Question

In the fall, Jay Thompson decided to live in a university dormitory. He signed a dorm contract under which he was obligated to pay the room rent for the full college year. One clause stated that if he moved out during the year, he could sell his dorm contract to another student who would move into the dormitory as his replacement. The dorm cost was $5000 for the two semesters, which Jay had already paid A month after he moved into the dorm, he decided he would prefer to live in an apartment. That week, after some searching for a replacement to fulfill his dorm contract, Jay had two offers. One student offered to move in immediately and to pay Jay $300 per month for the eight remaining months of the school year. A second student offered to move in the second semester and pay $2500 to Jay. Jay estimates his food cost per month is $500 if he lives in the dorm and $450 if he lives in an apartment with three other students. His share of the apartment rent and utilities will be $414 per month. Assume each semester is 4.5 months long. Disregard the small differences in the timing of the disbursements or receipts. What is the cost of the cheapest alternative?

Answer 1

ans...
a) Jay can stay in the dorm and spend $500 on food evry month.


Or Jay can move out immediately and rent the dorm for the first student.


Or Jay can move in the second semester and rent the dorm to the second student.


b) The $5000 Jay paid for room rent is sunk cost and has no bearing on the future expenses:


1st case: Jay's expenses will be 8 months* $500 = $4000.


-Or in the second case(first offer), Jay's expenses wuld be (450+400)*8 = $6800
But he would get dorm rent of $300 per month, so his total expenses are $(850-300) per month =$550*8 = $4400


-Or else in the third case (2nd offer), his expenses for 3 and 1/2 months in dorm is = 3.5*500 = $ 1750.
Expenses for the remaining 4 and 1/2 months in apartment = (4.5)*(450+400) = $ 3825
total expenses = $(1750+3825) = $ 5575, but with the dorm rent of $2500, his expenses become $(5575-2500) = $3075.


c) I recommend that Jay stay the remainder of the semester in the dorm room and take up the second offer for $2,500 for the second semester as this is the most economical way for Jay.