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???? |
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
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