In this "Time Value of Money: The Buy Versus Rent Decision" case study, a recent MBA graduate had been renting an apartment while a similar flat had been listed for sale. The graduate is now facing the typical buy versus rent decision. Hence the grad decided to apply some of her analytical tools acquired in business school to make this decision for her personal life.

Sean Cleary, Stephen R. Foerster

Ivey (W14403-PDF-ENG)

August 28, 2014

### Case questions answered:

Calculate the best route for the graduate’s housing situation, developing your understanding of the time value of money (TVM) concepts and calculations. Describe your assumptions, methodology, and results in your discussion narrative, and attach a simple spreadsheet supporting your analysis.

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## Case answers for Time Value of Money: The Buy Versus Rent Decision

This case solution includes an Excel file with calculations.

In **scenario 1** (see included spreadsheet), it is assumed that Rebecca Young, rents the condo and continues to invest the $122,000. The FV of the investment at year 2 is $131,955, at year 5 is $148,432 and year 10 is $ 180,590 given that the interest rate is 4% annually.

After deducting the net cash outflow for rent (# of months x $3,000) for each time period, the net gain on the investment (net FV of the investment) at these periods is as follows: $59,955, -$31,568 and -$179,410. Clearly, after 2 years it is no longer economically reasonable to rent the unit.

In **scenario 2** (see attached spreadsheet), it is assumed that she purchases the condo for $600,000 and uses the $122,000 for a down-payment and associated closing costs. She takes out a mortgage for $480,000 amortized over 25 years with an APR of 4%. In this case, her monthly mortgage payments are $2560.48. From the amortization table, it can be seen that her ending balance on the loan at years 2, 5, and 10 are $456,487.49, $417,572.87, and $341,620.73, respectively.

Assuming the following scenarios:

**1.** Condo price remains unchanged: When she sells the unit, after paying back her mortgage and associated costs, her net gain on her initial investment will be $77,793 at year 2, $66,127 at year 5 and $57,779 at year 10. This is a better choice compared to renting.

**2.** Condo prices drop 10% over the next 2 years, back to the original price at year 5, and increases by 10% at year 10: When she sells the unit, after paying back her mortgage and associated costs, her net gain on her initial investment will be $…

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