Question

Jefferson Inc. just signed a contract to lease office space for 9 years. The appropriate discount rate is 6% per year. Show Your work.

A)If the annual lease payment is fixed at $3 million and the first payment is made one year from today, what is the current value of these lease payments?

B)If the annual lease payment starts at $2 million one year from today and grows every year after by 10% per year, what is the current value of these lease payments?

C)If the annual lease payment is fixed at $3 million and the first payment is today, what is the current value of these lease payments?

Answer 1

PV = Present value or current value ; PMT = Payment; G = Growth rate; R = Rate; N = Years

Answers below are provided in two decimal rounding in million dollars as well as in Dollar value.

a.

Present value of lease annuity:

PV = PMT x ((1-(1+R)^-N)/R

PV = 3 x ((1-(1+6%)^-9)/6%

PV = 20.40507682 = $20.41 million or $204,050,768.23

b.

Present value of growing lease annuity:

PV = PMT /(R-G) x (1-((1+G)/(1+R))^N)

PV = 2 /(6%-10%) x (1-((1+10%)/(1+6%))^9)

PV = 19.78328077 = $19.78 Million or $19,783,280.77

c.

Present value of annuity due:

PV = PMT + PMT x ((1-(1+R)^-(N-1))/R

PV = 3 + 3 x ((1-(1+6%)^-(9-1))/6%

PV = 21.62938143 = $21.62938143 or $21,629,381.43