Chapter 15, Problem 15.24E

Calculation of annual lease payments; residual value

• LO15–2, LO15–6

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.

Required:

For each situation, determine:

a. The amount of the annual lease payments as calculated by the lessor.

b. The amount the lessee would record as a right-of-use asset and a lease liability.

To determine

Lease

Lease is a contractual agreement whereby the right to use an asset for a particular period of time is provided by the owner of the asset to the user of the asset. The owner, who possesses the asset, is termed as ‘Lessor’ and user, to whom the right is transferred to, is termed as ‘Lessee’.

To Determine: the annual lease payments as calculated by the lessor.

Explanation of Solution

$\begin{array}{c}\text{Annual lease payments}=\frac{\text{Amount to be recovered }\left(Fair\text{ Value}\right)}{\text{PVIFA}\left(10\%,4\right)}\\ =\frac{\$50,000}{3.48685}\\ =\$14,340\end{array}$

The lease payments at the beginning of each year is calculated by dividing fair value of the leased asset by present value of annuity for 4 years at the rate of 10%.

Conclusion

Therefore, annual lease payment as calculated by lessor is $14,340.

To determine

the amount that would be recorded as right-of-use asset and lease liability by the lessee.

Explanation of Solution

The lessor cost of lease asset is reported by the lessee as right-of-use asset$50,000.

Conclusion

Therefore, amount the lessee would record as right-of-use and lease liability is $50,000.

To determine

the annual lease payments as calculated by the lessor.

Explanation of Solution

$\begin{array}{c}\text{Annual lease payments}=\frac{\text{Amount to be recovered }\left(Fair\text{ Value}\right)}{\text{PVIFA}\left(11\%,7\right)}\\ =\frac{\$325,917\left(2\right)}{5.23054}\\ =\$62,310\end{array}$ (3)

Working notes:

Calculate the present value of residual value

$\begin{array}{c}\text{Present value of residual value}=\text{Residual value}\left(Estimated\right)\times PVIF\left(11\%,7\right)\\ =\$50,000\times 0.48166\\ =\$24,083\end{array}$ (1)

Calculate the amount to be recovered through periodic lease payments

Particulars	Amounts ($)
Amount to be recovered (Fair value)	350,000
Less: Present value of residual value (1)	24,083
Amount to be recovered through periodic lease payments	325,917

(2)

In case of lessor, even if the residual value is not guaranteed, the lessor is expected to receive. So, the lessor will assess the residual asset as contributing to amount needed to recover its investment causing the lessee’s lease payments to be lower.

Conclusion

Therefore, annual lease payment as calculated by lessor is $62,310.

To determine

the amount that would be recorded as right-of-use asset and lease liability by the lessee.

Explanation of Solution

Calculate the lessee would record as right-of-use asset and lease liability

$\begin{array}{c}\begin{array}{l}\text{Value to be recorded as }\\ \text{right-of-use asset }\\ \text{and lease liability}\end{array}\}=\text{Lease payments}\times PVIFA\left(11\%,7\right)\\ =\$62,310\left(3\right)\times 5.23054\\ =\$325,917\end{array}$

Conclusion

Therefore, amount the lessee would record as right-of-use and lease liability is $325,917.

To determine

the annual lease payments as calculated by the lessor.

Explanation of Solution

$\begin{array}{c}\text{Annual lease payments}=\frac{\text{Amount to be recovered }\left(Fair\text{ Value}\right)}{\text{PVIFA}\left(9\%,5\right)}\\ =\frac{\$70,450\left(5\right)}{4.23972}\\ =\$16,617\end{array}$ (6)

Working notes:

Calculate the present value of residual value

$\begin{array}{c}\text{Present value of residual value}=\text{Residual value}\left(Estimated\right)\times PVIF\left(9\%,5\right)\\ =\$7,000\times 0.64993\\ =\$4,550\end{array}$ (4)

Calculate the amount to be recovered through periodic lease payments

Particulars	Amounts ($)
Amount to be recovered (Fair value)	75,000
Less: Present value of residual value (4)	4,550
Amount to be recovered through periodic lease payments	70,450

(5)

In case of lessor, even if the residual value is not guaranteed, the lessor is expected to receive. So, the lessor will assess the residual asset as contributing to amount needed to recover its investment causing the lessee’s lease payments to be lower.

Conclusion

Therefore, annual lease payment as calculated by lessor is $16,617.

To determine

the amount that would be recorded as right-of-use asset and lease liability by the lessee.

Explanation of Solution

Calculate the lessee would record as right-of-use asset and lease liability

$\begin{array}{c}\begin{array}{l}\text{Value to be recorded as }\\ \text{right-of-use asset }\\ \text{and lease liability}\end{array}\}=\text{Lease payments}\times PVIFA\left(9\%,5\right)\\ =\$16,617\left(6\right)\times 4.23972\\ =\$70,450\end{array}$

Conclusion

Therefore, amount the lessee would record as right-of-use and lease liability is $70,450.

To determine

the annual lease payments as calculated by the lessor.

Explanation of Solution

$\begin{array}{c}\text{Annual lease payments}=\frac{\text{Amount to be recovered }\left(Fair\text{ Value}\right)}{\text{PVIFA}\left(12\%,8\right)}\\ =\frac{\$444,806\left(9\right)}{5.56376}\\ =\$79,947\end{array}$ (10)

Working notes:

Calculate the present value of excess guaranteed residual value

$\begin{array}{c}\begin{array}{l}\text{Present value of }\\ \text{excess guaranteed }\\ \text{residual value}\end{array}\}=\left[\begin{array}{l}\text{Residual value}\left(Guaranteed\right)\\ -\text{Residual value}\left(Estimated\right)\end{array}\right]\times PVIF\left(12\%,8\right)\\ =\left[\$50,000-\$45,000\right]\times 0.40388\\ =\$2,019\end{array}$ (7)

Calculate the present value of residual value

$\begin{array}{c}\text{Present value of residual value}=\text{Residual value}\left(Estimated\right)\times PVIF\left(12\%,8\right)\\ =\$45,000\times 0.40388\\ =\$18,175\end{array}$ (8)

Calculate the amount to be recovered through periodic lease payments

Particulars	Amounts ($)
Amount to be recovered (Fair value)	465,000
Less: Present value of excess guaranteed residual value (7)	2,019
Less: Present value of residual value (8)	18,175
Amount to be recovered through periodic lease payments	444,806

(9)

If a lessee guaranteed residual value is expected, the present value of the payments is added to the present value of lease payments which the lessee records as right-of-use of asset and lease liability. In case of a finance lease, the lessor records it as lease receivable.

Conclusion

Therefore, annual lease payment as calculated by lessor is $79,947.

To determine

the amount that would be recorded as right-of-use asset and lease liability by the lessee.

Explanation of Solution

Calculate the lessee would record as right-of-use asset and lease liability

$\begin{array}{c}\begin{array}{l}\text{Value to be recorded as }\\ \text{right-of-use asset }\\ \text{and lease liability}\end{array}\}=\left[\begin{array}{l}\text{Present value of periodic }\\ \text{lease payments + Present value of }\\ \text{excess guaranteed residual value}\end{array}\right]\\ =\left[\$444,806\left(9\right)+\$2,019\left(7\right)\right]\\ =\$446,825\end{array}$

Conclusion

Therefore, amount the lessee would record as right-of-use and lease liability is $446,825.