# Lease Obligation Present Value Calculation

## What is the present value of a lease obligation with fixed payments that increase over time?

You have signed a new lease today to rent office space for five years. The lease payments are fixed at $4,500 per month for years 1 and 2, but rise to $5,500 for years 3 to 5. What is the present value of this lease obligation if the appropriate discount rate is 8%?

The present value of the lease obligation is $22,810.95.

Present value is the value today of a sum of money which is payable or receivable in the future. It is a core concept of financial management. The formula for calculating the present value of an annuity is given by:

**PV = A[(1 - (1 + r)^-n) / r]**

Where:

- PV is the present value of the lease obligation
- A is the annual payment
- r is the discount rate per annum
- n is the number of years

Therefore, given the information in the question, the present value of the lease obligation is:

**For years 1 and 2:**

Annual payment = $4,500

The payment is made for 2 years. Therefore, n = 2

Discount rate, r = 8% = 0.08

Using the formula:

**PV = $4,500[(1 - (1 + 0.08)^-2) / 0.08] = $8,194.14**

**For years 3 to 5:**

Annual payment = $5,500

The payment is made for 3 years. Therefore, n = 3

Discount rate, r = 8% = 0.08

Using the formula:

**PV = $5,500[(1 - (1 + 0.08)^-3) / 0.08] = $14,616.81**

Therefore, the total present value of the lease obligation is:

$8,194.14 + $14,616.81 = $22,810.95

Thus, the present value of the lease obligation is $22,810.95.