Question

Ariel, an office administrator, is evaluating the following quotation that she received for the purchase of a printer for her office:

Lease Option: Make payments of $85 at the beginning of every month for 4 years. At the end of 4 years, make the final payment of $750.

Purchase Option: Make a payment of $3,850 immediately.

1)What is the present value of the lease option if money is worth 7.8% compounded semi-annually?

2)Which option would be economically better?

3) What is the present value of the lease option if money is worth 10.8% compounded semi-annually?

4) Which option would be economically better?

Answer 1

1)Rate Semi annually =7.8%
Monthly Rate =(1+7.8%/2)^(1/6)-1 =0.639682486883975%
Number of months =4*12 =48
PV of lease option =(1+r)*PMT*((1-(1+r)^-n)/r)+Final Payment/(1+r)^n
=(1+0.639682486883975%)*85*
(((1-(1+0.639682486883975%)^-48)/0.639682486883975%)+750/(1+0.639682486883975%)^48
=4078.20

2) Lease option is more economical.

3)Rate Semi annually =10.8%
Monthly Rate =(1+10.8%/2)^(1/6)-1 =0.880393703592963%
Number of months =4*12 =48
PV of lease option =(1+r)*PMT*((1-(1+r)^-n)/r)+Final Payment/(1+r)^n
=(1+0.880393703592963%)*85*
(((1-(1+0.880393703592963%)^-48)/0.880393703592963%)+750/(1+0.880393703592963%)^48
=3837.44

4) Immediate payment of 3850 is better than lease.