Question

Skysong Company leases an automobile with a fair value of $18,680 from John Simon Motors, Inc., on the following terms:

1.		Non-cancelable term of 50 months.
2.		Rental of $380 per month (at the beginning of each month).
3.		Skysong guarantees a residual value of $1,870. Delaney expects the probable residual value to be $1,870 at the end of the lease term.
4.		Estimated economic life of the automobile is 60 months.
5.		Skysong’s incremental borrowing rate is 6% a year (0.5% a month). Simon’s implicit rate is unknown.

What is the present value of the lease payments to determine the lease liability? (Round answer to 0 decimal places, e.g. 5,275.)

Present value of the lease payments????

Answer 1

PV of monthly lease rent = $16859 (Note 1)

PV of guaranteed residual value = $1457 (Note 2)

Present value(PV) of lease payment = PV of monthly payment + PV of guaranteed residual value = $16859+$1457 =$18316

Working Notes

Note 1 - Calculation of Present Value of Monthly Lease rent is as follows (for first month PV factor is 1 because payment is made at the beginning)

Month	Cash flow at the beginning of month (A)	Pv factor @ 0.5% per month (B)	Discounted cash flow (A x B)
1	$380.00	1.00000	$380.00
2	$380.00	0.99502	$378.11
3	$380.00	0.99007	$376.23
4	$380.00	0.98515	$374.36
5	$380.00	0.98025	$372.49
6	$380.00	0.97537	$370.64
7	$380.00	0.97052	$368.80
8	$380.00	0.96569	$366.96
9	$380.00	0.96089	$365.14
10	$380.00	0.95610	$363.32
11	$380.00	0.95135	$361.51
12	$380.00	0.94661	$359.71
13	$380.00	0.94191	$357.92
14	$380.00	0.93722	$356.14
15	$380.00	0.93256	$354.37
16	$380.00	0.92792	$352.61
17	$380.00	0.92330	$350.85
18	$380.00	0.91871	$349.11
19	$380.00	0.91414	$347.37
20	$380.00	0.90959	$345.64
21	$380.00	0.90506	$343.92
22	$380.00	0.90056	$342.21
23	$380.00	0.89608	$340.51
24	$380.00	0.89162	$338.82
25	$380.00	0.88719	$337.13
26	$380.00	0.88277	$335.45
27	$380.00	0.87838	$333.78
28	$380.00	0.87401	$332.12
29	$380.00	0.86966	$330.47
30	$380.00	0.86533	$328.83
31	$380.00	0.86103	$327.19
32	$380.00	0.85675	$325.56
33	$380.00	0.85248	$323.94
34	$380.00	0.84824	$322.33
35	$380.00	0.84402	$320.73
36	$380.00	0.83982	$319.13
37	$380.00	0.83564	$317.55
38	$380.00	0.83149	$315.97
39	$380.00	0.82735	$314.39
40	$380.00	0.82323	$312.83
41	$380.00	0.81914	$311.27
42	$380.00	0.81506	$309.72
43	$380.00	0.81101	$308.18
44	$380.00	0.80697	$306.65
45	$380.00	0.80296	$305.12
46	$380.00	0.79896	$303.61
47	$380.00	0.79499	$302.10
48	$380.00	0.79103	$300.59
49	$380.00	0.78710	$299.10
50	$380.00	0.78318	$297.61
.	.	Total	$16,859.

Present Value of Lease rentals= $16859

Note 2 - Calculation of Present value of Guaranteed residual value

Present value factor for payment at the end of 50th month at 0.50% = 0.77929

PV of Guaranteed residual value = $1870 x 0.77929 = $1457