To solve the problem, we need to calculate the present value of the lease payments, determine the amount to be reported on the balance sheet, and identify the amounts to be reported in the income statement. Let's go through each requirement step by step.
Lease Details:
- Lease term: 5 years
- Lease payments: $530,475 annually
- Rent-free period: 3 months
- Incremental borrowing rate: 6%
Since there is a 3-month rent-free period, the first payment will be made at the end of the first year. Therefore, the lease payments are an ordinary annuity starting at the end of the first year.
Present Value Calculation:
To find the present value of the lease payments, we use the Present Value of an Ordinary Annuity (PVOA) formula:
\[ PV = P \times \left(1 - (1 + r)^{-n}\right) / r \]
Where:
- \( P = 530,475 \) (annual lease payment)
- \( r = 0.06 \) (annual interest rate)
- \( n = 5 \) (number of payments)
\[ PV = 530,475 \times \left(1 - (1 + 0.06)^{-5}\right) / 0.06 \]
\[ PV = 530,475 \times 4.21236 \] (using a PVOA factor for 5 years at 6%)
\[ PV = 2,234,000 \] (rounded to the nearest whole dollar)
By December 31, 2024, half a year has passed since the lease commenced. The balance sheet will report the lease liability and the right-of-use asset.
Lease Liability:
The lease liability is initially the present value of the lease payments, which is $2,234,000. By December 31, 2024, interest will have accrued on this liability.
Interest for 6 months = \( 2,234,000 \times 0.06 \times \frac{6}{12} = 67,020 \)
The first lease payment of $530,475 will be made at the end of the first year, so the lease liability on December 31, 2024, remains $2,234,000 plus accrued interest.
Right-of-Use Asset:
The right-of-use asset is initially equal to the lease liability. It will be amortized over the lease term. However, since no payment has been made by December 31, 2024, the right-of-use asset remains at its initial value of $2,234,000.
Interest Expense:
The interest expense for the year is the interest accrued on the lease liability:
Interest Expense = $67,020
Amortization Expense:
The right-of-use asset is amortized over the lease term. The annual amortization expense is:
Amortization Expense = \( \frac{2,234,000}{5} = 446,800 \)
Income Statement Reporting:
- Interest Expense: $67,020
- Amortization Expense: $446,800
- Present Value of Lease Payments: $2,234,000
- Balance Sheet Amount on December 31, 2024:
- Lease Liability: $2,234,000
- Right-of-Use Asset: $2,234,000
- Income Statement Amounts for 2024:
- Interest Expense: $67,020
- Amortization Expense: $446,800