’re buying their house?

- Research the annual wages of their jobs from the U.S. Bureau of Labor Statistics’ public database: Record the
- Estimate the
**present and future values of the property purchased.**- Download from Zillow.com’s Home Value Index (ZHVI) database data sets on the following. (These will be pretty large files; you can delete every row except the one containing the appropriate data for your city.)
*Median Home Value per Square Foot*– by*City**ZHVI Time Series*for the appropriate number of bedrooms – by*City*

- Use the first file (median value-per-square-foot) to predict the value of the buyers’ house in January of each year from 2009 to 2018.
- Use the second file (ZHVI time series) to predict the value of the buyers’ house in January of each year from 2009 to 2018.
- Based on both models,
**decide on an estimated median value for the buyers’ house in January 2018.** - Create a scatter plot and fit a
*linear regression*to the models in #2 and #3 above. Use these models to**decide on an estimated median value for the buyers’ house in January 2028.** - Write a page (and/or a slide) describing your findings. You may wish to address questions such as
- Do the data suggest the housing market is strong (values generally increasing) or weak (values remaining level and/or declining) in the buyers’ local area?
- Are the square-footage model and the number-of-bedrooms model both telling the same story? How did you incorporate both in determining your estimate?
**Compare your estimate to the**Are they significantly different? How might you (or the show’s producers) explain the difference?*House Hunters*sale price.

- Download from Zillow.com’s Home Value Index (ZHVI) database data sets on the following. (These will be pretty large files; you can delete every row except the one containing the appropriate data for your city.)
- Calculate the
**monthly payment on the house’s mortgage**under several scenarios.- Select several mortgage lenders (example) and research the annual percentage rate (APR) they are offering for at least the following types of mortgages. Use data from several lenders to estimate the APR they can expect for each.
- Conventional 30-year fixed rate
*(Down payment: 20%)* - Conventional 15-year fixed rate
*(Down payment: 20%)* - FHA 30-year fixed rate
*(Down payment: 3.5%)*

- Conventional 30-year fixed rate
- For each type of loan above, use the
*House Hunters*sale price of the home to determine the minimum down payment the buyers would need. - Then, deduct this down payment from the sale price and use a compound interest formula to determine the
**total value of the mortgage**over the full term (15 years or 30 years as appropriate). Split these amounts into**monthly payments**for each loan type. - Compare each monthly payment to the buyers’ estimated monthly income (Step 2).
**What would their mortgage payment be, as a % of their gross income?**(This is called their LTI —**loan-to-income ratio.**)

- Lenders and financial planners typically recommend that borrowers carry no more than 36% of their gross income as debt. (That includes a mortgage as well as credit card payments, car payments, alimony, child support, student loans, etc.)
**Is this reasonable for your buyers?**Would you expect them to have these other types of debts as well? - Write a page (and/or a slide) describing your findings. You may wish to address questions such as
- Based on your analysis, do you believe the buyers can afford their home?
**If yes,**which type of loan would you recommend they apply for? (What are the advantages and disadvantages of each for them?)**If no,**suggest at least 1–2 changes that would make the house affordable for them. For example: should they increase their down payment? By how much? Would reducing the APR by 0.5% make it affordable? What about 1.0%?

- Select several mortgage lenders (example) and research the annual percentage rate (APR) they are offering for at least the following types of mortgages. Use data from several lenders to estimate the APR they can expect for each.
- Write your final report — either a paper of approximately 1500 words or a slide presentation of approximately 8–10 slides — giving your professional decision. (You may include the writing you did in Parts (1)-(4) as an appendix, but the report itself must be original.)
**Is this house affordable for these****buyers?***If a written report:*Your audience is the producers of*House Hunters*. They are more comfortable with technical details, so you can include more data tables, math vocabulary words, and algebra in your written report.*If a slide presentation:*Your audience is the buyers. They’re not experts in financial matters, but you still need to justify your decision and your calculations to them. You may wish to rely more heavily on graphs and visuals to make your points, and take care to use accurate but accessible language.

**Criteria for success:** Your final report will be assessed as successful if it meets *all* of the following criteria.

For a score of **P** (Progressing): All of the following

- Research findings from all of steps (1) through (5) are present in the final report, such as in an appendix or attachment.
- Each of the following estimates is clearly stated in the final report:
- Buyers’ estimated (annual and monthly) income
- House’s estimated value in 2018 and in 2028
- Total value, and monthly payment, for mortgage for each loan type
- Buyers’ loan-to-income ratio for each loan type

- A final decision is clearly stated, and there is sufficient evidence in the report to justify that decision.
- Report is submitted by the due date and meets appropriate length requirements.
- Report is free of errors in spelling and grammar, conforming to the conventions of standard written English.

For a score of **S** (Satisfactory): All of the criteria for** P**, plus the following

- Research findings from all of steps (1) through (5) are integrated into the final report, with the writing/visuals showing how each one is used to support the final decision.
- Each of the estimates in #2 above has supporting work (data tables, graphs/charts, algebra) that show exactly how they were determined from the evidence.
- The final decision is both clearly stated
*and*explicitly supported by references to research findings. - At least one alternative scenario is provided, with specific recommendations for either down payments or interest rates, under which the buyers
**can**afford the house they’ve selected. - The written, graphical, numerical, and algebraic communication used is appropriate for the selected audience.

For a score of **E** (Exemplary): All of the criteria for **S**, plus the following

- Two versions of the final report are prepared that meet
**S**criteria from among the following three options.- A written report appropriate for a more technical audience
- A slide presentation appropriate for a less technical audience
- A video or audio presentation appropriate for a less technical audience.