Chapter 15, Problem 15.26E

Lease concepts; finance/sales-type leases; guaranteed and unguaranteed residual value

• LO15–2, LO15–6

Each of the four independent situations below describes a sales-type lease in which annual lease payments of $100,000 are payable at the beginning of each year. Each is a finance lease for the lessee. Determine the following amounts at the beginning of the lease:

A. The lessor’s:

1. Lease payments

2. Gross investment in the lease

3. Net investment in the lease

B. The lessee’s:

4. Lease payments

5. Right-of-use asset

6. Lease liability

To determine

the amounts at the beginning of lease for the lessor at each independent situation.

Explanation of Solution

	Situation
	1	2	3	4
Lessor
Lease payments	(1)700,000	(2) 700,000	(3)800,000	(4)800,000
Gross investment   in the lease	(5)700,000	(6)750,000	(7)808,000	(8)860,000
Net investment   in the lease	(9)548,592	(10)547,137	(11)590,574	(12)580,609

Table (1)

Working note:

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\\ =\left(\$100,000\times 7\right)\\ =\$700,000\end{array}$ (1)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\\ =\left(\$100,000\times 7\right)\\ =\$700,000\end{array}$ (2)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\\ =\left(\$100,000\times 8\right)\\ =\$800,000\end{array}$ (3)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\\ =\left(\$100,000\times 8\right)\\ =\$800,000\end{array}$ (4)

The gross investment in lease is calculated as follows:

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$700,000+\$0+\$0\right]\\ =\$700,000\end{array}$ (5)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$700,000+\$50,000+\$0\right]\\ =\$750,000\end{array}$ (6)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$800,000+\$8,000+\$0\right]\\ =\$808,000\end{array}$ (7)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$800,000+\$0+\$60,000\right]\\ =\$860,000\end{array}$ (8)

The net investment in the lease is calculated as follows:

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 1}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(9\%,7\right)\right]\\ =\left[\$100,000\times 5.48592\right]\\ =\$548,592\end{array}$ (9)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,7\right)\right]\\ +\left[\text{Guaranteed lease payments}\times \text{PVIF}\left(11\%,7\right)\right]\end{array}\right]\\ =\left[\left(\$100,000\times 5.23054\right)+\left(\$50,000\times 0.48166\right)\right]\\ =\$547,137\end{array}$ (10)

586,842

24,083

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \times \text{PVIFA}\left(10\%,8\right)\end{array}\right]\\ +\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \times \text{PVIF}\left(10\%,8\right)\end{array}\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$100,000\times 5.86842\right)\\ +\left(\$8,000\times 0.46651\right)\end{array}\right]\\ =\$590,574\end{array}$ (11)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \times \text{PVIFA}\left(12\%,8\right)\end{array}\right]\\ +\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \times \text{PVIF}\left(12\%,8\right)\end{array}\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$100,000\times 5.56376\right)\\ +\left(\$60,000\times 0.40388\right)\end{array}\right]\\ =\$580,609\end{array}$ (12)

To determine

the amounts at the beginning of lease for the lessee at each independent situation.

Explanation of Solution

	Situation
	1	2	3	4
Lessor
Lease payments	(13) 700,000	(14) 700,000	(15) 800,000	(16) 810,000
Right-of-use asset	(17)548,592	(18)523,054	(19)586,842	(20)560,415
Lease payable	(17) 548,592	(18)523,054	(19)586,842	(20)560,415

Table (2)

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 7\right)+\$0\right]\\ =\$700,000\end{array}$ (13)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 7\right)+\$0\right]\\ =\$700,000\end{array}$ (14)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 8\right)+\$0\right]\\ =\$800,000\end{array}$ (15)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 8\right)+\left(\$60,000-\$50,000\right)\right]\\ =\$810,000\end{array}$ (16)

The amount to be recorded as right-of-use asset and lease liability is calculated as follows:

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 1}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(9\%,7\right)\right]\\ =\left[\$100,000\times 5.48592\right]\\ =\$548,592\end{array}$ (17)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 2}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,7\right)\right]\\ =\left[\$100,000\times 5.23054\right]\\ =\$523,054\end{array}$ (18)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 3}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(10\%,8\right)\right]\\ =\left[\$100,000\times 5.86842\right]\\ =\$586,842\end{array}$ (19)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \times \text{PVIFA}\left(12\%,8\right)\end{array}\right]\\ +\left[\begin{array}{l}\text{Excess lessee-guaranteed }\\ \text{residual value}\times \text{PVIF}\left(12\%,8\right)\end{array}\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$100,000\times 5.56376\right)\\ +\left(\$10,000\times 0.40388\right)\end{array}\right]\\ =\$560,415\end{array}$ (20)