Question

Ace Leasing acquires equipment and leases it to customers under long-term sales-type leases. Ace earns interest under these arrangements at a 8% annual rate. Ace leased a machine it purchased for $800,000 under an arrangement that specified annual payments beginning at the commencement of the lease for four years. The lessee had the option to purchase the machine at the end of the lease term for $300,000 when it was expected to have a residual value of $360,000.

Required:
Calculate the amount of the annual lease payments.

Answer 1

Answer:

Amount to be recovered = $650,000

Present value of bargain purchase option = $150,000 * PV factor at 6% for 6th period

= $150,000 * 0.704961 = $105,744

Amount to be recoverd through periodic lease payment = $650,000 - $105,744 = $544,256

Annual lease payment = $544,256 / Cumulative PV factor for annuity due at 6% for 6 periods

= $544,256 / 5.212364

= $104,416

Explanation:

Amount to be recovered = $650,000

Present value of bargain purchase option = $150,000 * PV factor at 6% for 6th period

= $150,000 * 0.704961 = $105,744

Amount to be recoverd through periodic lease payment = $650,000 - $105,744 = $544,256

Annual lease payment = $544,256 / Cumulative PV factor for annuity due at 6% for 6 periods

= $544,256 / 5.212364

= $104,416

Answer 2

Answer:

Lease payment:  $ 162,000.371

Explanation:

Ace Leasing wants to yield 8% on theri investment:

F0 (800,000)

Then at F4 It will receive the bargain option of 300,000

we solve for its PV:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $300,000.00

time  4.00

rate  0.08000

$\frac{300000}{(1 + 0.08)^{4} } = PV$  

PV   220,508.9558

The difference will be handled throguh the lease payment:

800,000 - 220,508.96 = 579.491,04‬

We solve for the installment of a 4 years annuity-due at % discount rate:

$PV \div \frac{1-(1+r)^{-time} }{rate} (1+r)= C$

PV 579,491.04

time 4

rate 0.08

$579491.04 \div \frac{1-(1+0.08)^{-4} }{0.08}(1+0.08) = C$

C  $ 162,000.371