Chapter 15, Problem 15.15E

A)

To determine

Purchase option

Purchase option is provision of certain lease contracts which provides the lessee the option to purchase the leased asset during the period of lease or at the end of the lease term at a particular exercise price.

Capital Lease

This type of lease is a situation whereby the lessor (owner) transfers the ownership of leased asset to the lessee (user) on the maturity period of terms of lease. This is non-cancellable in nature and it extends to long term and can also be capitalized

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) 750,000	(3) 800,000	(4) 840,000
Gross investment   in the lease	(5) 700,000	(6) 750,000	(7) 850,000	(8) 900,000
Net investment   in the lease	(9) 548,592	(10) 547,137	(11) 610,168	(12) 596,764

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)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \text{×Number of fixed payments}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Residual}\text{Value}\\ \text{guaranteed by}\text{lessee}\end{array}\right)\\ \text{=}\left(\text{\$100,000×7}\right)\text{+}\left(\text{\$50,000}\right)\\ \text{=\$750,000}\end{array}$ (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)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \text{×Number of fixed payments}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Residual}\text{Value}\\ \text{guaranteed by}\text{lessee}\end{array}\right)\\ \text{=}\left(\text{\$100,000×8}\right)\text{+}\left(\text{\$40,000}\right)\\ \text{=\$840,000}\end{array}$ (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)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ \text{+ Unguaranteed residual value}\end{array}\right]\\ \text{=}\left[\text{\$800,000+\$0+\$50,000}\right]\\ \text{=\$850,000}\end{array}$ (7)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\text{Lease payments + Guaranteed residual value}\\ \text{+ Unguaranteed residual value}\end{array}\right]\\ \text{=}\left[\text{\$800,000+\$40,000+\$60,000}\right]\\ \text{=\$900,000}\end{array}$ (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)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \text{×PVIFA}\left(\text{10\%,8}\right)\end{array}\right]\\ \text{+}\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \text{×PVIF}\left(\text{10\%,8}\right)\end{array}\right]\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(\text{\$100,000×5}\text{.86842}\right)\\ \text{+}\left(\text{\$50,000×0}\text{.46651}\right)\end{array}\right]\\ \text{=\$610,168}\end{array}$ (11)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \text{×PVIFA}\left(\text{12\%,8}\right)\end{array}\right]\\ \text{+}\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \text{×PVIF}\left(\text{12\%,8}\right)\end{array}\right]\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(\text{\$100,000×5}\text{.56376}\right)\text{+}\left(\text{\$40,000×0}\text{.40388}\right)\\ \text{+}\left(\text{\$60,000×0}\text{.40388}\right)\end{array}\right]\\ \text{=\$596,764}\end{array}$ (12)

(B)

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) 750,000	(15) 800,000	(16) 840,000
Right-of-use asset	(17) 548,592	(18) 547,137	(19) 586,842	(20) 572,531
Lease payable	(17) 548,592	(18) 547,137	(19) 586,842	(20) 572,531

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)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \text{×Number of fixed payments}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Residual}\text{Value}\\ \text{guaranteed by}\text{lessee}\end{array}\right)\\ \text{=}\left(\text{\$100,000×7}\right)\text{+}\left(\text{\$50,000}\right)\\ \text{=\$750,000}\end{array}$ (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)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left(\begin{array}{l}\text{Annual lease payments}\\ \text{×Number of fixed payments}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Residual}\text{Value}\\ \text{guaranteed by}\text{lessee}\end{array}\right)\\ \text{=}\left(\text{\$100,000×8}\right)\text{+}\left(\text{\$40,000}\right)\\ \text{=\$840,000}\end{array}$ (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)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(11\%,7\right)\right]\\ +\left[\text{Guaranteed lease payments}\times \text{PVIF}\left(11\%,7\right)\right]\end{array}\right]\\ =\left[\left(\$100,000\times 5.23054\right)+\left(\$50,000\times 0.48166\right)\right]\\ =\$547,137\end{array}$ (18)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 3}\right)\text{ =}\left[\text{Annual lease payments×PVIFA}\left(\text{10\%,8}\right)\right]\\ \text{=}\left[\text{\$100,000×5}\text{.86842}\right]\\ \text{=\$586,842}\end{array}$ (19)

$\begin{array}{c}\text{Lessee's value of lease }\left(\text{Situation 4}\right)\text{ =}\left[\begin{array}{l}\left[\begin{array}{l}\text{Annual lease payments}\\ \text{×PVIFA}\left(\text{12\%,8}\right)\end{array}\right]\\ \text{+}\left[\begin{array}{l}\text{Excess lessee-guaranteed }\\ \text{residual value×PVIF}\left(\text{12\%,8}\right)\end{array}\right]\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(\text{\$100,000×5}\text{.56376}\right)\\ \text{+}\left(\text{\$40,000×0}\text{.40388}\right)\end{array}\right]\\ \text{=\$572,531}\end{array}$ (20)