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.