Answer :
To calculate the lease liability and interest charges, we need to understand that the lease liability is calculated based on the present value of lease payments, discounted at the discount rate (10% in this case).
Here's a step-by-step calculation:
Calculate Present Value of Lease Payments:
The lease rentals are ₹250,000 per annum for 5 years. We discount these lease payments to present value using the discount rate of 10%.
The present value of annuity formula is:
[tex]PV = P \times \left( 1 - (1 + r)^{-n} \right) / r[/tex]
Where:
- [tex]P = ₹250,000[/tex] (annual lease payment)
- [tex]r = 10\% = 0.10[/tex] (discount rate)
- [tex]n = 5[/tex] (number of years)
Substitute the values:
[tex]PV = 250,000 \times \left( 1 - (1 + 0.10)^{-5} \right) / 0.10[/tex]
[tex]PV = 250,000 \times 3.7908[/tex]
[tex]PV = ₹947,700[/tex]
Calculate Present Value of Guaranteed Residual Value (GRV):
GRV at the end of the lease term is ₹250,000, which is also discounted back to present value.
[tex]PV_{GRV} = F / (1 + r)^n[/tex]
Where:
- [tex]F = ₹250,000[/tex] (guaranteed residual value)
- [tex]r = 0.10[/tex]
- [tex]n = 5[/tex]
Substitute the values:
[tex]PV_{GRV} = 250,000 / (1 + 0.10)^5[/tex]
[tex]PV_{GRV} = 250,000 / 1.61051[/tex]
[tex]PV_{GRV} = ₹155,250[/tex]
Calculate Total Lease Liability:
Total lease liability = Present value of lease payments + Present value of GRV:
[tex]Total\ Lease\ Liability = ₹947,700 + ₹155,250 = ₹1,102,950[/tex]
Calculate Interest Charges for Each Year:
At the beginning of each year, the interest charge is based on the outstanding liability:
- Year 1 Interest: ₹1,102,950 \times 0.10 = ₹110,295
- Year 2 Interest: (Outstanding liability at end of Year 1) \times 0.10
- Repeat for subsequent years using the declining balance after deducting each year's lease payment.
The outstanding liability decreases each year by the amount of the lease payment minus the interest charge.
