# ACC-0005: Initial measurement of a lease under AASB 16

This is a benchmarking hypothetical, not accounting advice.

## Answer

- **(a) Initial lease liability: $102,504.94**
- **(b) Initial right-of-use asset: $102,504.94**

**Governing standard: AASB 16 *Leases*** (the Australian Accounting Standards Board
standard, equivalent to IFRS 16 *Leases* issued by the IASB).

## Facts

| Input | Value |
|---|---|
| Lease term | 5 years |
| Annual payment | $25,000, paid at the **end** of each year (in arrears) |
| Discount rate | 7% (the lessee's incremental borrowing rate, used because the rate implicit in the lease cannot be readily determined) |
| Initial direct costs | nil |
| Lease incentives | nil |
| Prepaid lease payments | nil |
| Restoration / dismantling costs | nil |

## (a) Initial lease liability

AASB 16 paragraph 26 measures the lease liability at commencement as the present
value of the lease payments not yet paid, discounted using the interest rate implicit
in the lease, or, where that rate cannot be readily determined, the lessee's
incremental borrowing rate (AASB 16 para 26). Here that rate is 7%.

Because the five payments are made in arrears (end of each year), this is an ordinary
annuity:

$$
\text{Liability} = \sum_{t=1}^{5} \frac{25{,}000}{(1.07)^{t}}
$$

Discounting each payment:

| Year *t* | Payment | Discount factor 1/(1.07)^t | Present value |
|---:|---:|---:|---:|
| 1 | 25,000 | 0.934579439 | 23,364.485981 |
| 2 | 25,000 | 0.873438728 | 21,835.968207 |
| 3 | 25,000 | 0.816297877 | 20,407.446922 |
| 4 | 25,000 | 0.762895212 | 19,072.380301 |
| 5 | 25,000 | 0.712986179 | 17,824.654487 |
| **Total** | | **4.100197436** | **102,504.935899** |

Cross-check using the ordinary-annuity present-value factor:

$$
\text{Factor} = \frac{1 - (1.07)^{-5}}{0.07} = 4.100197436
$$

$$
\text{Liability} = 25{,}000 \times 4.100197436 = 102{,}504.9359
$$

Rounded to the nearest cent:

> **Initial lease liability = $102,504.94**

## (b) Initial right-of-use asset

AASB 16 paragraph 23 measures the right-of-use asset at cost, and paragraph 24
defines that cost as:

1. the amount of the initial measurement of the lease liability; **plus**
2. any lease payments made at or before the commencement date, less any lease
   incentives received; **plus**
3. any initial direct costs incurred by the lessee; **plus**
4. an estimate of dismantling, removal and restoration costs (AASB 16 para 24 /
   AASB 137 obligations).

In this scenario components 2, 3 and 4 are all nil (no prepaid payments, no
incentives, no initial direct costs, no restoration costs). The ROU asset therefore
equals the initial lease liability.

> **Initial right-of-use asset = $102,504.94**

## Summary

| Item | Amount (AUD) |
|---|---:|
| (a) Initial lease liability | **$102,504.94** |
| (b) Initial right-of-use asset | **$102,504.94** |
| Governing standard | **AASB 16 *Leases*** (IFRS 16 equivalent) |

## Approach

I treated the five $25,000 payments as an ordinary annuity (paid in arrears) and
discounted each at the 7% incremental borrowing rate to commencement date, per AASB 16
para 26. The raw present value is $102,504.935899, which rounds to $102,504.94. I
verified this two ways: (i) summing the five individually discounted payments, and
(ii) applying the closed-form ordinary-annuity factor (1 - 1.07^-5)/0.07 = 4.100197436;
both give the same figure. Calculations were done in Python's `decimal` module with
`ROUND_HALF_UP` to avoid floating-point and rounding error. Because there are no
initial direct costs, incentives, prepayments, or restoration costs (AASB 16 para 24
components 2-4 = nil), the right-of-use asset cost equals the initial lease liability.