You are planning to live in the city of Houston, Texas for 5 years. You are deci

Question

You are planning to live in the city of Houston, Texas for 5 years. You are deciding to rent or to buy a house for this 5-year period.

Rent:   Monthly rental cost will be $1,200 paid at the end of each month.

Buy:    The purchase price of the house you intend to buy is $220,000. You will pay cash. You believe you can sell the house for $250,000 at the end of 5 years.

Which option (buy or rent) is better, and by how much? The interest rate is 5.76% COMPOUNDED MONTHLY. Ignore income taxes. Also ignore any other factors not specifically mentioned in the data above.

  Rent is better. The difference is $30,000.

  Buy is better. The difference is $24,020.

  Rent is better. The difference is $24,020.

  Buy is better. The difference is $30,000.

  Rent is better. The difference is $30,000.

  Buy is better. The difference is $24,020.

  Rent is better. The difference is $24,020.

  Buy is better. The difference is $30,000.

Explanation / Answer

Answer:

To evaluate both the options, we need to calculate first the Present Value of Cash Outflow required under each option...

Since the interest is compounded monthly, the no. of periods = 5 years x 12 month per year = 60

Interest Rate = 5.76% p.a. or 5.76/12 = 0.48% per month

Rent Option

Present Value of Cash Outflow = Montlhy Rental x PVIFA (0.48%, 60) = $1,200 x 52.025 = $62,430

Buy Option

Present Value of Cash Outflow = Purchase Price of House at year 0 - PV of Sale Proceeds of house at end of 5 year = $220,000 - [($250,000 x PVIF (0.48%, 60)] = $220,000 - ($250,000 x 0.75027835) = $220,000 - $187,570 = $32,430

By looking the Present Value of both the option.....Rent Option require PV of Cash Outlfow $62,430 and Buy Option require PV of Cash Outflow $32,430

Buy Option is better since PV of Cash Outflow is less than Rent Option by $30,000 ($62,430 - $32,430)

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