Computing the present value of 5 payments of $25,000 at 7%.

PV factors:
- t=1: 25000/1.07 = 23364.485981...
- t=2: 25000/1.07² = 21835.968206...
- t=3: 25000/1.07³ = 20407.447856...
- t=4: 25000/1.07⁴ = 19072.381173...
- t=5: 25000/1.07⁵ = 17824.655302...

Sum = 102504.938519... = $102,504.94

Let me verify with the annuity formula: 25000 × (1 − 1.07⁻⁵)/0.07.

1.07⁵ = 1.4025517307; 1.07⁻⁵ = 0.712986179...; 1 − 0.712986179 = 0.287013821; /0.07 = 4.100197437; ×25000 = 102504.9359. Rounds to $102,504.94.

# AASB 16 Lease - Initial Measurement

## Answer

**(a) Initial lease liability: $102,504.94**

**(b) Initial right-of-use (ROU) asset: $102,504.94**

**Governing standard: AASB 16 *Leases*** (the Australian equivalent of IFRS 16).

## Working

The lease liability is the present value of the 5 annual payments of $25,000, each paid in arrears, discounted at the lessee's incremental borrowing rate of 7% (used because the rate implicit in the lease cannot be readily determined).

Discounting each payment:

| Year (t) | Payment | Discount factor 1/(1.07)^t | Present value |
|---------|---------|----------------------------|---------------|
| 1 | $25,000 | 0.93457944 | $23,364.49 |
| 2 | $25,000 | 0.87343873 | $21,835.97 |
| 3 | $25,000 | 0.81629788 | $20,407.45 |
| 4 | $25,000 | 0.76289521 | $19,072.38 |
| 5 | $25,000 | 0.71298618 | $17,824.65 |
| **Total** | | | **$102,504.94** |

Equivalently, using the ordinary-annuity formula:

Liability = 25,000 × [1 − (1.07)^−5] / 0.07 = 25,000 × 4.10019744 = **$102,504.94**

Because there are no initial direct costs, no lease incentives, no prepaid lease payments, and no restoration/dismantling costs, the right-of-use asset on initial recognition equals the lease liability:

ROU asset = lease liability = **$102,504.94**

## Approach

I identified this as an AASB 16 initial-measurement problem: the lease liability is the present value of the outstanding lease payments discounted at the incremental borrowing rate (7%), and the ROU asset, absent any of the listed adjustments, equals that liability. I computed the present value of the five in-arrears payments both payment-by-payment and via the ordinary-annuity formula as a cross-check; both give $102,504.94 to the nearest cent.