Each of the four independent situations below describes a finance lease in which
ID: 2567139 • Letter: E
Question
Each of the four independent situations below describes a finance lease in which annual lease payments are payable at the beginning of each year. The lessee is aware of the lessor’s implicit rate of return.
Situation
1
2
3
4
Lease term (years)
4
7
5
8
Lessor’s rate of return
10%
11%
9%
12%
Fair value of lease asset
$50,000
$350,000
$75,000
$465,000
Lessor’s cost of lease asset
$50,000
$350,000
$45,000
$465,000
Residual value:
Estimated fair value
0
$ 50,000
$ 7,000
$ 45,000
Guaranteed fair value
0
0
$ 7,000
$ 50,000
Required:
For each situation, determine:
The amount of the annual lease payments as calculated by the lessor.
The amount the lessee would record as a right-of-use asset and a lease liability.
Situation
1
2
3
4
Lease term (years)
4
7
5
8
Lessor’s rate of return
10%
11%
9%
12%
Fair value of lease asset
$50,000
$350,000
$75,000
$465,000
Lessor’s cost of lease asset
$50,000
$350,000
$45,000
$465,000
Residual value:
Estimated fair value
0
$ 50,000
$ 7,000
$ 45,000
Guaranteed fair value
0
0
$ 7,000
$ 50,000
Explanation / Answer
The problem requires the calculation of Annual Lease Payment.
Please note that it has been given that, such payments are payable at beginning of the period. Hence, it refers to the annuity due. Rent is a classic example of annuity due.
Calculation of Present Value for Annuity Due:
Since payment is made at the beginning of the period, the formula of annuity due present value discounts one period ahead.
Fair Value will be the amount to be recovered through payment of lease payments.
Situation 1:
Amount to be Recovered or Fair Value = $50,000
Present Value of Annuity Due of $1 with relation to n=4, i=10% = 3.48685
Annual Lease Payments starting with beginning of the Year = 50,000/ 3.48685 = $14,339.590 = $14,340
Situation 2:
Amount to be Recovered or Fair Value = $350,000
Present Value of Annuity Due of $1 with relation to n=7, i=11% = 5.23053
Annual Lease Payments starting with beginning of the Year = 350,000/ 5.23053 = $66,914.825 = $66,915
Situation 3:
Amount to be Recovered or Fair Value = $75,000
Present Value of Annuity Due of $1 with relation to n=5, i=9% = 4.23971
Annual Lease Payments starting with beginning of the Year = 75,000/ 4.23971 = $17,689.889 = $17,690
Situation 4:
Amount to be Recovered or Fair Value = $465,000
Present Value of Annuity Due of $1 with relation to n=8, i=12% = 5.11140
Annual Lease Payments starting with beginning of the Year = 465,000/ 5.11140 = $90,973.118 = $90,973
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