Question

Joe got a job offer and he decided to rent his own apartment. He visited apartment A and was very satisfied. He has already paid a deposit of $1,000 on a 12-month apartment lease, but he still has NOT paid the first month’s rent and signed any contract yet. The monthly rent for apartment A is $1,000, and the deposit is refundable at the end of twelve months upon completion of the lease contract.

The next day, Joe finds a different apartment B that he likes just as well, but its monthly rent is only $900. If he rents this apartment, he would again have to pay a deposit of $900 and that is refundable at the end of the 12-month contract.

Joe now faces a dilemma - whether he should stay in the apartment A, or switch to the cheaper apartment (apartment B) and forego the deposit that he just paid. He decided to make a decision by comparing the present value of the FUTURE cash flows associated with the two apartment leases.

It is assumed that the discount rate is 2% per month. The rent for each month is paid at the beginning of the month in advance, and the deposit is returned at the end of twelve months.

Note: In the calculation, all the cash outflows are in negative values and all the cash inflows are in positive value. For example, the monthly rent of $900 is the amount you have to pay, so it should be -$900 in your calculation.

(a) What is the present value of the future cash flows (negative value for cash outflow and positive value for cash inflow) associated with apartment A?

Answer 1

Answer A: Present Value of the Future Cash Flows for apartment A is

Present value formula = Cash Flow / ( 1 + Discount rate ) ^ ( no. of period)

Discount rate is 2% per month

For Apartment A, at time 0 in the starting we will have to pay 2 amounts of 1000 each as rent is also paid in the starting,

after that we will pay 11 equal amounts of 1000 each at the starting of every month.

at the end of 12th month we will get 1000 back

Use the present value formula mentioned above, Cash Flow present value would be

	0	1	2	3	4	5	6	7	8	9	10	11	12
Cash Flow	-2000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	-1000	1000
Present Value	-2000	-980.39	-961.17	-942.32	-923.85	-905.73	-887.97	-870.56	-853.49	-836.76	-820.35	-804.26	788.49