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.
-1-
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.
What is the present value of the cash flows (negative value for cash outflow and positive value for cash inflow) associated with apartment B.
Answer : Present value formula : Cash flow/(1+ discount rate)^(no of periods)
Discount rate = 2% per month
In the starting we will have to pay 1800 (900 deposit and 900 first month rent as it is to be paid in advance)
Assumption : Only apartment B cash flow is considered i.e. 1000 deposit that we will have to forego of apartment A is not considered in this calculation. Cash flow related to apartment B only has been asked to be considered in question
| Month | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Cash Flow | -1800 | -900 | -900 | -900 | -900 | -900 | -900 | -900 | -900 | -900 | -900 | -900 | 900 |
| Present Value | -1800 | -882.35 | -865.05 | -848.09 | -831.46 | -815.16 | -799.17 | -783.50 | -768.14 | -753.08 | -738.31 | -723.84 | 709.64 |
| Net Present value | -9898.52 |
Present value of the cash flows is coming out to be -9898.52.
Get Answers For Free
Most questions answered within 1 hours.