Question

What is the price of an apartment if the monthly rent is $3,500, the monthly discount rate is 0.6%, and the monthly growth rate is 0.3%. Assume that for a special offer the first three month of rent are free.

Answer 1

Answer: $1,156,197.95

Calculation:

As Rent is growing and it is continuous, it becomes a case of a continuous growing perpetuity.

The present value (PV) of this perpetuity becomes the price or value of this apartment.

PV of growing perpetuity can be derived using...

PV = rent / (r-g)

Where rent is $3500, r = discount rate, g= growth rate.

PV = $3500 / (0.006-0.003) ( Here we took 0.006 for discount and 0.003 for growth because values are in percentage to use here we have to divide it by 100)

= $ 1,166,666.67

However, for a special offer, the first three months of rent is free. So, we have to reduce this value from PV.

Rent for month - 1 is $3,500

Rent for the month - 2 is $3,510.5 (0.3% growth over previous month rent)

Rent for the month - 3 is $3,521.0315

The present value of all three is

PV of Rent - 1 is $3,500

PV of month-2 rent is $3489.563 (which is $3510.5 - rent of month-2 discounted at 0.6% rate)

PV of month-3 rent is $3479.156

The Sum of all three rents is (3500 + 3489.563 + 3479.156) = $10,468.72

subtracting the value of the first three months...

= $ 1,166,666.67 - $10,468.72

= $1,156,197.95