Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a simple annual rate of 5 percent. By what amount would your net worth change if you accept the new lease?

Change in Net worth = $133.62

Explanation:

The two lease options require that the leasee (the tenant) commit himself to pay a series of equal amount of rent installment at the different time period in the future.

These series of equal periodic cash flows occurring in the future are called annuities.

To have a meaningful comparison, the two annuities should be compared based on their present values. So we compute the present value of the two using the formula below:

Present Value (PV) = (A * (1 - (1+r) ^ (-n)) / r

Option 1:Current lease

PV = 500 * 1 - (1+0.05) ^ (12)

= 500 * 8.863251636

= $4,431.62

Option 2: New Offer

This will be done in two steps:

PV of lease in year 3

PV = 700 * (1 - (1+0.05) ^ (-9))

= 700 * 7.107821676

=4,975.47

PV of lease in year 0

PV = FV * (1+r) ^ (-3)

=4,975.47 * 0.8638

=$4,298.00

My net worth would change by the amount of the difference between the two PV of the two annuities:

Difference in PV = $4,431.62-$4,298.00

Change in Net worth = $133.62