Question

A young couple has made a nonrefundable deposit of the first month's rent (equal to $1,000) on a 6-month apartment lease. The next day they find a different apartment that they like just as wekk, but its monthly rent is only $900. They plan to be in the apartment only six months. Should they switch to the new apartment? What if they plane to stay 1 year? Assume an interest rate of 12%.

Answer 1

In case the couple continues with the orginal choice of the Apartment, they will pay $1000 per month out of which they have already paid non-refundable $1000 for first month rent. Their total 6 month outflow = $ 6000.

If now they intend to move to the another apartment with $900 rent, their (marginal or incremental) cash flows - compared to origina flat chosen above - will look like: -1000 (non refundable rent on first flat), -900 (first month rent) and then they will save $100 per month in rent for next 5 months since the rent on this secon flat is lower by $100.

-1000,-900, 100, 100, 100, 100, 100 - we see that the total cash flows are negative hence if they only wish to stay for only 6 months, they should not switch the apartment. We dont even need to do pv of the cash flows since even without pv the net incremental cash flows are negative (-$1400) and the total cash outflow if they switch will be (900*6 + 1000) = $ 6400 which is more than the out lay in case they stick with the first apartment.

If the couple was to planning to stay for 1 year, the total cash outlay will be (12*900 + 1000) = $11800 which in nominal terms is better than the first apartment but we will do a pv of the cash flows for both the apartments at 12% pa or (12%/12) = 1% per month rate as below:

?Hence we see that the PV of the cash outflow at 12 months for the second apartment is lower hence they should switch if they wish to stay in that apartment for 12 months. Please note the following in this calculation:

• ?The Month 1 cash flows have not been discounted since for Apartment 1 the nonrefundable deposit has been paid in present time. The same terms have been assumed for first month Apartment 2 rent also to make a fair comparison
• Month 1 cash outflow of Apartment 2 includes $900 of rent and $1000 of nonrefunable deposit paid on Apartment 1.