Chapter 15, Problem 15.9P

Lease concepts; 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 $10,000 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.

1. A.   The lessor’s:
   1. 1. Lease payments
   2. 2. Gross investment in the lease
   3. 3. Net investment in the lease
2. B.   The lessee’s:
   1. 4. Lease payments
   2. 5. Right-of-use asset
   3. 6. Lease liability

To determine

Lessee guaranteed residual value

The lessee guaranteed residual value of leased asset is an estimation of the commercial value of the asset at the end of lease term. The present value is considered when determining the lease classification criteria (Criteria 4). Lessee guaranteed residual value is added to lease receivable and also added to sales revenue.

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) 40,000	(2) 40,000	(3) 40,000	(4)33,000
Gross investment in the lease	(5)40,000	(6)44,000	(7)44,000	(8)33,000
Net investment   in the lease	(9)34,437	(10)37,072	(11)37,072	(12)29,319

Table (1)

Working note:

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (1)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (2)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (3)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$10,000\times 3\right)+\$3,000\right]\\ =\$33,000\end{array}$ (4)

The gross investment in lease is calculated as follows:

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$40,000+\$0+\$0\right]\\ =\$40,000\end{array}$ (5)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$40,000+\$4,000+\$0\right]\\ =\$44,000\end{array}$ (6)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$40,000+\$2,000+\$2,000\right]\\ =\$44,000\end{array}$ (7)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$33,000+\$0+\$0\right]\\ =\$33,000\end{array}$ (8)

The net investment in the lease is calculated as follows:

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 1}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ =\left[\$10,000\times 3.44371\right]\\ =\$34,437\end{array}$ (9)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ +\left[\text{Guaranteed lease payments}\times \text{PVIF}\left(11\%,4\right)\right]\end{array}\right]\\ =\left[\left(\$10,000\times 3.44371\right)+\left(\$4,000\times 0.65873\right)\right]\\ =\$37,072\end{array}$ (10)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ +\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \times \text{PVIF}\left(11\%,4\right)\end{array}\right]\\ +\left[\begin{array}{l}\text{Unguaranteed lease payments}\\ \times \text{PVIF}\left(11\%,4\right)\end{array}\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$10,000\times 3.44371\right)\\ +\left(\$2,000\times 0.65873\right)+\\ \left(\$2,000\times 0.65873\right)\end{array}\right]\\ =\$37,072\end{array}$ (11)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,3\right)\right]\\ +\left[\text{Exercise price}\times \text{PVIF}\left(11\%,3\right)\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$10,000\times 2.71252\right)\\ +\left(\$2,000\times 0.73119\right)\end{array}\right]\\ =\$29,319\end{array}$ (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
Lessee
Lease payments	(13) 40,000	(14) 40,000	(15) 40,000	(16)33,000
Right-of-use asset	(17)34,437	(18) 34,437	(19) 34,437	(20)29,319
Lease payable	(17) 34,437	(18) 34,437	(19) 34,437	(20) 29,319

Table (2)

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (13)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (14)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$10,000\times 4\right)+\$0\right]\\ =\$40,000\end{array}$ (15)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$10,000\times 3\right)+\$3,000\right]\\ =\$33,000\end{array}$ (16)

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

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 1}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ =\left[\$10,000\times 3.44371\right]\\ =\$34,437\end{array}$ (17)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 2}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ =\left[\$10,000\times 3.44371\right]\\ =\$34,437\end{array}$ (18)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 3}\right)\text{ =}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,4\right)\right]\\ =\left[\$10,000\times 3.44371\right]\\ =\$34,437\end{array}$ (19)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \times \text{PVIFA}\left(11\%,3\right)\end{array}\right]\\ +\left[\text{Exercise price}\times \text{PVIF}\left(11\%,3\right)\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$10,000\times 2.71252\right)\\ +\left(\$2,000\times 0.73119\right)\end{array}\right]\\ =\$29,319\end{array}$ (20)