Chapter 15, Problem 15.13P

A)

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
Minimum  Lease payments	(1)400,000	(2) 553,000	(3) 640,000	(4) 510,000
Gross investment   in the lease	(5)430,000	(6) 553,000	(7) 675,000	(8) 550,000
Net investment   in the lease	(9)369,175	(10) 433,809	(11) 533,685	(12) 451,137
Sales revenue	(13)348,685	(14)433,809	(15) 512,816	(16) 423,817
Cost of goods sold	(17)348,685	(18)449,896	(19) 479,131	(20) 372,680
Dealers profit	(21) $0	(22)$(16,087)	(23) $33,685	(24) $51,137

Table (1)

Working note:

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$100,000\times 4\right)+\$0\right]\\ =\$400,000\end{array}$ (1)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$100,000\times 5\right)+\$53,000+\$0\right]\\ =\$553,000\end{array}$ (2)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$100,000\times 6\right)+\$40,000+\$0\right]\\ =\$640,000\end{array}$ (3)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Exercise price for options whose exercise }\\ \text{is deemed reasonably certain}\end{array}\right]\\ =\left[\left(\$100,000\times 4\right)+\$50,000+\$60,000\right]\\ =\$510,000\end{array}$ (4)

The gross investment in lease is calculated as follows:

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\text{Minimum Lease payments}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$400,000+\$30,000\right]\\ =\$430,000\end{array}$ (5)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\text{Minimum Lease payments}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$553,000+\$0\right]\\ =\$553,000\\ =\$553,000\end{array}$ (6)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 3}\right)\text{ = }\left[\begin{array}{l}\text{Minimum Lease payments}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$640,000+\$35,000\right]\\ =\$675,000\end{array}$ (7)

$\begin{array}{c}\text{Gross investment in lease}\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\text{Minimum Lease payments}\\ +\text{ Unguaranteed residual value}\end{array}\right]\\ =\left[\$510,000+\$40,000\right]\\ =\$550,000\end{array}$ (8)

The net investment in the lease is calculated as follows:

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 1}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual }\\ \text{lease }\\ \text{payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(10\%,4\right)\end{array}\right)\right]+\left[\left(\begin{array}{l}\text{residual}\\ \text{value}\end{array}\right)\text{×}\text{PVIF}\right]\\ =\left[\$100,000\times 3.48685\right]+\left[30,000\times 0.68301\right]\\ =\$348,685+\$20,490\\ =\$369,175\end{array}$ (9)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 2}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual }\\ \text{lease }\\ \text{payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(12\%,5\right)\end{array}\right)\right]+\left[\left(\begin{array}{l}\text{residual}\\ \text{value}\end{array}\right)\text{×}\text{PVIF}\right]\\ =\left[\$100,000\times 4.03735\right]+\left[53,000\times 0.56743\right]\\ =\$403,735+\$30,074\\ =\$433,809\end{array}$ (10)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 3}\right)\text{ =}\left[\begin{array}{l}\left[\text{Annual lease payments}\times \text{PVIFA}\left(9\%,6\right)\right]\\ +\left[\begin{array}{l}\text{Guaranteed lease payments}\\ \times \text{PVIF}\left(9\%,6\right)\end{array}\right]\\ +\left[\begin{array}{l}\text{Unguaranteed lease payments}\\ \times \text{PVIF}\left(9\%,6\right)\end{array}\right]\end{array}\right]\\ =\left[\begin{array}{l}\left(\$100,000\times 4.88965\right)\\ +\left(\$40,000\times 0.59627\right)+\\ \left(\$35,000\times 0.59627\right)\end{array}\right]\\ =\$533,685\end{array}$ (11)

$\begin{array}{c}\text{Net investment in lease}\left(\text{Situation 4}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual }\\ \text{lease }\\ \text{payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(10\%,4\right)\end{array}\right)\right]+\left[\left(\begin{array}{l}\text{residual}\\ \text{value}\end{array}\right)\text{×}\text{PVIF}\right]\\ =\left[\$100,000\times 3.48685\right]+\left[150,000\times 0.68301\right]\\ =\$348,685+\$102,452\\ =\$451,137\end{array}$ (12)

Sales revenue is calculated as follows:

$\begin{array}{c}\text{Sales revenue}\left(\text{Situation 1}\right)\text{ =}\left[\text{net}\text{investment}\right]-\left[\left(\begin{array}{l}\text{unguaranteed }\\ \text{residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF}\\ 4,10\%\end{array}\right)\right]\\ =\left[\$369,175\right]-\left[30,000\times 0.68301\right]\\ =\$369,175-\$20,490\\ =\$348,685\end{array}$ (13)

$\begin{array}{c}\text{Sales revenue}\left(\text{Situation 2}\right)\text{ =}\left[\text{net}\text{investment}\right]-\left[\left(\begin{array}{l}\text{unguaranteed }\\ \text{residual}\text{value}\end{array}\right)\text{×}\text{PVIF 5, 12\%}\right]\\ =\left[\$433,809\right]-\left[\$0\times 0.56743\right]\\ =\$433,809-\$0\\ =\$433,809\end{array}$ (14)

$\begin{array}{c}\text{Sales revenue}\left(\text{Situation 3}\right)\text{ =}\left[\text{net}\text{investment}\right]-\left[\left(\begin{array}{l}\text{unguaranteed }\\ \text{residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF}\\ \text{ 6, 9\%}\end{array}\right)\right]\\ =\left[\$533,685\right]-\left[\$35,000\times 0.59627\right]\\ =\$533,685-\$20,869\\ =\$512,816\end{array}$ (15)

$\begin{array}{c}\text{Sales revenue}\left(\text{Situation 4}\right)\text{ =}\left[\text{net}\text{investment}\right]-\left[\left(\begin{array}{l}\text{unguaranteed }\\ \text{residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF}\\ \text{ 4, 10\%}\end{array}\right)\right]\\ =\left[\$451,137\right]-\left[\$40,000\times 0.68301\right]\\ =\$451,137-\$27,320\\ =\$423,817\end{array}$ (16)

Cost of goods sold is calculated as follows:

$\begin{array}{c}\text{Cost of goods sold}\left(\text{Situation 1}\right)\text{ =}\left[\text{Lessor's}\text{cost}\right]-\left[\left(\begin{array}{l}\text{unguaranteed}\\ \text{ residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF }\\ \text{4, 10\%}\end{array}\right)\right]\\ =\left[\$369,175\right]-\left[\$30,000\times 0.68301\right]\\ =\$369,175-\$20,490\\ =\$348,685\end{array}$ (17)

$\begin{array}{c}\text{Cost of goods sold}\left(\text{Situation 2}\right)\text{ =}\left[\text{Lessor's}\text{cost}\right]-\left[\left(\begin{array}{l}\text{unguaranteed}\\ \text{ residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF }\\ \text{5, 12\%}\end{array}\right)\right]\\ =\left[\$449,896\right]-\left[\$0\times 0.56743\right]\\ =\$449,896-\$0\\ =\$449,896\end{array}$ (18)

$\begin{array}{c}\text{Cost of goods sold}\left(\text{Situation 3}\right)\text{ =}\left[\text{Lessor's}\text{cost}\right]-\left[\left(\begin{array}{l}\text{unguaranteed}\\ \text{ residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF }\\ \text{6, 9\%}\end{array}\right)\right]\\ =\left[\$500,000\right]-\left[\$35,000\times 0.59627\right]\\ =\$500,000-\$20,869\\ =\$479,131\end{array}$ (19)

$\begin{array}{c}\text{Cost of goods sold}\left(\text{Situation 4}\right)\text{ =}\left[\text{Lessor's}\text{cost}\right]-\left[\left(\begin{array}{l}\text{unguaranteed}\\ \text{ residual}\text{value}\end{array}\right)\text{×}\left(\begin{array}{l}\text{PVIF }\\ \text{4, 10\%}\end{array}\right)\right]\\ =\left[\$400,000\right]-\left[\$40,000\times 0.68301\right]\\ =\$400,000-\$27,320\\ =\$372,680\end{array}$ (20)

Dealers profit is calculated as follows:

$\begin{array}{c}\text{Dealers}\text{profit}\left(\text{Situation 1}\right)\text{ =}\left[\text{Sales}\text{revenue}\right]\text{-}\left[\text{Cost}\text{of}\text{goods}\text{sold}\right]\\ =\left[\$348,685\right]-\left[\$348,685\right]\\ =\$0\end{array}$ (21)

$\begin{array}{c}\text{Dealers}\text{profit}\left(\text{Situation 1}\right)\text{ =}\left[\text{Sales}\text{revenue}\right]\text{-}\left[\text{Cost}\text{of}\text{goods}\text{sold}\right]\\ =\left[\$433,809\right]-\left[\$449,896\right]\\ =\left(\$16,087\right)\end{array}$ (22)

$\begin{array}{c}\text{Dealers}\text{profit}\left(\text{Situation 1}\right)\text{ =}\left[\text{Sales}\text{revenue}\right]\text{-}\left[\text{Cost}\text{of}\text{goods}\text{sold}\right]\\ =\left[\$512,816\right]-\left[\$479,131\right]\\ =\$33,685\end{array}$ (23)

$\begin{array}{c}\text{Dealers}\text{profit}\left(\text{Situation 1}\right)\text{ =}\left[\text{Sales}\text{revenue}\right]\text{-}\left[\text{Cost}\text{of}\text{goods}\text{sold}\right]\\ =\left[\$423,817\right]-\left[\$372,680\right]\\ =\$51,137\end{array}$ (24)

(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
Lessee
Lease payments	(25) 400,000	(26) 553,000	(27) 640,000	(28) 460,000
Leased asset	(29) 353,129	(30) 449,896	(31) 512,816	(32) 389,666
Lease payable	(29) 353,129	(30) 449,896	(31) 512,816	(32) 389,666

Table (2)

The lease payment is calculated as follows:

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 1}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 4\right)+\$0\right]\\ =\$400,000\end{array}$ (25)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 2}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 5\right)+\$53,000\right]\\ =\$553,000\end{array}$ (26)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 3}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 6\right)+\$40,000\right]\\ =\$640,000\end{array}$ (27)

$\begin{array}{c}\text{Lease payments }\left(\text{Situation 4}\right)\text{ = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Annual lease payments}\\ \times \text{Number of fixed payments}\end{array}\right)\text{ +}\\ \text{Excess lessee guaranteed residual value}\end{array}\right]\\ =\left[\left(\$100,000\times 4\right)+\$60,000\right]\\ =\$460,000\end{array}$ (28)

The amount to be recorded as leased asset and lease liability is calculated as follows:

$\begin{array}{c}\text{Leased asset }\left(\text{Situation 1}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual lease}\\ \text{ payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(10\%,4\right)\end{array}\right)\right]+\left[\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{residual}\\ \text{value}\text{guaranteed}\\ \text{by}\text{lessee}\end{array}\right]\\ =\left[\$100,000\times 3.53129\right]+\left[\$0\times 0.70843\right]\\ =\$353,129+\$0\\ =\$353,129\end{array}$ (29)

$\begin{array}{c}\text{Leased asset }\left(\text{Situation 2}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual lease}\\ \text{ payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(10\%,5\right)\end{array}\right)\right]+\left[\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{residual}\\ \text{value}\text{guaranteed}\\ \text{by}\text{lessee}\end{array}\right]\\ =\left[\$100,000\times 4.16987\right]+\left[\$53,000\times 0.62092\right]\\ =\$416,987+\$32,909\\ =\$449,896\end{array}$ (30)

$\begin{array}{c}\text{Leased asset }\left(\text{Situation 3}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual lease}\\ \text{ payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(9\%,6\right)\end{array}\right)\right]+\left[\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{residual}\\ \text{value}\text{guaranteed}\\ \text{by}\text{lessee}\end{array}\right]\\ =\left[\$100,000\times 4.88965\right]+\left[\$40,000\times 0.59627\right]\\ =\$488,965+\$23,851\\ =\$512,816\end{array}$ (31)

$\begin{array}{c}\text{Leased asset }\left(\text{Situation 4}\right)\text{ =}\left[\left(\begin{array}{l}\text{Annual lease}\\ \text{ payments}\end{array}\right)\times \left(\begin{array}{l}\text{PVIFA}\\ \left(10\%,4\right)\end{array}\right)\right]+\left[\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{residual}\\ \text{value}\text{guaranteed}\\ \text{by}\text{lessee}\end{array}\right]\\ =\left[\$100,000\times 3.48685\right]+\left[\$60,000\times 0.68301\right]\\ =\$348,685+\$40,981\\ =\$389,666\end{array}$ (32)

Note:

Present value of the minimum lease payments and leased asset is calculated based on the discounted rates at lower of lessor and lessee.